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• 1. Aaghabali, M.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Upper bounds on the number of perfect matchings and directed 2-factors in graphs with given number of vertices and edges2015Inngår i: European journal of combinatorics (Print), ISSN 0195-6698, E-ISSN 1095-9971, Vol. 45, s. 132-144Artikkel i tidsskrift (Fagfellevurdert)

We give an upper bound on the number of perfect matchings in simple graphs with a given number of vertices and edges. We apply this result to give an upper bound on the number of 2-factors in a directed complete bipartite balanced graph on 2n vertices. The upper bound is sharp for even n. For odd n we state a conjecture on a sharp upper bound.

• 2. Adamaszek, Michal
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
On a lower bound for the connectivity of the independence complex of a graph2011Inngår i: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 311, nr 21, s. 2566-2569Artikkel i tidsskrift (Fagfellevurdert)

Aharoni, Berger and Ziv proposed a function which is a lower bound for the connectivity of the independence complex of a graph. They conjectured that this bound is optimal for every graph. We give two different arguments which show that the conjecture is false.

• 3.
Blekinge Tekniska Högskola, Sektionen för teknik, Avdelningen för telekommunikationssystem.
Security Issues in Wireless Systems2009Independent thesis Advanced level (degree of Master (One Year))Oppgave

ireless Communication is one of the fields of Telecommunications which is growing with the tremendous speed. With the passage of time wireless communication devices are becoming more and more common. It is not only the technology of business but now people are using it to perform their daily tasks, be it for calling, shopping, checking their emails or transfer their money. Wireless communication devices include cellular phones, cordless phones and satellite phones, smart phones like Personal Digital Assistants (PDA), two way pagers, and lots of their devices are on their way to improve this wireless world. In order to establish two way communications, a wireless link may be using radio waves or Infrared light. The Wireless communication technologies have become increasingly popular in our everyday life. The hand held devices like Personal Digital Assistants (PDA) allow the users to access calendars, mails, addresses, phone number lists and the internet. Personal digital assistants (PDA) and smart phones can store large amounts of data and connect to a broad spectrum of networks, making them as important and sensitive computing platforms as laptop PCs when it comes to an organization’s security plan. Today’s mobile devices offer many benefits to enterprises. Mobile phones, hand held computers and other wireless systems are becoming a tempting target for virus writers. Mobile devices are the new frontier for viruses, spam and other potential security threats. Most viruses, Trojans and worms have already been created that exploit vulnerabilities. With an increasing amount of information being sent through wireless channels, new threats are opening up. Viruses have been growing fast as handsets increasingly resemble small computers that connect with each other and the internet. Hackers have also discovered that many corporate wireless local area networks (WLAN) in major cities were not properly secured. Mobile phone operators say that it is only a matter of time before the wireless world is hit by the same sorts of viruses and worms that attack computer software.

• 4. Akbari, Saieed
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
On 1-sum flows in undirected graphs2016Inngår i: The Electronic Journal of Linear Algebra, ISSN 1537-9582, E-ISSN 1081-3810, Vol. 31, s. 646-665Artikkel i tidsskrift (Fagfellevurdert)

Let G = (V, E) be a simple undirected graph. For a given set L subset of R, a function omega: E -> L is called an L-flow. Given a vector gamma is an element of R-V , omega is a gamma-L-flow if for each v is an element of V, the sum of the values on the edges incident to v is gamma(v). If gamma(v) = c, for all v is an element of V, then the gamma-L-flow is called a c-sum L-flow. In this paper, the existence of gamma-L-flows for various choices of sets L of real numbers is studied, with an emphasis on 1-sum flows. Let L be a subset of real numbers containing 0 and denote L* := L \ {0}. Answering a question from [S. Akbari, M. Kano, and S. Zare. A generalization of 0-sum flows in graphs. Linear Algebra Appl., 438:3629-3634, 2013.], the bipartite graphs which admit a 1-sum R* -flow or a 1-sum Z* -flow are characterized. It is also shown that every k-regular graph, with k either odd or congruent to 2 modulo 4, admits a 1-sum {-1, 0, 1}-flow.

• 5.
Umeå University.
Umeå University. Umeå University.
Fast multiplication of matrices over a finitely generated semiring2008Inngår i: Information Processing Letters, ISSN 0020-0190, E-ISSN 1872-6119, Vol. 107, nr 6, s. 230-234Artikkel i tidsskrift (Fagfellevurdert)
• 6.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Avoiding Arrays of Odd Order by Latin Squares2013Inngår i: Combinatorics, probability & computing, ISSN 0963-5483, E-ISSN 1469-2163, Vol. 22, nr 2, s. 184-212Artikkel i tidsskrift (Fagfellevurdert)

We prove that there is a constant c such that, for each positive integer k, every (2k + 1) x (2k + 1) array A on the symbols 1, ... , 2k + 1 with at most c(2k + 1) symbols in every cell, and each symbol repeated at most c(2k + 1) times in every row and column is avoidable; that is, there is a (2k + 1) x (2k + 1) Latin square S on the symbols 1, ... , 2k + 1 such that, for each i, j is an element of {1, ... , 2k + 1}, the symbol in position (i, j) of S does not appear in the corresponding cell in Lambda. This settles the last open case of a conjecture by Haggkvist. Using this result, we also show that there is a constant rho, such that, for any positive integer n, if each cell in an n x n array B is assigned a set of m <= rho n symbols, where each set is chosen independently and uniformly at random from {1, ... , n}, then the probability that B is avoidable tends to 1 as n -> infinity.

• 7.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
On the Ising problem and some matrix operations2007Doktoravhandling, med artikler (Annet vitenskapelig)

The first part of the dissertation concerns the Ising problem proposed to Ernst Ising by his supervisor Wilhelm Lenz in the early 20s. The Ising model, or perhaps more correctly the Lenz-Ising model, tries to capture the behaviour of phase transitions, i.e. how local rules of engagement can produce large scale behaviour.

Two decades later Lars Onsager solved the Ising problem for the quadratic lattice without an outer field. Using his ideas solutions for other lattices in two dimensions have been constructed. We describe a method for calculating the Ising partition function for immense square grids, up to linear order 320 (i.e. 102400 vertices).

In three dimensions however only a few results are known. One of the most important unanswered questions is at which temperature the Ising model has its phase transition. In this dissertation it is shown that an upper bound for the critical coupling Kc, the inverse absolute temperature, is 0.29 for the tree dimensional cubic lattice.

To be able to get more information one has to use different statistical methods. We describe one sampling method that can use simple state generation like the Metropolis algorithm for large lattices. We also discuss how to reconstruct the entropy from the model, in order to obtain parameters as the free energy.

The Ising model gives a partition function associated with all finite graphs. In this dissertation we show that a number of interesting graph invariants can be calculated from the coefficients of the Ising partition function. We also give some interesting observations about the partition function in general and show that there are, for any N, N non-isomorphic graphs with the same Ising partition function.

The second part of the dissertation is about matrix operations. We consider the problem of multiplying them when the entries are elements in a finite semiring or in an additively finitely generated semiring. We describe a method that uses O(n3 / log n) arithmetic operations.

We also consider the problem of reducing n x n matrices over a finite field of size q using O(n2 / logq n) row operations in the worst case.

• 8.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Avoidability by Latin squares of arrays of even orderManuskript (preprint) (Annet vitenskapelig)

We prove that for any k and any 2k × 2k array A such that no cell in A contains more than   k/2550 symbols, and no symbol occurs more than k/2550 times in any row or column, there is a Latin square such that no 2550cell in the Latin square contains a symbol that occurs in the corresponding cell in A. This proves a conjecture of Häggkvist [8] in the special case of arrays with even side.

• 9.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Avoidability of random arraysManuskript (preprint) (Annet vitenskapelig)

An n×n array that in each cell contains a subset of the symbols 1, . . . , n is avoidable if there exists a Latin square of order n such that no cell in the Latin square contains a symbol which belongs to the set of symbols in the corresponding cell of the array. Some results on deterministic conditions for avoidability of arrays have been found, but here we study the problem of having an array with randomly assigned subsets of C in its cells. This is equivalent to the problem of list-edge-coloring $K_{n,n}$ with randomly assigned lists from the set {1, . . . , n}. We show that an array where each symbol appears in each cell with probability p will be avoidable with very high probability even if p is such that the expected number of symbols forbidden in each cell is slightly higher than what deterministic theorems can prove is avoidable.

• 10.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Avoiding (m, m, m)-arrays of order n = 2kManuskript (preprint) (Annet vitenskapelig)

An (m, m, m)-array of order n is an n × n array such that each cell is assigned a set of at most m symbols from {1,...,n} such that no symbol occurs more than m times in any row or column. An (m,m,m)- array is called avoidable if there exists a Latin square such that no cell in the Latin square contains a symbol that also belongs to the set assigned to the corresponding cell in the array. We show that there is a constant γ such that if m ≤ γ2k, then any (m,m,m)-array of order 2k is avoidable. Such a constant γ has been conjectured to exist for all n by Häggkvist.

• 11.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
On Latin squares and avoidable arrays2010Doktoravhandling, med artikler (Annet vitenskapelig)

This thesis consists of the four papers listed below and a survey of the research area.

I Lina J. Andrén: Avoiding (m, m, m)-arrays of order n = 2k

II Lina J. Andrén: Avoidability of random arrays

III Lina J. Andr´en: Avoidability by Latin squares of arrays with even order

IV Lina J. Andrén, Carl Johan Casselgren and Lars-Daniel Öhman: Avoiding arrays of odd order by Latin squares

Papers I, III and IV are all concerned with a conjecture by Häggkvist saying that there is a constant c such that for any positive integer n, if m ≤ cn, then for every n × n array A of subsets of {1, . . . , n} such that no cell contains a set of size greater than m, and none of the elements 1, . . . , n belongs to more than m of the sets in any row or any column of A, there is a Latin square L on the symbols 1, . . . , n such that there is no cell in L that contains a symbol that belongs to the set in the corresponding cell of A. Such a Latin square is said to avoid A. In Paper I, the conjecture is proved in the special case of order n = 2k . Paper III improves on the techniques of Paper I, expanding the proof to cover all arrays of even order. Finally, in Paper IV, similar methods are used together with a recoloring theorem to prove the conjecture for all orders. Paper II considers another aspect of the problem by asking to what extent way a deterministic result concerning the existence of Latin squares that avoid certain arrays can be used when the sets in the array are assigned randomly.

• 12.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Avoiding arrays of odd order by Latin squaresManuskript (preprint) (Annet vitenskapelig)

We prove that there exists a constant c such that for each pos- itive integer k every (2k+1)×(2k+1) array A on the symbols 1,...,2k+1 with at most c(2k + 1) symbols in every cell, and each symbol repeated at most c(2k+1) times in every row and column is avoidable; that is, there is a (2k+1)×(2k+1) Latin square S on the symbols 1,...,2k+1 such that for each cell (i, j) in S the symbol in (i, j) does not appear in the corresponding cell in A. This settles the last open case of a conjecture by Häggkvist.

• 13.
Department of Applied Mathematics and Statistics, Stony Brook University, USA .
Institute of Computer Science, Freie Universität Berlin, Germany . Institute of Computer Science, Universität Bayreuth, Germany . Department of Applied Mathematics and Statistics, Stony Brook University, USA . Helsinki Institute for Information Technology, CS Dept, University of Helsinki, Finland . Institute of Computer Science, Freie Universität Berlin, Germany . Department of Computer Science, Stony Brook University, USA .
Convex transversals2014Inngår i: Computational Geometry, ISSN 0925-7721, Vol. 47, nr 2, s. 224-239Artikkel i tidsskrift (Fagfellevurdert)

We answer the question initially posed by Arik Tamir at the Fourth NYU Computational Geometry Day (March, 1987): “Given a collection of compact sets, can one decide in polynomial time whether there exists a convex body whose boundary intersects every set in the collection?”

We prove that when the sets are segments in the plane, deciding existence of the convex stabber is NP-hard. The problem remains NP-hard if the sets are regular polygons. We also show that in 3D the stabbing problem is hard when the sets are balls. On the positive side, we give a polynomial-time algorithm to find a convex transversal of a maximum number of pairwise-disjoint segments in 2D if the vertices of the transversal are restricted to a given set of points. Our algorithm also finds a convex stabber of the maximum number of a set of convex pseudodisks in the plane.

The stabbing problem is related to “convexity” of point sets measured as the minimum distance by which the points must be shifted in order to arrive in convex position; we give a PTAS to find the minimum shift in 2D, and a 2-approximation in any dimension. We also consider stabbing with vertices of a regular polygon – a problem closely related to approximate symmetry detection.

• 14.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. University of Southern Denmark, Denmark.
Solution of Vizings Problem on Interchanges for the case of Graphs with Maximum Degree 4 and Related Results2016Inngår i: Journal of Graph Theory, ISSN 0364-9024, E-ISSN 1097-0118, Vol. 82, nr 4, s. 350-373Artikkel i tidsskrift (Fagfellevurdert)

Let G be a Class 1 graph with maximum degree 4 and let t amp;gt;= 5 be an integer. We show that any proper t-edge coloring of G can be transformed to any proper 4-edge coloring of G using only transformations on 2-colored subgraphs (so-called interchanges). This settles the smallest previously unsolved case of a well-known problem of Vizing on interchanges, posed in 1965. Using our result we give an affirmative answer to a question of Mohar for two classes of graphs: we show that all proper 5-edge colorings of a Class 1 graph with maximum degree 4 are Kempe equivalent, that is, can be transformed to each other by interchanges, and that all proper 7-edge colorings of a Class 2 graph with maximum degree 5 are Kempe equivalent. (C) 2015 Wiley Periodicals, Inc.

• 15.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. Yerevan State University, Armenia; National Academic Science, Armenia.
Some results on cyclic interval edge colorings of graphs2018Inngår i: Journal of Graph Theory, ISSN 0364-9024, E-ISSN 1097-0118, Vol. 87, nr 2, s. 239-252Artikkel i tidsskrift (Fagfellevurdert)

A proper edge coloring of a graph G with colors 1,2,,t is called a cyclic interval t-coloring if for each vertex v of G the edges incident to v are colored by consecutive colors, under the condition that color 1 is considered as consecutive to color t. We prove that a bipartite graph G of even maximum degree (G)4 admits a cyclic interval (G)-coloring if for every vertex v the degree dG(v) satisfies either dG(v)(G)-2 or dG(v)2. We also prove that every Eulerian bipartite graph G with maximum degree at most eight has a cyclic interval coloring. Some results are obtained for (a,b)-biregular graphs, that is, bipartite graphs with the vertices in one part all having degree a and the vertices in the other part all having degree b; it has been conjectured that all these have cyclic interval colorings. We show that all (4, 7)-biregular graphs as well as all (2r-2,2r)-biregular (r2) graphs have cyclic interval colorings. Finally, we prove that all complete multipartite graphs admit cyclic interval colorings; this proves a conjecture of Petrosyan and Mkhitaryan.

• 16.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. Southern Polytechnic State University, Marietta, Georgia. University of Illinois, Urbana, Illinois.
Proper path-factors and interval edge-coloring of (3,4)-biregular bigraphs2009Inngår i: Journal of Graph Theory, ISSN 0364-9024, E-ISSN 1097-0118, Vol. 61, nr 2, s. 88-97Artikkel i tidsskrift (Fagfellevurdert)

An interval coloring of a graph G is a proper coloring of E(G) by positive integers such that the colors on the edges incident to any vertex are consecutive. A (3,4)-biregular bigraph is a bipartite graph in which each vertex of one part has degree 3 and each vertex of the other has degree 4; it is unknown whether these all have interval colorings. We prove that G has an interval coloring using 6 colors when G is a (3,4)-biregular bigraph having a spanning subgraph whose components are paths with endpoints at 3-valent vertices and lengths in {2, 4, 6, 8}. We provide several sufficient conditions for the existence of such a subgraph.

• 17.
KTH, Skolan för datavetenskap och kommunikation (CSC), Teoretisk datalogi, TCS.
Dense Subset Sum may be the hardest2016Inngår i: Leibniz International Proceedings in Informatics, LIPIcs, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing , 2016Konferansepaper (Fagfellevurdert)

The Subset Sum problem asks whether a given set of n positive integers contains a subset of elements that sum up to a given target t. It is an outstanding open question whether the O∗(2n/2)-time algorithm for Subset Sum by Horowitz and Sahni [J. ACM 1974] can be beaten in the worst-case setting by a "truly faster", O∗(2(0.5-δ)n)-time algorithm, with some constant δ &gt; 0. Continuing an earlier work [STACS 2015], we study Subset Sum parameterized by the maximum bin size β, defined as the largest number of subsets of the n input integers that yield the same sum. For every ∈ &gt; 0 we give a truly faster algorithm for instances with β ≤ 2(0.5-∈)n, as well as instances with β ≥ 20.661n. Consequently, we also obtain a characterization in terms of the popular density parameter n/log2 t: if all instances of density at least 1.003 admit a truly faster algorithm, then so does every instance. This goes against the current intuition that instances of density 1 are the hardest, and therefore is a step toward answering the open question in the affirmative. Our results stem from a novel combinatorial analysis of mixings of earlier algorithms for Subset Sum and a study of an extremal question in additive combinatorics connected to the problem of Uniquely Decodable Code Pairs in information theory.

• 18. Averkov, Gennadiy
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Largest integral simplices with one interior integral point: Solution of Hensley's conjecture and related results2015Inngår i: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 274, s. 118-166Artikkel i tidsskrift (Fagfellevurdert)

For each dimension d, d-dimensional integral simplices with exactly one interior integral point have bounded volume. This was first shown by Hensley. Explicit volume bounds were determined by Hensley, Lagarias and Ziegler, Pikhurko, and Averkov. In this paper we determine the exact upper volume bound for such simplices and characterize the volume-maximizing simplices. We also determine the sharp upper bound on the coefficient of asymmetry of an integral polytope with a single interior integral point. This result confirms a conjecture of Hensley from 1983. Moreover, for an integral simplex with precisely one interior integral point, we give bounds on the volumes of its faces, the barycentric coordinates of the interior integral point and its number of integral points. Furthermore, we prove a bound on the lattice diameter of integral polytopes with a fixed number of interior integral points. The presented results have applications in toric geometry and in integer optimization.

• 19. Ayyer, Arvind
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Some genelalized juggling processes (extended abstract)2015Inngår i: DMTCS proc. FPSAC'15, Nancy, France, 2015, s. 925-936Konferansepaper (Fagfellevurdert)

We consider generalizations of juggling Markov chains introduced by Ayyer, Bouttier, Corteel and Nunzi. We first study multispecies generalizations of all the finite models therein, namely the MJMC, the add-drop and the annihilation models. We then consider the case of several jugglers exchanging balls. In all cases, we give explicit product formulas for the stationary probability and closed-form expressions for the normalization factor if known.

• 20.
University of St Andrews, Scotland.
University of St Andrews, Scotland. Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för matematik och ämnesdidaktik.
Sesqui-arrays, a generalisation of triple arrays2018Inngår i: The Australasian Journal of Combinatorics, ISSN 1034-4942, Vol. 71, nr 3, s. 427-451Artikkel i tidsskrift (Fagfellevurdert)

A triple array is a rectangular array containing letters, each letter occurring equally often with no repeats in rows or columns, such that the number of letters common to two rows, two columns, or a rowand a column are (possibly different) non-zero constants. Deleting the condition on the letters common to a row and a column gives a double array. We propose the term sesqui-array for such an array when only the condition on pairs of columns is deleted. In this paper we give three constructions for sesqui-arrays. Therst gives $(n + 1)\times n^2$ arrays on n(n + 1) letters for $n\geq 2$. (Suchan array for n = 2 was found by Bagchi.) This construction uses Latin squares. The second uses the Sylvester graph, a subgraph of the Hoffman--Singleton graph, to build a good block design for 36 treatments in 42 blocks of size 6, and then uses this in a 736 sesqui-array for 42 letters.We also give a construction for K(K-1)(K-2)/2 sesqui-arrays on K(K-1)/2 letters from biplanes. The construction starts with a block of a biplane and produces an array which satises the requirements for a sesqui-array except possibly that of having no repeated letters in a row or column. We show that this condition holds if and only if the Hussain chains for the selected block contain no 4-cycles. A sufficient condition for the construction to give a triple array is that each Hussain chain is a union of 3-cycles; but this condition is not necessary, and we give a few further examples. We also discuss the question of which of these arrays provide good designs for experiments.

• 21.
Universitat Politècnica de Catalunya, Barcelona, Spain.
The University of Western Australia, Crawley, WA, Australia. The University of Western Australia, Crawley, WA, Australia. Universitat Rovira i Virgili, Tarragona, Spain.
An alternative way to generalise the pentagon2013Inngår i: Journal of combinatorial designs (Print), ISSN 1063-8539, E-ISSN 1520-6610, Vol. 21, nr 4, s. 163-179Artikkel i tidsskrift (Fagfellevurdert)

We introduce the concept of a pentagonal geometry as a generalization of the pentagon and the Desargues configuration, in the same vein that the generalized polygons share the fundamental properties of ordinary polygons. In short, a pentagonal geometry is a regular partial linear space in which for all points x, the points not collinear with the point x, form a line. We compute bounds on their parameters, give some constructions, obtain some nonexistence results for seemingly feasible parameters and suggest a cryptographic application related to identifying codes of partial linear spaces.

• 22.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Classifications and volume bounds of lattice polytopes2017Licentiatavhandling, monografi (Annet vitenskapelig)

In this licentiate thesis we study relations among invariants of lattice polytopes, with particular focus on bounds for the volume.In the first paper we give an upper bound on the volume vol(P^*) of a polytope P^* dual to a d-dimensional lattice polytope P with exactly one interiorlattice point, in each dimension d. This bound, expressed in terms of the Sylvester sequence, is sharp, and is achieved by the dual to a particular reflexive simplex. Our result implies a sharp upper bound on the volume of a d-dimensional reflexive polytope. In the second paper we classify the three-dimensional lattice polytopes with two lattice points in their strict interior. Up to unimodular equivalence thereare 22,673,449 such polytopes. This classification allows us to verify, for this case only, the sharp conjectural upper bound for the volume of a lattice polytope with interior points, and provides strong evidence for more general new inequalities on the coefficients of the h^*-polynomial in dimension three.

• 23.
Christian-Albrechts Universität Kiel.
Christian-Albrechts Universität Kiel. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. Christian-Albrechts Universität Kiel. Christian-Albrechts Universität Kiel.
Exact and heuristic algorithms for the Travelling Salesman Problem with Multiple Time Windows and Hotel Selection2015Inngår i: Journal of the Operational Research Society, ISSN 0160-5682, E-ISSN 1476-9360, Vol. 66, nr 4, s. 615-626Artikkel i tidsskrift (Fagfellevurdert)

We introduce and study the Travelling Salesman Problem with Multiple Time Windows and Hotel Selection (TSP-MTWHS), which generalises the well-known Travelling Salesman Problem with Time Windows and the recently introduced Travelling Salesman Problem with Hotel Selection. The TSP-MTWHS consists in determining a route for a salesman (eg, an employee of a services company) who visits various customers at different locations and different time windows. The salesman may require a several-day tour during which he may need to stay in hotels. The goal is to minimise the tour costs consisting of wage, hotel costs, travelling expenses and penalty fees for possibly omitted customers. We present a mixed integer linear programming (MILP) model for this practical problem and a heuristic combining cheapest insert, 2-OPT and randomised restarting. We show on random instances and on real world instances from industry that the MILP model can be solved to optimality in reasonable time with a standard MILP solver for several small instances. We also show that the heuristic gives the same solutions for most of the small instances, and is also fast, efficient and practical for large instances.

• 24.
Christian-Albrechts Universität Kiel, Germany.
Christian-Albrechts Universität Kiel, Germany. Christian-Albrechts Universität Kiel, Germany.
Construction of Sparse Asymmetric Connectors2003Inngår i: Proceedings of European Conference on Combinatorics, Graph Theory and Applications (Eurocomb 2003), 2003Konferansepaper (Fagfellevurdert)
• 25.
Christian-Albrechts-Universität Kiel, Germany.
Christian-Albrechts-Universität Kiel, Germany. Christian-Albrechts-Universität Kiel, Germany.
Constructions of Sparse Asymmetric Connectors2003Inngår i: Proceedings of 23rd Conference of Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2003) / [ed] P.K. Lodaya and J. Radhakrishnan, Berlin-Heidelberg: Springer Berlin/Heidelberg, 2003, s. 13-22Konferansepaper (Fagfellevurdert)
• 26.
Mathematisches seminar, Christian-Albrechts-Universität zu Kiel, Germany.
Mathematisches seminar, Christian-Albrechts-Universität zu Kiel, Germany. Mathematisches seminar, Christian-Albrechts-Universität zu Kiel, Germany.
Constructions of Sparse Asymmetric Connectors with Number Theoretic Methods2005Inngår i: Networks, ISSN 0028-3045, E-ISSN 1097-0037, Vol. 45, nr 3, s. 119-124Artikkel i tidsskrift (Fagfellevurdert)

We consider the problem of connecting a set I of n inputs to a set O of N outputs (n ≤ N) by as few edges as possible such that for every injective mapping f : I → O there are n vertex disjoint paths from i to f(i) of length k for a given k $\in \mathbb{N}$. For k = Ω(log N + log$^{2}$n) Oruς (1994) gave the presently best (n,N)-connector with O(N+n·log n) edges. For k=2 and N the square of a prime, Richards and Hwang (1985) described a construction using $N\left[\sqrt{n+5/4-1/2}\right] + n\left[\sqrt{n+5/4-1/2} \right]\sqrt{N}$edges. We show by a probabilistic argument that an optimal (n,N)-connector has Θ (N) edges, if $n\leq N^{1/2-\varepsilon}$for some ε>0. Moreover, we give explicit constructions based on a new number theoretic approach that need at most $N\left[\sqrt{3n/4} \right]+2n\left[\sqrt{3n/4} \right]\left[\sqrt{N} \right]$edges for arbitrary choices of n and N. The improvement we achieve is based on applying a generalization of the Erdös-Heilbronn conjecture on the size of restricted sums.

• 27. Barak, B.
KTH, Skolan för datavetenskap och kommunikation (CSC), Teoretisk datalogi, TCS.
Making the long code shorter2015Inngår i: SIAM journal on computing (Print), ISSN 0097-5397, E-ISSN 1095-7111, Vol. 44, nr 5, s. 1287-1324Artikkel i tidsskrift (Fagfellevurdert)

The long code is a central tool in hardness of approximation especially in questions related to the Unique Games Conjecture. We construct a new code that is exponentially more efficient but can still be used in many of these applications. Using the new code we obtain exponential improvements over several known results including the following: (1) For any ε &gt; 0, we show the existence of an n-vertex graph G where every set of o(n) vertices has expansion 1-ε but G's adjacency matrix has more than exp(logδ n) eigenvalues larger than 1 - ε, where δ depends only on ε. This answers an open question of Arora, Barak, and Steurer [Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, 2010, pp. 563-572] who asked whether one can improve over the noise graph on the Boolean hypercube that has poly(log n) such eigenvalues. (2) A gadget that reduces Unique Games instances with linear constraints modulo K into instances with alphabet k with a blowup of kpolylog(K) , improving over the previously known gadget with blowup of kω(K). (3) An n-variable integrality gap for Unique Games that survives exp(poly(log log n)) rounds of the semidefinite programming version of the Sherali-Adams hierarchy, improving on the previously known bound of poly(log log n). We show a connection between the local testability of linear codes and Small-Set Expansion in certain related Cayley graphs and use this connection to derandomize the noise graph on the Boolean hypercube.

• 28.
Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE).
Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
Meshfree methods in option pricing2011Independent thesis Advanced level (degree of Master (One Year)), 10 poäng / 15 hpOppgave

A meshfree approximation scheme based on the radial basis function methods is presented for the numerical solution of the options pricing model. This thesis deals with the valuation of the European, Barrier, Asian, American options of a single asset and American options of multi assets. The option prices are modeled by the Black-Scholes equation. The θ-method is used to discretize the equation with respect to time. By the next step, the option price is approximated in space with radial basis functions (RBF) with unknown parameters, in particular, we con- sider multiquadric radial basis functions (MQ-RBF). In case of Ameri- can options a penalty method is used, i.e. removing the free boundary is achieved by adding a small and continuous penalty term to the Black- Scholes equation. Finally, a comparison of analytical and finite difference solutions and numerical results from the literature is included.

• 29.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Shellability and the strong gcd-condition2009Inngår i: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 16, nr 2Artikkel i tidsskrift (Fagfellevurdert)

Shellability is a well-known combinatorial criterion on a simplicial complex for verifying that the associated Stanley-Reisner ring k[] is Cohen-Macaulay. Anotion familiar to commutative algebraists, but which has not received as muchattention from combinatorialists as the Cohen-Macaulay property, is the notion ofa Golod ring. Recently, J¨ollenbeck introduced a criterion on simplicial complexesreminiscent of shellability, called the strong gcd-condition, and he together with theauthor proved that it implies Golodness of the associated Stanley-Reisner ring. Thetwo algebraic notions were earlier tied together by Herzog, Reiner and Welker, whoshowed that if k[∨] is sequentially Cohen-Macaulay, where ∨ is the Alexanderdual of , then k[] is Golod. In this paper, we present a combinatorial companionof this result, namely that if ∨ is (non-pure) shellable then satisfies the stronggcd-condition. Moreover, we show that all implications just mentioned are strict ingeneral but that they are equivalences if is a flag complex.

• 30.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Shellability and the strong gcd-condition2009Inngår i: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 16, nr 2Artikkel i tidsskrift (Fagfellevurdert)

Shellability is a well-known combinatorial criterion on a simplicial complex for verifying that the associated Stanley-Reisner ring k[] is Cohen-Macaulay. Anotion familiar to commutative algebraists, but which has not received as muchattention from combinatorialists as the Cohen-Macaulay property, is the notion ofa Golod ring. Recently, J¨ollenbeck introduced a criterion on simplicial complexesreminiscent of shellability, called the strong gcd-condition, and he together with theauthor proved that it implies Golodness of the associated Stanley-Reisner ring. Thetwo algebraic notions were earlier tied together by Herzog, Reiner and Welker, whoshowed that if k[∨] is sequentially Cohen-Macaulay, where ∨ is the Alexanderdual of , then k[] is Golod. In this paper, we present a combinatorial companionof this result, namely that if ∨ is (non-pure) shellable then satisfies the stronggcd-condition. Moreover, we show that all implications just mentioned are strict ingeneral but that they are equivalences if is a flag complex.

• 31. Bhattacharya, S.
KTH, Skolan för datavetenskap och kommunikation (CSC), Teoretisk datalogi, TCS.
New deterministic approximation algorithms for fully dynamic matching2016Konferansepaper (Fagfellevurdert)

We present two deterministic dynamic algorithms for the maximum matching problem. (1) An algorithm that maintains a (2 + ϵ)-approximate maximum matching in general graphs with O(poly(log n, 1/ϵ)) update time. (2) An algorithm that maintains an αk approximation of the value of the maximum matching with O(n2/K) update time in bipartite graphs, for every sufficiently large constant positive integer K. Here, 1 ≤ αk ≤ 2 is a constant determined by the value of K. Result (1) is the first deterministic algorithm that can maintain an o(log n)-approximate maximum matching with polylogarithmic update time, improving the seminal result of Onak et al. [STOC 2010]. Its approximation guarantee almost matches the guarantee of the best randomized polylogarithmic update time algorithm [Baswana et al. FOCS 2011]. Result (2) achieves a better-than-two approximation with arbitrarily small polynomial update time on bipartite graphs. Previously the best update time for this problem was O(m1/4) [Bernstein et al. ICALP 2015], where m is the current number of edges in the graph.

• 32. Bierbrauer, Jürgen
Örebro universitet, Institutionen för naturvetenskap.
Almost independent and weakly biased arrays: efficient constructions and cryptologic applications2000Inngår i: Advances in cryptology: CRYPTO 2000 / [ed] Mihir Bellare, Springer Berlin/Heidelberg, 2000, s. 533-543Konferansepaper (Annet vitenskapelig)
• 33.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Department of Information Science, Stellenbosch University, Stellenbosch, South Africa.
Minimization of Finite State Automata Through Partition Aggregation2016Inngår i: Logical Aspects of Computational Linguistics: Celebrating 20 Years of LACL (1996–2016) / [ed] Amblard, M DeGroote, P Pogodalla, S Retore, C, SPRINGER-VERLAG BERLIN , 2016, s. 328-328Konferansepaper (Fagfellevurdert)
• 34.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
Graphical representations of Ising and Potts models: Stochastic geometry of the quantum Ising model and the space-time Potts model2009Doktoravhandling, monografi (Annet vitenskapelig)

HTML clipboard Statistical physics seeks to explain macroscopic properties of matter in terms of microscopic interactions. Of particular interest is the phenomenon of phase transition: the sudden changes in macroscopic properties as external conditions are varied. Two models in particular are of great interest to mathematicians, namely the Ising model of a magnet and the percolation model of a porous solid. These models in turn are part of the unifying framework of the random-cluster representation, a model for random graphs which was first studied by Fortuin and Kasteleyn in the 1970’s. The random-cluster representation has proved extremely useful in proving important facts about the Ising model and similar models.

In this work we study the corresponding graphical framework for two related models. The first model is the transverse field quantum Ising model, an extension of the original Ising model which was introduced by Lieb, Schultz and Mattis in the 1960’s. The second model is the space–time percolation process, which is closely related to the contact model for the spread of disease. In Chapter 2 we define the appropriate space–time random-cluster model and explore a range of useful probabilistic techniques for studying it. The space– time Potts model emerges as a natural generalization of the quantum Ising model. The basic properties of the phase transitions in these models are treated in this chapter, such as the fact that there is at most one unbounded fk-cluster, and the resulting lower bound on the critical value in .

In Chapter 3 we develop an alternative graphical representation of the quantum Ising model, called the random-parity representation. This representation is based on the random-current representation of the classical Ising model, and allows us to study in much greater detail the phase transition and critical behaviour. A major aim of this chapter is to prove sharpness of the phase transition in the quantum Ising model—a central issue in the theory— and to establish bounds on some critical exponents. We address these issues by using the random-parity representation to establish certain differential inequalities, integration of which gives the results.

In Chapter 4 we explore some consequences and possible extensions of the results established in Chapters 2 and 3. For example, we determine the critical point for the quantum Ising model in and in ‘star-like’ geometries.

• 35.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
On the connectivity of manifold graphs2015Inngår i: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 143, nr 10, s. 4123-4132Artikkel i tidsskrift (Fagfellevurdert)

This paper is concerned with lower bounds for the connectivity of graphs (one-dimensional skeleta) of triangulations of compact manifolds. We introduce a structural invariant b_M for simplicial d-manifolds M taking values in the range 0 <= b_M <= d-1. The main result is that b_M influences connectivity in the following way: The graph of a d-dimensional simplicial compact manifold M is (2d - b_M)-connected. The parameter b_M has the property that b_M = 0 if the complex M is flag. Hence, our result interpolates between Barnette's theorem (1982) that all d-manifold graphs are (d+1)-connected and Athanasiadis' theorem (2011) that flag d-manifold graphs are 2d-connected. The definition of b_M involves the concept of banner triangulations of manifolds, a generalization of flag triangulations.

• 36. Bogart, Tristram
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Finitely many smooth d-polytopes with n lattice points2015Inngår i: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 207, nr 1, s. 301-329Artikkel i tidsskrift (Fagfellevurdert)

We prove that for fixed n there are only finitely many embeddings of ℚ-factorial toric varieties X into ℙ n that are induced by a complete linear system. The proof is based on a combinatorial result that implies that for fixed nonnegative integers d and n, there are only finitely many smooth d-polytopes with n lattice points. We also enumerate all smooth 3-polytopes with ≤ 12 lattice points.

• 37.
Uppsala universitet, Fakultetsövergripande enheter, Centrum för bildanalys. Uppsala universitet, Fakultetsövergripande enheter, Centrum för bildanalys. Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Datoriserad bildanalys.
Kedjekod - ett sätt att beskriva former i digitala bilder2005Inngår i: Problemlösning är # 1, Liber, Stockholm , 2005, s. 38-42Kapittel i bok, del av antologi (Annet vitenskapelig)
• 38.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. -.
On Minimal Non-(2, 1)-Colorable Graphs2017Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave

A graph is (2, 1)-colorable if it allows a partition of its vertices into two classes such that both induce graphs with maximum degree at most one. A non-(2, 1)-colorable graph is minimal if all proper subgraphs are (2, 1)-colorable. We prove that such graphs are 2-edge-connected and that every edge sits in an odd cycle. Furthermore, we show properties of edge cuts and particular graphs which are no induced subgraphs. We demonstrate that there are infinitely many minimal non-(2, 1)-colorable graphs, at least one of order n for all n ≥ 5. Moreover, we present all minimal non-(2, 1)- colorable graphs of order at most seven. We consider the maximum degree of minimal non-(2, 1)-colorable graphs and show that it is at least four but can be arbitrarily large. We prove that the average degree is greater than 8/3 and give sufficient properties for graphs with average degree greater than 14/5. We conjecture that all minimal non-(2, 1)-colorable graphs fulfill these properties.

• 39.
Universitat Rovira i Virgili, Catalonia, Spain.
Universitat Rovira i Virgili, Catalonia, Spain. Universitat Rovira i Virgili, Catalonia, Spain.
Configuraciones combinatóricas y recuperación privada de información por pares2009Konferansepaper (Annet vitenskapelig)
• 40.
Universitat Rovira i Virgili, Tarragona, Catalonia, Spain.
Universitat Rovira i Virgili, Tarragona, Catalonia, Spain.
On the existence of combinatorial configurations2010Inngår i: 3rd International Workshop on Optimal Networks Topologies, 2010, 2010, s. 145-167Konferansepaper (Annet vitenskapelig)
• 41.
Universitat Rovira i Virgili, Tarragona, Catalonia, Spain .
Universitat Rovira i Virgili, Tarragona, Catalonia, Spain .
The semigroup of combinatorial configurations2012Inngår i: Semigroup Forum, ISSN 0037-1912, E-ISSN 1432-2137, Vol. 84, nr 1, s. 91-96Artikkel i tidsskrift (Fagfellevurdert)

We elaborate on the existence and construction of the so-called combinatorial configurations. The main result is that for fixed degrees the existence of such configurations is given by a numerical semigroup. The proof is constructive giving a method to obtain combinatorial configurations with parameters large enough.

• 42.
Universitat Rovira i Virgili, Tarragona, Catalonia, Spain.
Universitat Rovira i Virgili, Tarragona, Catalonia, Spain. University College Dublin, Ireland.
Problems related to combinatorial configurations with applications to P2P-user private information retrieval2010Konferansepaper (Annet vitenskapelig)
• 43.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Matematik.
Leonardo da Pisa: Inger Christensen och Fibonacci2008Inngår i: Lyrikvännen, ISSN 0460-0762, Vol. 55, nr 6, s. 33-38Artikkel i tidsskrift (Annet (populærvitenskap, debatt, mm))

Den danska poeten Inger Christensen byggde sin diktsamling Alfabet på Fibonaccis talserie. Artikeln är en kort historisk essä över Fibonacci, och beskriver även hur talserien är konstruerad.

• 44.
Univ Kentucky, Dept Math, Lexington, KY 40506 USA..
Michigan State Univ, Dept Math, E Lansing, MI 48824 USA.. KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
Detecting the integer decomposition property and Ehrhart unimodality in reflexive simplices2018Inngår i: Advances in Applied Mathematics, ISSN 0196-8858, E-ISSN 1090-2074, Vol. 100, s. 122-142Artikkel i tidsskrift (Fagfellevurdert)

A long-standing open conjecture in combinatorics asserts that a Gorenstein lattice polytope with the integer decomposition property (IDP) has a unimodal (Ehrhart) h*-polynomial. This conjecture can be viewed as a strengthening of a previously disproved conjecture which stated that any Gorenstein lattice polytope has a unimodal h*-polynomial. The first counterexamples to unimodality for Gorenstein lattice polytopes were given in even dimensions greater than five by Mustata and Payne, and this was extended to all dimensions greater than five by Payne. While there exist numerous examples in support of the conjecture that IDP reflexives are h*-unimodal, its validity has not yet been considered for families of reflexive lattice simplices that closely generalize Payne's counterexamples. The main purpose of this work is to prove that the former conjecture does indeed hold for a natural generalization of Payne's examples. The second purpose of this work is to extend this investigation to a broader class of lattice simplices, for which we present new results and open problems.

• 45.
Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
Linköpings universitet, Institutionen för datavetenskap, Artificiell intelligens och integrerade datorsystem. Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för datavetenskap, Artificiell intelligens och integrerade datorsystem. Linköpings universitet, Tekniska högskolan.
Local Search for Hop-constrained Directed Steiner Tree Problem with Application to UAV-based Multi-target Surveillance2014Rapport (Annet vitenskapelig)

We consider the directed Steiner tree problem (DSTP) with a constraint on the total number of arcs (hops) in the tree. This problem is known to be NP-hard, and therefore, only heuristics can be applied in the case of its large-scale instances.   For the hop-constrained DSTP, we propose local search strategies aimed at improving any heuristically produced initial Steiner tree. They are based on solving a sequence of hop-constrained shortest path problems for which we have recently developed ecient label correcting algorithms.   The presented approach is applied to nding suitable 3D locations where unmanned aerial vehicles (UAVs) can be placed to relay information gathered in multi-target monitoring and surveillance. The eciency of our algorithms is illustrated by results of numerical experiments involving problem instances with up to 40 000 nodes and up to 20 million arcs.

• 46.
Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
Linköpings universitet, Institutionen för datavetenskap, Artificiell intelligens och integrerade datorsystem. Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för datavetenskap, Artificiell intelligens och integrerade datorsystem. Linköpings universitet, Tekniska högskolan.
Local Search for Hop-constrained Directed Steiner Tree Problem with Application to UAV-based Multi-target Surveillance2014Inngår i: Examining Robustness and Vulnerability of Networked Systems / [ed] Butenko, S., Pasiliao, E.L., Shylo, V., IOS Press, 2014, s. 26-50Konferansepaper (Fagfellevurdert)

We consider the directed Steiner tree problem (DSTP) with a constraint on the total number of arcs (hops) in the tree. This problem is known to be NP-hard, and therefore, only heuristics can be applied in the case of its large-scale instances.For the hop-constrained DSTP, we propose local search strategies aimed at improving any heuristically produced initial Steiner tree. They are based on solving a sequence of hop-constrained shortest path problems for which we have recently developed efficient label correcting algorithms.The presented approach is applied to finding suitable 3D locations where unmanned aerial vehicles (UAVs) can be placed to relay information gathered in multi-target monitoring and surveillance. The efficiency of our algorithms is illustrated by results of numerical experiments involving problem instances with up to 40 000 nodes and up to 20 million arcs.

• 47.
Plymouth State University, NH, USA.
MIT, MA, USA. Bard Coll Simons Rock, MA, USA. Portola Valley, CA USA. MIT, MA, USA. Swiss Federal Institute Technology, Switzerland. The University of Electro-Communications, Chofu, Japan. University of Iibre Bruxelles, Belgium. Bard Coll Simons Rock, MA, USA. University of Utrecht, Netherlands. Bard Coll Simons Rock, MA, USA. Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska fakulteten. University of Elect Communicat, Japan. Japan Adv Institute Science and Technology, Japan. Osaka Prefecture University, Japan. Bard Coll Simons Rock, MA, USA.
Single-Player and Two-Player Buttons & Scissors Games2016Inngår i: DISCRETE AND COMPUTATIONAL GEOMETRY AND GRAPHS, JCDCGG 2015 / [ed] Akiyama, J., Ito, H., Sakai, T., Uno, Y., SPRINGER INT PUBLISHING AG , 2016, Vol. 9943, s. 60-72Konferansepaper (Fagfellevurdert)

We study the computational complexity of the Buttons amp; Scissors game and obtain sharp thresholds with respect to several parameters. Specifically we show that the game is NP-complete for C = 2 colors but polytime solvable for C = 1. Similarly the game is NP-complete if every color is used by at most F = 4 buttons but polytime solvable for F amp;lt;= 3. We also consider restrictions on the board size, cut directions, and cut sizes. Finally, we introduce several natural two-player versions of the game and show that they are PSPACE-complete.

• 48.
Linköpings universitet, Institutionen för datavetenskap, Programvara och system. Linköpings universitet, Tekniska fakulteten.
Linköpings universitet, Institutionen för datavetenskap, Programvara och system. Linköpings universitet, Tekniska fakulteten.
Time and Space Bounds for Planning2017Inngår i: The journal of artificial intelligence research, ISSN 1076-9757, E-ISSN 1943-5037, Vol. 60, s. 595-638Artikkel i tidsskrift (Fagfellevurdert)

There is an extensive literature on the complexity of planning, but explicit bounds on time and space complexity are very rare. On the other hand, problems like the constraint satisfaction problem (CSP) have been thoroughly analysed in this respect. We provide a number of upper- and lower-bound results (the latter based on various complexity-theoretic assumptions such as the Exponential Time Hypothesis) for both satisficing and optimal planning. We show that many classes of planning instances exhibit a dichotomy: either they can be solved in polynomial time or they cannot be solved in subexponential time and thus require O (2(cn)) time for some c amp;gt; 0. In many cases, we can even prove closely matching upper and lower bounds; for every epsilon amp;gt; 0, the problem can be solved in time O (2((1+epsilon)n)) but not in time O (2((1-epsilon)n)). Our results also indicate, analogously to CSPs, the existence of sharp phase transitions. We finally study and discuss the trade-off between time and space. In particular, we show that depth-first search may sometimes be a viable option for planning under severe space constraints.

• 49.
Högskolan Dalarna, Akademin Industri och samhälle, Statistik.
Högskolan Dalarna, Akademin Industri och samhälle, Statistik. Högskolan Dalarna, Akademin Industri och samhälle, Informatik. Högskolan Dalarna, Akademin Industri och samhälle, Datateknik.
Testing the gravity p-median model empirically2015Inngår i: Operations Research Perspectives, ISSN 2214-7160, Vol. 2, nr 124, artikkel-id 132Artikkel i tidsskrift (Fagfellevurdert)

Regarding the location of a facility, the presumption in the widely used p-median model is that the customer opts for the shortest route to the nearest facility. However, this assumption is problematic on free markets since the customer is presumed to gravitate to a facility by the distance to and the attractiveness of it. The recently introduced gravity p-median model offers an extension to the p-median model that account for this. The model is therefore potentially interesting, although it has not yet been implemented and tested empirically. In this paper, we have implemented the model in an empirical problem of locating vehicle inspections, locksmiths, and retail stores of vehicle spare-parts for the purpose of investigating its superiority to the p-median model. We found, however, the gravity p-median model to be of limited use for the problem of locating facilities as it either gives solutions similar to the p-median model, or it gives unstable solutions due to a non-concave objective function.

• 50.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
On avoiding some families of arrays2012Inngår i: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 312, nr 5, s. 963-972Artikkel i tidsskrift (Fagfellevurdert)

An n×n array A with entries from {1,…,n} is avoidable if there is an n×n Latin square L such that no cell in L contains a symbol that occurs in the corresponding cell in A. We show that the problem of determining whether an array that contains at most two entries per cell is avoidable is NP-complete, even in the case when the array has entries from only two distinct symbols. Assuming that PNP, this disproves a conjecture by Öhman. Furthermore, we present several new families of avoidable arrays. In particular, every single entry array (arrays where each cell contains at most one symbol) of order n≥2k with entries from at most k distinct symbols and where each symbol occurs in at most n−2 cells is avoidable, and every single entry array of order n, where each of the symbols 1,…,n occurs in at most cells, is avoidable. Additionally, if k≥2, then every single entry array of order at least n≥4, where at most k rows contain non-empty cells and where each symbol occurs in at most nk+1 cells, is avoidable.

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