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Solving Temporal CSPs via Enumeration and SAT Compilation
Linköping University, Department of Computer and Information Science.
2019 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

The constraint satisfaction problem (CSP) is a powerful framework used in theoretical computer science for formulating a  multitude of problems.

The CSP over a constraint language Γ (CSP(Γ)) is the decision problem of verifying whether a set of constraints based on the relations in Γ admits a satisfying assignment or not.

Temporal CSPs are a special subclass of CSPs frequently encountered in AI.

Here, the relations are first-order definable in the structure (Q;<), i.e the rationals with the usual order.

These problems have previously often been solved by either enumeration or SAT compilation.

We study a restriction of temporal CSPs where the constraint language is limited to logical disjunctions of <-, =-, ≠- and ≤-relations, and were each constraint contains at most k such basic relations (CSP({<,=,≠,≤}∨k)).

 

Every temporal CSP with a finite constraint language Γ is polynomial-time reducible to CSP({<,=,≠,≤}∨k) where k is only dependent on Γ.

As this reduction does not increase the number of variables, the time complexity of CSP(Γ) is never worse than that of CSP({<,=,≠,≤}∨k).

This makes the complexity of CSP({<,=,≠,≤}∨k) interesting to study.

 

We develop algorithms combining enumeration and SAT compilation to solve CSP({<,=,≠,≤}∨k), and study the asymptotic behaviour of these algorithms for different classes.

Our results show that all finite constraint languages Γ first order definable over (Q;<) are solvable in O*(((1/(eln(2))-ϵk)n)^n) time for some ϵk>0 dependent on Γ.

This is strictly better than O*((n/(eln(2)))^n), i.e. O*((0.5307n)^n), achieved by enumeration algorithms.

Some examples of upper bounds on time complexity achieved in the thesis are CSP({<}∨2) in O*((0.1839n)^n) time,

CSP({<,=,≤}∨2) in O*((0.2654n)^n) time, CSP({<,=,≠}∨3) in O*((0.4725n)^n) time and

CSP({<,=,≠,≤}∨3) in O*((0.5067n)^n) time.

For CSP({<}∨2) this should be compared to the bound O*((0.3679n)^n), from previously known enumeration algorithms.

 

 

 

Place, publisher, year, edition, pages
2019. , p. 36
Keywords [en]
CSP, Algorithms
National Category
Computer Sciences
Identifiers
URN: urn:nbn:se:liu:diva-162482ISRN: LIU-IDA/LITH-EX-A--19/094--SEOAI: oai:DiVA.org:liu-162482DiVA, id: diva2:1376008
Subject / course
Computer science
Supervisors
Examiners
Available from: 2019-12-10 Created: 2019-12-06 Last updated: 2019-12-10Bibliographically approved

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