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Plan Reordering and Parallel Execution -- A Parameterized Complexity View
Linköping University, Department of Computer and Information Science, Software and Systems. Linköping University, Faculty of Science & Engineering. (TCSLAB)
Linköping University, Department of Computer and Information Science, Software and Systems. Linköping University, Faculty of Science & Engineering. (TCSLAB)
2017 (English)Conference paper, Published paper (Refereed)
Abstract [en]

Bäckström has previously studied a number of optimization problems for partial-order plans, like finding a minimum deordering (MCD) or reordering (MCR), and finding the minimum parallel execution length (PPL), which are all NP-complete. We revisit these problems, but applying parameterized complexity analysis rather than standard complexity analysis. We consider various parameters, including both the original and desired size of the plan order, as well as its width and height. Our findings include that MCD and MCR are W[2]-hard and in W[P] when parameterized with the desired order size, and MCD is fixed-parameter tractable (fpt) when parameterized with the original order size. Problem PPL is fpt if parameterized with the size of the non-concurrency relation, but para-NP-hard in most other cases. We also consider this problem when the number (k) of agents, or processors, is restricted, finding that this number is a crucial parameter; this problem is fixed-parameter tractable with the order size, the parallel execution length and k as parameter, but para-NP-hard without k as parameter.

Place, publisher, year, edition, pages
AAAI Press, 2017.
Keyword [en]
Partially ordered plan, Parameterized complexity, Complexity of planning, Plan reordering, Parallel plan execution
National Category
Computer Systems
Identifiers
URN: urn:nbn:se:liu:diva-136279OAI: oai:DiVA.org:liu-136279DiVA: diva2:1087085
Conference
Thirty-First AAAI Conference on Artificial Intelligence (AAAI-17)
Available from: 2017-04-05 Created: 2017-04-05 Last updated: 2017-05-17Bibliographically approved
In thesis
1. Computational Complexity of some Optimization Problems in Planning
Open this publication in new window or tab >>Computational Complexity of some Optimization Problems in Planning
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Automated planning is known to be computationally hard in the general case. Propositional planning is PSPACE-complete and first-order planning is undecidable. One method for analyzing the computational complexity of planning is to study restricted subsets of planning instances, with the aim of differentiating instances with varying complexity. We use this methodology for studying the computational complexity of planning. Finding new tractable (i.e. polynomial-time solvable) problems has been a particularly important goal for researchers in the area. The reason behind this is not only to differentiate between easy and hard planning instances, but also to use polynomial-time solvable instances in order to construct better heuristic functions and improve planners. We identify a new class of tractable cost-optimal planning instances by restricting the causal graph. We study the computational complexity of oversubscription planning (such as the net-benefit problem) under various restrictions and reveal strong connections with classical planning. Inspired by this, we present a method for compiling oversubscription planning problems into the ordinary plan existence problem. We further study the parameterized complexity of cost-optimal and net-benefit planning under the same restrictions and show that the choice of numeric domain for the action costs has a great impact on the parameterized complexity. We finally consider the parameterized complexity of certain problems related to partial-order planning. In some applications, less restricted plans than total-order plans are needed. Therefore, a partial-order plan is being used instead. When dealing with partial-order plans, one important question is how to achieve optimal partial order plans, i.e. having the highest degree of freedom according to some notion of flexibility. We study several optimization problems for partial-order plans, such as finding a minimum deordering or reordering, and finding the minimum parallel execution length.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2017. 35 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1854
National Category
Computer Systems
Identifiers
urn:nbn:se:liu:diva-136280 (URN)10.3384/diss.diva-136280 (DOI)978-91-7685-519-5 (ISBN)
Public defence
2017-06-16, Ada Lovelace, B-hus, Linköping University, SE-58183 Linköping, Linköping, 13:15 (English)
Opponent
Supervisors
Funder
CUGS (National Graduate School in Computer Science)
Available from: 2017-05-17 Created: 2017-04-05 Last updated: 2017-09-01Bibliographically approved

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