A complete parameterized complexity analysis of bounded planning

Bäckström, Christer; Jönsson, Peter; Ordyniak, Sebastian; Szeider, Stefan

doi:10.1016/j.jcss.2015.04.002

Cited by 11 publications

(12 citation statements)

References 38 publications

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“…There has, thus, been a recent interest in applying parameterised complexity theory, which allows for more fine-grained results, where the complexity depends both on the problem itself and the choice of parameters. Bäckström, Jonsson, Ordyniak, and Szeider (2015) analysed LOP using plan length as parameter for all subclasses of SAS + using the PUBS restrictions, finding that the problem is W[2]-complete in the general case, but drops to W[1]-complete or even fixed-parameter tractable for some interesting subclasses. Kronegger, Pfandler, and Pichler (2013) perfomed a multi-parameter analysis of LOP for PSN using various combinations of parameters, including plan length.…”

Section: Introductionmentioning

confidence: 99%

Time and Space Bounds for Planning

Bäckström¹,

Jönsson²

2017

jair

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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 complexitytheoretic 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 > 0. In many cases, we can even prove closely matching upper and lower bounds; for every ε > 0, the problem can be solved in time O(2 (1+ε)n ) but not in time O(2 (1−ε)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.

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Section: Introductionmentioning

confidence: 99%

Time and Space Bounds for Planning

Bäckström¹,

Jönsson²

2017

jair

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“…the survey by Lokshtanov et al [22]. It is also gaining more and more popularity when studying central problems in AI such as planning and constraint satisfaction [1, 3,4,19,31]. The theory of NP-hardness provides evidence that many computational problems are unlikely to be solvable in polynomial time, but this theory does not give any concrete lower time bounds.…”

Section: Introductionmentioning

confidence: 99%

Refining complexity analyses in planning by exploiting the exponential time hypothesis

Aghighi

Bäckström

Jönsson

et al. 2016

Ann Math Artif Intell

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The use of computational complexity in planning, and in AI in general, has always been a disputed topic. A major problem with ordinary worst-case analyses is that they do not provide any quantitative information: they do not tell us much about the running time of concrete algorithms, nor do they tell us much about the running time of optimal algorithms. We address problems like this by presenting results based on the exponential time hypothesis (ETH), which is a widely accepted hypothesis concerning the time complexity of 3-SAT. By using this approach, we provide, for instance, almost matching upper and lower bounds onthe time complexity of propositional planning.

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“…The complexity of STRIPS planning varies from constant time to undecidable depending on which restrictions we make. These restrictions can be syntactic restrictions, such as restrictions on the number of preconditions and effects [2,9,18], or restrictions on action types [7,10,11,36,49]; semantic restrictions, such as restrictions on the variable dependencies [42,43,46,48,49].…”

Section: Complexity Of Planningmentioning

confidence: 99%

“…Downey, Fellows, and Stege [26] showed that STRIPS planning is W[1]-hard parameterized by the plan length (Later, Bäckström, Jonsson, Ordyniak, and Szeider [9] strengthened this result and showed that LOP parameterized by the plan length is W[2]-complete). Since then, the parameterized complexity of PSAT, LOP, COP and NBP has been studied under various restrictions and different parameterizations [1,6,9,12,39,56].…”

Section: Complexity Of Planningmentioning

confidence: 99%

Computational Complexity of some Optimization Problems in Planning

Aghighi¹

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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 also 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.The research presented in this thesis has been partially funded by the National Graduate School of Computer Science in Sweden (CUGS).iii Populärvetenskaplig sammanfattningHuvudtemat i denna avhandling är studiet av beräkningskomplexitet för automatisk planering. På en hög nivå kan man betrakta planeringsproblemet så här; man utgår från en värld eller ett system, som ett obemannat fordon eller en autonom robot, och antar att det finns vissa handlingar som ändrar tillståndet i systemet. Man antar dessutom att det finns ett initial-och ett måltillstånd. Planering är problemet att hitta en sekvens av handlingar som tranformerar initialtillståndet till måltillståndet. En sådan sekvens av handlingar kallas en plan. En planerare är ett datorprogram som löser planeringsproblem, och planerare baseras ofta på sökning genom tillstånden i systemet. Vanligtvis vill man optimera sökningen och hitta en plan som är optimal med avseende på något kriterium. Vad man vill optimera beror på tillämpningen men det är ofta att hitta en kortaste eller b...

show abstract

A complete parameterized complexity analysis of bounded planning

Cited by 11 publications

References 38 publications

Time and Space Bounds for Planning

Time and Space Bounds for Planning

Refining complexity analyses in planning by exploiting the exponential time hypothesis

Computational Complexity of some Optimization Problems in Planning

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