A Refined View of Causal Graphs and Component Sizes: SP-Closed Graph Classes and Beyond

Author:

Bäckström C.,Jonsson P.

Abstract

The causal graph of a planning instance is an important tool for planning both in practice and in theory. The theoretical studies of causal graphs have largely analysed the computational complexity of planning for instances where the causal graph has a certain structure, often in combination with other parameters like the domain size of the variables. Chen and Giménez ignored even the structure and considered only the size of the weakly connected components. They proved that planning is tractable if the components are bounded by a constant and otherwise intractable. Their intractability result was, however, conditioned by an assumption from parameterised complexity theory that has no known useful relationship with the standard complexity classes. We approach the same problem from the perspective of standard complexity classes, and prove that planning is NP-hard for classes with unbounded components under an additional restriction we refer to as SP-closed. We then argue that most NP-hardness theorems for causal graphs are difficult to apply and, thus, prove a more general result; even if the component sizes grow slowly and the class is not densely populated with graphs, planning still cannot be tractable unless the polynomial hierachy collapses. Both these results still hold when restricted to the class of acyclic causal graphs. We finally give a partial characterization of the borderline between NP-hard and NP-intermediate classes, giving further insight into the problem.

Publisher

AI Access Foundation

Subject

Artificial Intelligence

Cited by 8 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Backdoors to planning;Artificial Intelligence;2019-04

2. Time and Space Bounds for Planning;Journal of Artificial Intelligence Research;2017-11-21

3. An initial study of time complexity in infinite-domain constraint satisfaction;Artificial Intelligence;2017-04

4. Refining complexity analyses in planning by exploiting the exponential time hypothesis;Annals of Mathematics and Artificial Intelligence;2016-07-29

5. Upper and Lower Time and Space Bounds for Planning;FRONT ARTIF INTEL AP;2016

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