On the Computational Complexity of Multi-Agent Pathfinding on Directed Graphs

The determination of the computational complexity of multi-agent pathfinding on directed graphs has been an open problem for many years. For undirected graphs, solvability can be decided in polynomial time, as has been shown already in the eighties. Further, recently it has been shown that a special case on directed graphs is solvable in polynomial time. In this paper, we show that the problem is NP-hard in the general case. In addition, some upper bounds are proven

Cooperative Epistemic Multi-Agent Planning for Implicit Coordination

Epistemic planning can be used for decision making in multi-agent situations with distributed knowledge and capabilities. Recently, Dynamic Epistemic Logic (DEL) has been shown to provide a very natural and expressive framework for epistemic planning. We extend the DEL-based epistemic planning framework to include perspective shifts, allowing us to define new notions of sequential and conditional planning with implicit coordination. With these, it is possible to solve planning tasks with joint goals in a decentralized manner without the agents having to negotiate about and commit to a joint policy at plan time. First we define the central planning notions and sketch the implementation of a planning system built on those notions. Afterwards we provide some case studies in order to evaluate the planner empirically and to show that the concept is useful for multi-agent systems in practice.Comment: In Proceedings M4M9 2017, arXiv:1703.0173

Plan reuse versus plan generation : a theoretical and empirical analysis

The ability of a planner to reuse parts of old plans is hypothesized to be a valuable tool for improving efficiency of planning by avoiding the repetition of the same planning effort. We test this hypothesis from an analytical and empirical point of view. A comparative worst-case complexity analysis of generation and reuse under different assumptions reveals that it is not possible to achieve a provable efficiency gain of reuse over generation. Further, assuming "conservative" plan modification, plan reuse can actually be strictly more difficult than plan generation. While these results do not imply that there won\u27t be an efficiency gain in the "average case", retrieval of a good plan may present a serious bottleneck for plan reuse systems, as we will show. Finally, we present the results of an empirical study of three different plan reuse systems, which leads us to the conclusion that the utility of plan-reuse techniques is limited and that these limits have not been determined yet

On the computational complexity of temporal projection and some related problems

One kind of temporal reasoning is temporal projection -the computation of the consequences for a set of events. This problem is related to a number of other temporal reasoning tasks such as story understanding, plan validation, and planning. We show that one particular simple case of temporal projection on partially ordered events turns out to be harder than previously conjectured. However, given the restrictions of this problem, planning and story understanding are easy. Additionally, we show that plan validation, one of the intended applications of temporal projection, is tractable for an even larger class of plans. The incomplete decision procedure for the temporal projection problem that has been proposed by other authors, however, fails to be complete in the case where we have shown plan validation to be tractable

Plan modifications versus plan generation : a complexity-theoretic perspective

The ability of a planner to modify a plan is considered as a valuable tool for improving efficiency of planning by avoiding the repetition of the same planning effort. From a computational complexity point of view, however, it is by no means obvious that modifying a plan is computationally as easy as planning from scratch if the modification has to follow the principle of "conservatism", i.e., to reuse as much of the old plan as possible. Indeed, considering propositional STRIPS planning, it turns out that conservative plan modification is as hard as planning and can sometimes be harder than plan generation. Furthermore, this holds even if we consider modification problems where the old and the new goal specification are similar. We put these results into perspective and discuss the relationship to existing plan modification systems. Although sometimes claimed otherwise, these systems do not address the modification problem, but use a non-conservative form of plan modification as a heuristic technique

When Are Behaviour Networks Well-Behaved?

Agents operating in the real world have to deal with a constantly changing and only partially predictable environment and are nevertheless expected to choose reasonable actions quickly. This problem is addressed by a number of action-selection mechanisms. Behaviour networks as proposed by Maes are one such mechanism, which is quite popular. In general, it seems not possible to predict when behaviour networks are well-behaved. However, they perform quite well in the robotic soccer context. In this paper, we analyse the reason for this success by identifying conditions that make behaviour networks goal converging, i.e., force them to reach the goals regardless of the details of the action selection scheme. In terms of STRIPS domains one could talk of self-solving planning domains

Reasoning about temporal relations : a maximal tractable subclass of Allen\u27s interval algebra

We introduce a new subclass of Allen\u27s interval algebra we call "ORD-Horn subclass", which is a strict superset of the "pointisable subclass". We prove that reasoning in the ORD-Horn subclass is a polynomial-time problem and show that the path-consistency method is sufficient for deciding satisfiability. Further, using an extensive machine-generated case analysis, we show that the ORD-Horn subclass is a maximal tractable subclass of the full algebra (assuming P neq NP). In fact, it is the unique greatest tractable subclass amongst the subclasses that contain all basic relations

Belief revision and default reasoning : syntax-based approaches

Belief revision leads to temporal nonmonotonicity, i.e., the set of beliefs does not grow monotonically with time. Default reasoning leads to logical nonmonotonicity, i.e., the set of consequences does not grow monotonically with the set of premises. The connection between these forms of nonmonotonicity will be studied in this paper focusing on syntax-based approaches. It is shown that a general form of syntax-based belief revision corresponds to a special kind of partial meet revision in the sense of variants of logics for default reasoning. Additionally, the computational complexity of the membership problem in revised belief sets and of the equivalent problem of derivability in default logics is analyzed, which turns out to be located at the lower end of the polynomial hierarchy

05491 Abstracts Collection -- Spatial Cognition: Specialization and Integration

From 04.12.05 to 09.12.05, the Dagstuhl Seminar 05491 ``Spatial Cognition: Specialization and Integration\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

An empirical analysis of optimization techniques for terminological representation systems : or: \u27Making KRIS get a move on\u27

We consider different methods of optimizing the classification process of terminological representation systems, and evaluate their effect on three different types of test data. Though these techniques can probably be found in many existing systems, until now there has been no coherent description of these techniques and their impact on the performance of a system. One goal of this paper is to make such a description available for future implementors of terminological systems. Building the optimizations that came off best into the KRIS system greatly enhanced its efficiency