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On the Complexity of Optimal Parallel Cooperative Path-Finding

Surynek P.

Fundamenta Informaticae

2015

Vol. 137, nr 4

517--548

A parallel version of the problem of cooperative path-finding (pCPF) is introduced in this paper. The task in CPF is to determine a spatio-temporal plan for each member of a group of agents. Each agent is given its initial location in the environment and its task is to reach the given goal location. Agents must avoid obstacles and must not collide with one another. The environment where agents are moving is modeled as an undirected graph. Agents are placed in vertices and they move along edges. At most one agent is placed in each vertex and at least one vertex remains unoccupied. An agent can only move into a currently unoccupied vertex in the standard version of CPF. In the parallel version, an agent can also move into a vertex being currently vacated by another agent supposing the character of this movement is not cyclic. The optimal pCPF where the task is to find the smallest possible solution of the makespan is particularly studied. The main contribution of this paper is the proof of NP-completeness of the decision version of the optimal pCPF. A reduction of propositional satisfiability (SAT) to the problem is used in the proof.

The Impact of a Bi-connected Graph Decomposition on Solving Cooperative Path-finding Problems

Surynek P., Surynková P., Chromý M.

Fundamenta Informaticae

2014

Vol. 135, nr 3

295--308

This paper proposes a framework for analyzing algorithms for inductive processing of bi-connected graphs. The BIBOX algorithm for solving cooperative path-finding problems over biconnected graphs is submitted for the suggested analysis. The algorithm proceeds according to a decomposition of a given bi-connected graph into handles. After finishing a handle, the handle is ruled out of consideration and the processing task is reduced to a task of the same type on a smaller graph. The handle decomposition for which the BIBOX algorithm performs best is theoretically identified. The conducted experimental evaluation confirms that the suggested theoretical analysis well corresponds to the real situation.