Feasibility of Motion Planning on Directed Graphs

Authors:
Zhilin Wu;Stéphane Grumbach
Affiliations:
CASIA-LIAMA,;INRIA-LIAMA,
Venue:
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Year:
2009

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Abstract

Because of irreversibility of movements, motion planning on directed graphs is much more intricate than that on graphs. Recently we showed that the feasibility of motion planning on acyclic and strongly connected directed graphs can be decided in time O (nm ) (n ,m are respectively the number of vertices and arcs of the directed graph), but left the feasibility of motion planning on (general) directed graphs open. In this paper, we complete the solution by showing that the feasibility of motion planning on directed graphs can be decided in time O (n 2 m ).