Using motion planning to study protein folding pathways
RECOMB '01 Proceedings of the fifth annual international conference on Computational biology
Optimal pebble motion on a tree
Information and Computation
Routing performance in the presence of unidirectional links in multihop wireless networks
Proceedings of the 3rd ACM international symposium on Mobile ad hoc networking & computing
Introduction to Algorithms
A Linear Time Algorithm for the Feasibility of Pebble Motion on Trees
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
Controllability, recognizability, and complexity issues in robot motion planning
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Planning Algorithms
Coordinating Pebble Motion On Graphs, The Diameter Of Permutation Groups, And Applications
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Digraphs: Theory, Algorithms and Applications
Digraphs: Theory, Algorithms and Applications
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Motion planning is a fundamental problem of robotics with applications in many areas of computer science and beyond. Its restriction to graphs has been investigated in the literature, for it allows one to concentrate on the combinatorial problem abstracting from geometric considerations. In this paper, we consider motion planning over directed graphs, which are of interest for asymmetric communication networks. Directed graphs generalize undirected graphs, while introducing a new source of complexity to the motion planning problem: moves are not reversible. We first consider the class of acyclic directed graphs and show that the feasibility can be solved in time linear in the product of the number of vertices and the number of arcs. We then turn to strongly connected directed graphs. We first prove a structural theorem for decomposing strongly connected directed graphs into strongly biconnected components. Based on the structural decomposition, we show that the feasibility of motion planning on strongly connected directed graphs can be decided in linear time.