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We consider the most basic visibility-based pursuit-evasion problem defined as follows: Given a polygonal region, a searcher with 360 • vision, and an unpredictable intruder that is arbitrarily faster than the searcher, plan the motion of the searcher so as to see the intruder. In this paper, we present simple necessary and sufficient conditions for a… (More)

We consider searching problems in robotics that a robot has to nd a path to a target by traveling in an unknown star-shaped polygon P. The goal is to minimize the ratio of the distance traveled by the robot to the length of the shortest start-to-target path. Let s be a starting point in P. We rst present a competitive strategy to nd a path from s to the… (More)

Visibility-based pursuit-evasion problems are as follows: given a polygonal region, one or more searchers with visibility, and an unpredictable intruder that is arbitrarily faster than the searcher, plan the motion of the searchers so as to see the intruder. In this paper, we consider several visibility-based pursuit-evasion problems with a single searcher:… (More)

A k-disjoint path cover of a graph is a set of k internally vertex-disjoint paths which cover the vertex set with k paths and each of which runs between a source and a sink. Given that each source and sink v is associated with an integer-valued demand d(v) ≥ 1, we are concerned with general-demand k-disjoint path cover in which every source and sink v is… (More)

A k-disjoint path cover of a graph is defined as a set of k internally vertex-disjoint paths connecting given sources and sinks in such a way that every vertex of the graph is covered by a path in the set. In this paper, we analyze the k-disjoint path cover of recursive circulant G(2 m , 4) under the condition that at most f faulty vertices and/or edges are… (More)

The 1-searcher is a mobile guard whose visibility is limited to a ray emanating from his position, where the direction of the ray can be changed continuously with bounded angular rotation speed. Given a polygonal region P with a specified boundary point d, is it possible for a 1-searcher to eventually see a mobile intruder that is arbitrarily faster than… (More)