SCG '86 Proceedings of the second annual symposium on Computational geometry
Computational complexity of art gallery problems
IEEE Transactions on Information Theory
Art gallery theorems and algorithms
Art gallery theorems and algorithms
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Triangulating a simple polygon in linear time
Discrete & Computational Geometry
Visibility properties of polygons
Visibility properties of polygons
Optimal linear-time algorithm for the shortest illuminating line segment in a polygon
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Visibility-based pursuit-evasion in a polygonal room with a door
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Finding all weakly-visible chords of a polygon in linear time
Nordic Journal of Computing
Coordinated exploration of unknown labyrinthine environments applied to the pursuit evasion problem
Proceedings of the fourth international joint conference on Autonomous agents and multiagent systems
Hide-and-seek: algorithms for polygonWalk problems
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
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In this paper we give optimal solutions for two versions of the two-guard problem. Given a simple polygon P with vertices s and t, the straight walk problem asks whether we can move two points monotonically on P from s to t, one clockwise and one counterclockwise, such that the points are always co-visible. In the counter walk problem, both points move clockwise, one from s to t and the other from t to s. We provide &THgr;(n) constructive algorithms for both problems. We obtain our results by examining the structure of the restrictions placed on the motion of the two points, and by employing properties of shortest paths and shortest path trees.