Computing simple paths among obstacles

Abstract Given a set X of points in the plane, two distinguished points s,t∈X , and a set Φ of obstacles represented by line segments, we wish to compute a simple polygonal path from s to t that uses only points in X as vertices and avoids the obstacles in Φ . We present two results: (1) we show that finding such simple paths among arbitrary obstacles is NP-complete, and (2) we give a polynomial-time algorithm that computes simple paths when the obstacles form a simple polygon P and X is inside P . Our algorithm runs in time O (m 2 n 2 ) , where m is the number of vertices of P and n is the number of points in X .

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