Computing simple paths among obstacles

Given a set X of points in the plane, two distinguished points s,t X, and a set 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 . 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(m2n2), where m is the number of vertices of P and n is the number of points in X.

• Type: Journal
• Year: 2000
• Where: COMGEO
• Authors: Qi Cheng, Marek Chrobak, Gopalakrishnan Sundaram
• Keywords: Applied Computing, COMGEO 2000, Line Segments, Simple Paths, Simple Polygonal Path