Finding shortest safari routes in simple polygons

Abstract

Let P be a simple polygon, and let P be a set of disjoint convex polygons inside P, each sharing one edge with P. The safari route problem asks for a shortest route inside P that visits each polygon in P . In this paper, we first present a dynamic programming algorithm with running time O( n 3) for computing the shortest safari route in the case that a starting point on the route is given, where n is the total number of vertices of P and polygons in P . (Ntafos in [Comput. Geom. 1 (1992) 149–170] claimed a more efficient solution, but as shown in Appendix A of this paper, the time analysis of Ntafos' algorithm is erroneous and no time bound is guaranteed for his algorithm.) The restriction of giving a starting point is then removed by a brute-force algorithm, which requires O( n 4) time. The solution of the safari route problem finds applications in watchman routes under limited visibility.