An Algorithm for Computing a Hamiltonian Cycle of Given Points in a Polygonal Region

Abstract

In this paper, for a point set X in a simple polygon P, we present an algorithm to compute a Hamiltonian cycle which avoids the boundary of P and accesses all points of X. Computing a Hamiltonian cycle of given points in a simple polygon is a novel transformation of the general Hamiltonian problems and the problem of finding simple paths on given obstacles in a simple polygon. In our solution, we first construct the geodesic convex hull G of X inside P, and then find simple paths turn only at the points of X for two adjacent vertices in X along the boundary of G which are invisible to each other. After an original Hamiltonian cycle is found, we insert the remaining points to it. Finally, we present an O((n 2 +m)nlogm) time algorithm (n is the number of points in X and m is the number of P's vertices) to report a Hamiltonian cycle if it exists or report that no such cycle exists.