Polynomial-time Instances of the Minimum Weight Triangulation Problem

Abstract Given a set of points S in the plane, the Minimum Weight Triangulation (MWT) problem is to find a set of edges of minimum total length that triangulates S . The complexity status of the MWT problem remains unresolved; in fact it is one of four remaining open problems from the original list in the Garey and Johnson book ‘Computers and Intractability’. Although considerable work has been done on the development and analysis of heuristics for the MWT problem very few restricted instances of the problem have been shown to have a polynomial time algorithm. The major result of this type is the case where S is the set of points of a polygon. In this paper we present a polynomial time algorithm for the MWT problem where the points are on a constant number of nested convex hulls. This immediately provides a polynomial time algorithm for other related restricted instances such as the points belonging to a constant number of parallel lines.

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