A New Balanced Subdivision of a Simple Polygon for Time-Space Trade-Off Algorithms

Abstract

Given a read-only memory for input and a write-only stream for output, an s-workspace algorithm, for a positive integer parameter s, is an algorithm using only O(s) words of workspace in addition to the memory for the input. In this paper, we present an O(n2/s)-time s-workspace algorithm for subdividing a simple n-gon into O(min{n/s,s}) subpolygons of complexity O(max{n/s,s}). As applications of the subdivision, the previously best known time-space trade-offs for the following three geometric problems are improved immediately by adopting the proposed subdivision: (1) computing the shortest path between two points inside a simple n-gon, (2) computing the shortest-path tree from a point inside a simple n-gon, (3) computing a triangulation of a simple n-gon. In addition, we improve the algorithm for problem (2) further by applying different approaches depending on the size of the workspace.