A Time-Space Trade-off for the Shortest Path Tree in a Simple Polygon

Abstract

A [Formula: see text]-workspace algorithm may use a workspace of [Formula: see text] words which can be read and written, in addition to their input, which is provided as a read-only array of [Formula: see text] items. We present a [Formula: see text]-workspace algorithm for constructing the shortest path tree of a simple polygon [Formula: see text] with [Formula: see text] vertices, with respect to a given point inside the polygon in [Formula: see text] time, where [Formula: see text] is the time for computing the visibility polygon of a given point inside a simple polygon with [Formula: see text] additional words of space.