Constructing approximate shortest path maps in three dimensions

Abstract

A new technique for constructing a data-structure that approximates shortest path maps in Rd is discussed. An algorithm that computes a subdivision of P of size O((n/ε)log(1/ε)) which can be used to answer efficiently approximate shortest path queries is introduced. An algorithm that computes a subdivision of R3, which can be used to answer efficiently approximate shortest path queries is presented.