Storing shortest paths for a polyhedron

Abstract

We present a new scheme for storing shortest path information for a polyhedron. This scheme is obtained with a new observation on the properties of shortest path information of a polyhedron. Our scheme separates in a clear sense the problem of finding shortest paths and the problem of storing the shortest path information for retrieval. A tradeoff between time complexity O(d log n/log d) and space complexity O(n log n/log d) is obtained, where d is an adjustable parameter. When d tends to infinity space complexity of o(n log n) can be achieved at the expense of increased time complexity.