Improved Distance Queries in Planar Graphs

Abstract

AbstractThere are several known data structures that answers distance queries between two arbitrary vertices in a planar graph. The tradeoff is among preprocessing time, storage space and query time. In this paper we present three data structures that answer such queries, each with its own advantage over previous data structures. The first one improves the query time of data structures of linear space. The second improves the preprocessing time of data structures with a space bound of O(n 4/3) or higher while matching the best known query time. The third data structure improves the query time for a similar range of space bounds, at the expense of a longer preprocessing time. The techniques that we use include modifying the parameters of planar graph decompositions, combining the different advantages of existing data structures, and using the Monge property for finding minimum elements of matrices.KeywordsData StructureShort PathPlanar GraphQuery TimeInternal VertexThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.