Computational study on a branch decomposition based exact distance oracle for planar graphs

We present a simple exact distance oracle for the point-to-point shortest distance problem in planar graphs. Given an edge weighted planar graph G of n vertices, we decompose G into subgraphs by a branch-decomposition of G, compute the shortest distances between each vertex in a subgraph and the vertices in the boundary of the subgraph, and keep the shortest distances in the oracle. Let bw(G) be the branchwidth of G. Our oracle has O(bw(G)) query time, O(bw(G)n log(n)) size and O(n^2 log(n)) pre-processing time. Computational studies show that our oracle is much faster than Dijkstra’s algorithm for answering point-to-point shortest distance queries for several classes of planar graphs.