Fast and Compact Oracles for Approximate Distances in Planar Graphs

We present an experimental evaluation of an approximate distance oracle recently suggested by Thorup [1] for undirected planar graphs. The oracle uses the existence of graph separators for planar graphs, discovered by Lipton and Tarjan [2], in order to divide the graph into smaller subgraphs. For a planar graph with n nodes, the algorithmic variant considered uses O(n(log n)3 / ) preprocessing time and O(n(log n)2 / ) space to answer factor (1 + ) distance queries in O((log n)2 / ) time. By performing experiments on randomly generated planar graphs and on planar graphs derived from real world road networks, we investigate some key characteristics of the oracle, such as preprocessing time, query time, precision, and characteristics related to the underlying data structure, including space consumption. For graphs with one million nodes, the average query time is less than 20μs.

• Type: Conference
• Year: 2007
• Where: ESA
• Authors: Laurent Flindt Muller, Martin Zachariasen
• Keywords: ESA 2007, Planar Graphs, Query Time, Undirected Planar Graphs