Exact Shortest Path Queries for Planar Graphs Using Linear Space

We provide the first linear-space data structure with provable sublinear query time for exact point-topoint shortest path queries in planar graphs. We prove that for any planar graph G with non-negative arc lengths and for any > 0 there is a data structure that supports exact shortest path and distance queries in G with the following properties: the data structure can be created in time O(n lg(n) lg(1/ )), the space required is O(n lg(1/ )), and the query time is O(n1/2+ ). Previous data structures by Fakcharoenphol and Rao (JCSS'06), Klein, Mozes, and Weimann (TransAlg'10), and Mozes and Wulff-Nilsen (ESA'10) with query time O(n1/2 lg2 n) use space at least (n lg n/ lg lg n).

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Shay Mozes, Christian Sommer
• Keywords: CORR 2010, Data Structures, Education, Planar Graph, Query Time