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CORR
2010
Springer

Exact Shortest Path Queries for Planar Graphs Using Linear Space

9 years 2 months ago
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).
Shay Mozes, Christian Sommer
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2010
Where CORR
Authors Shay Mozes, Christian Sommer
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