Approximate Distance Oracles for Planar Graphs with Improved Query Time-Space Tradeoff
Christian Wulff‐Nilsen · 2015
We consider approximate distance oracles for edge-weighted n-vertex undirected planar graphs. Given fixed ∊ > 0, we present a (1 + ∊)-approximate distance oracle with O(n(log log n)2) space and O((log log n)3) query time. This improves the previous best product of query time and space of the oracles of Thorup (FOCS 2001, J. ACM 2004) and Klein (SODA 2002) from O(n log n) to O(n(log log n)5).