Optimal Approximate Distance Oracle for Planar Graphs

A ($1+\epsilon$) -approximate distance oracle of an edge-weighted graph is a data structure that returns an approximate shortest path distance between any two query vertices up to a ($1+\epsilon$) factor. Thorup (FOCS 2001, JACM 2004) and Klein (SODA 2002) independently constructed a ($1+\epsilon$) -approximate distance oracle with $O(n\log n)$ space, me...