We consider the point-to-point (approximate) shortest-path query problem, which is the
following generalization of the classical single-source (SSSP) and all-pairs shortest-path …

In this article, we show how to compute for n-vertex planar graphs in O (n 11/6 polylog (n))
expected time the diameter and the sum of the pairwise distances. The algorithms work for …

We present an explicit and efficient construction of additively weighted Voronoi diagrams on
planar graphs. Let G be a planar graph with n vertices and b sites that lie on a constant …

We present an O (n 1.5)-space distance oracle for directed planar graphs that answers
distance queries in O (log n) time. Our oracle both significantly simplifies and significantly …

A (1+ϵ)-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+ϵ) …

We study vertex sparsification for distances, in the setting of planar graphs with distortion:
Given a planar graph G (with edge weights) and a subset of k terminal vertices, the goal is to …

In a recent breakthrough, Charalampopoulos, Gawrychowski, Mozes, and Weimann [9]
showed that exact distance queries on planar graphs could be answered in no (1) time by a …

The following algorithm partitions road networks surprisingly well:(i) sort the vertices by
longitude (or latitude, or some linear combination) and (ii) compute the maximum flow from …

We present new tradeoffs between space and query-time for exact distance oracles in
directed weighted planar graphs. These tradeoffs are almost optimal in the sense that they …

For a given a graph, a distance oracle is a data structure that answers distance queries
between pairs of vertices. We introduce an O (n 5/3)-space distance oracle which answers …