This paper introduces a near-linear time sequential algorithm for constructing a sparse neighborhood cover. This implies analogous improvements (from quadratic to near-linear time)...
Geometric shortest paths are a major topic in computational geometry; see the survey paper by Mitchell [12]. A shortest path between two points in a simple polygon can be found in...
We present an improved oracle for the distance sensitivity problem. The goal is to preprocess a directed graph G = (V, E) with non-negative edge weights to answer queries of the f...
Given a planar graph on n nodes with costs weights on its edges, de ne the distance between nodes i and j as the length of the shortest path between i and j. Consider this as an i...
Sanjeev Arora, Michelangelo Grigni, David R. Karge...