Near-Linear Time Construction of Sparse Neighborhood Covers

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) for any problem whose solution relies on network decompositions, including small edge cuts in planar graphs, approximate shortest paths, and weight- and distance-preserving graph spanners. In particular, an O(log n) approximation to the k-shortest paths problem on an n-vertex, E-edge graph is obtained that runs in ˜O (n + E + k) time. Key words. neighborhood covers, network decompositions, approximate shortest paths, spanners AMS subject classifications. 05C85, 68R10, 05C65, 05C70 PII. S0097539794271898

• Type: Journal
• Year: 1998
• Where: SIAMCOMP
• Authors: Baruch Awerbuch, Bonnie Berger, Lenore Cowen, David Peleg
• Keywords: Near-linear Time, Network Decompositions, Shortest Paths, SIAMCOMP 1998