Object location using path separators

We study a novel separator property called k-path separable. Roughly speaking, a k-path separable graph can be recursively separated into smaller components by sequentially removing k shortest paths. Our main result is that every minor free weighted graph is k-path separable. We then show that k-path separable graphs can be used to solve several object location problems: (1) a small-worldization with an average poly-logarithmic number of hops; (2) an (1 + ε)approximate distance labeling scheme with O(log n) space labels; (3) a stretch-(1 + ε) compact routing scheme with tables of poly-logarithmic space; (4) an (1 + ε)-approximate distance oracle with O(n log n) space and O(log n) query time. Our results generalizes to much wider classes of weighted graphs, namely to bounded-dimension isometric sparable graphs. Categories and Subject Descriptors: C.2.1 [ComputerCommunication Networks]: Network Architecture and Design – Distributed networks; G.2.2 [Discrete Mathematics]: Graph Theo...

• Type: Conference
• Year: 2006
• Where: PODC
• Authors: Ittai Abraham, Cyril Gavoille
• Keywords: Distributed And Parallel Computing, Free Weighted Graph, K-path Separable Graphs, PODC 2006, Weighted Graphs