Forbidden-Set Distance Labels for Graphs of Bounded Doubling Dimension

Author:

Abraham Ittai1,Chechik Shiri2,Gavoille Cyril3,Peleg David4

Affiliation:

1. VMware Research, Palo Alto, CA, USA

2. Tel-Aviv University, Tel-Aviv, Israel

3. Université de Bordeaux, LaBRI, IUF, France

4. The Weizmann Institute of Science, Rehovot, Israel

Abstract

This article proposes a forbidden-set labeling scheme for the family of unweighted graphs with doubling dimension bounded by α. For an n -vertex graph G in this family, and for any desired precision parameter ϵ > 0, the labeling scheme stores an O (1 + ϵ − 1 ) log 2 n -bit label at each vertex. Given the labels of two end-vertices s and t , and the labels of a set F of “forbidden” vertices and/or edges, our scheme can compute, in O (1 + ϵ − 1 ) · | F | 2 log n time, a 1 + ϵ stretch approximation for the distance between s and t in the graph GF . The labeling scheme can be extended into a forbidden-set labeled routing scheme with stretch 1 + ϵ for graphs of bounded doubling dimension.

Funder

United States-Israel Binational Science Foundation

Israel Science Foundation

Israel Ministry of Science and Technology

Publisher

Association for Computing Machinery (ACM)

Subject

Mathematics (miscellaneous)

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