Forbidden-set distance labels for graphs of bounded doubling dimension

Ittai Abraham, Shiri Chechik, Cyril Gavoille, David Peleg

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

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) log2 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) · |F|2 log n time, a 1 + ϵ stretch approximation for the distance between s and t in the graph G \ F. The labeling scheme can be extended into a forbidden-set labeled routing scheme with stretch 1 + ϵ for graphs of bounded doubling dimension.

Original languageEnglish
Article number22
JournalACM Transactions on Algorithms
Volume12
Issue number2
DOIs
StatePublished - Feb 2016

Funding

FundersFunder number
United States-Israel Binational Science Foundation2008348
Israel Science Foundation894/09
Ministry of Science and Technology, Israel

    Keywords

    • Compact routing
    • Distance labeling
    • Doubling dimension
    • Fault-tolerance
    • Forbidden sets

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