Improved sparse covers for graphs excluding a fixed minor

Costas Busch; Ryan Lafortune; Srikanta Tirthapura

doi:10.1145/1281100.1281112

Improved sparse covers for graphs excluding a fixed minor

Costas Busch, Ryan Lafortune, Srikanta Tirthapura

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

21 Scopus citations

Abstract

We consider the construction of sparse covers for planar graphs and other graphs that exclude a fixed minor. We present an algorithm that gives a cover for the -neighborhood of each node. For planar graphs, the cover has radius no more than 24-8 and degree (maximum cluster overlaps) no more than 18. For every n node graph that excludes a fixed minor, we present an algorithm that yields a cover with radius no more than 4 and degree O(log n). This is a significant improvement over previous results for planar graphs and for graphs excluding a fixed minor; in order to obtain clusters with radius of O(), it was required to have degree polynomial in n. Since sparse covers have many applications in distributed computing, including compact routing, distributed directories and synchronizers, our improved cover construction results in improved algorithms for all these problems, for the class of graphs that exclude a fixed minor.

Original language	English (US)
Title of host publication	PODC'07
Subtitle of host publication	Proceedings of the 26th Annual ACM Symposium on Principles of Distributed Computing
Pages	61-70
Number of pages	10
DOIs	https://doi.org/10.1145/1281100.1281112
State	Published - 2007
Externally published	Yes
Event	PODC'07: 26th Annual ACM Symposium on Principles of Distributed Computing - Portland, OR, United States Duration: Aug 12 2007 → Aug 15 2007

Publication series

Name	Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

Conference

Conference	PODC'07: 26th Annual ACM Symposium on Principles of Distributed Computing
Country/Territory	United States
City	Portland, OR
Period	8/12/07 → 8/15/07

Keywords

Compact routing
Minor free graph
Path separator
Planar graph
Sparse cover

ASJC Scopus subject areas

Software
Hardware and Architecture
Computer Networks and Communications

Access to Document

10.1145/1281100.1281112

Cite this

Improved sparse covers for graphs excluding a fixed minor. / Busch, Costas; Lafortune, Ryan; Tirthapura, Srikanta.
PODC'07: Proceedings of the 26th Annual ACM Symposium on Principles of Distributed Computing. 2007. p. 61-70 (Proceedings of the Annual ACM Symposium on Principles of Distributed Computing).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Busch, C, Lafortune, R & Tirthapura, S 2007, Improved sparse covers for graphs excluding a fixed minor. in PODC'07: Proceedings of the 26th Annual ACM Symposium on Principles of Distributed Computing. Proceedings of the Annual ACM Symposium on Principles of Distributed Computing, pp. 61-70, PODC'07: 26th Annual ACM Symposium on Principles of Distributed Computing, Portland, OR, United States, 8/12/07. https://doi.org/10.1145/1281100.1281112

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Improved sparse covers for graphs excluding a fixed minor

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

Access to Document

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