TY - GEN

T1 - Improved sparse covers for graphs excluding a fixed minor

AU - Busch, Costas

AU - Lafortune, Ryan

AU - Tirthapura, Srikanta

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

KW - Compact routing

KW - Minor free graph

KW - Path separator

KW - Planar graph

KW - Sparse cover

UR - http://www.scopus.com/inward/record.url?scp=36949014083&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36949014083&partnerID=8YFLogxK

U2 - 10.1145/1281100.1281112

DO - 10.1145/1281100.1281112

M3 - Conference contribution

AN - SCOPUS:36949014083

SN - 1595936165

SN - 9781595936165

T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

SP - 61

EP - 70

BT - PODC'07

T2 - PODC'07: 26th Annual ACM Symposium on Principles of Distributed Computing

Y2 - 12 August 2007 through 15 August 2007

ER -