Strong-diameter decompositions of minor free graphs

Authors:
Ittai Abraham;Cyril Gavoille;Dahlia Malkhi;Udi Wieder
Affiliations:
Hebrew University of Jerusalem, Jerusalem, Israel;University of Bordeaux, Bordeaux, France;Hebrew University of Jerusalem and Microsoft Research, Silicon Valley Center;Microsoft Research, Silicon Valley Center
Venue:
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Year:
2007

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Abstract

We provide the first sparse covers and probabilistic partitions for graphs excluding a fixed minor that have strong diameter bounds; i.e. each set of the cover/partition has a small diameter as an induced sub-graph. Using these results we provide improved distributed name-independent routing schemes. Specifically, given a graph excluding a minor on r vertices and a parameter ρ 0 we obtain the flowing results: (1) a polynomial algorithm that constructs a set of clusters such that each cluster has a strong-diameter of O(r2ρ) and each vertex belongs to 2O(r)r! clusters; (2) a name-independent routing scheme with a stretch of O(r2) and tables of size 2O(r)r! log4n bits; (3) a randomized algorithm that partitions the graph such that each cluster has strong-diameter O(r6r ρ) and the probability an edge (u, v) is cut is O(r d(u, v)/ρ).