Strong Diameter Decompositions of Minor Free Graphs

Ittai Abraham Cyril Gavoille Dahlia Malkhi Udi Wieder	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(r^2 ρ) and each vertex belongs to 2^O(r)r! clusters; (2) a name-independent routing scheme with a stretch of O(r^2) and tables of size 2^O(r)r! log^4 n bits; (3) a randomized algorithm that partitions the graph such that each cluster has strong-diameter O(r6^r ρ) and the probability an edge (u, v) is cut is O(r d(u, v)/ρ).
	[SPAA 07 version pdf]