Ittai Abraham, Cyril Gavoille, Dahlia Malkhi, and Udi Wieder
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 following 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), headers of O(log n+r log r) bits, and tables of size 2O(r)r! log4 n/ log log n bits; (3) a randomized algorithm that partitions the graph such that each cluster has strong-diameter O(r6rρ) and the probability an edge (u, v) is cut is O(r d(u, v)/ρ).
|Published in||Theory of Computing Systems|