Strong-Diameter Decompositions of Minor Free Graphs |
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Authors: | Ittai Abraham Cyril Gavoille Dahlia Malkhi Udi Wieder |
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Affiliation: | 1. Hebrew University of Jerusalem, Jerusalem, Israel 2. University of Bordeaux, Bordeaux, France 3. Microsoft Research, Silicon Valley Center, Mountain View, CA, USA
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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 following 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), headers of O(log n+rlog r) bits, and tables of size 2
O(r)
r! log 4
n/log log 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). |
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Keywords: | |
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