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2004
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Lower bounds for graph embeddings and combinatorial preconditioners

8 years 11 months ago
Lower bounds for graph embeddings and combinatorial preconditioners
Given a general graph G, a fundamental problem is to find a spanning tree H that best approximates G by some measure. Often this measure is some combination of the congestion and dilation of an embedding of G into H. One example is the routing time ρ(G, H) ≤ O(congestion + dilation), the number of steps necessary to route pairwise demands G on network links H in the store-and-forward packet routing model. Another is the condition number κf (G, H) ≤ O(congestion·dilation), the square root of which bounds the number of iterations necessary to solve a linear system with coefficient matrix G preconditioned by H using the classical conjugate gradient method. The algorithmic applications of being able to find (efficiently) a good tree approximation H for a graph G are numerous; but what if no good tree exists? In this paper, we seek to identify the class of graphs G which are intrinsically difficult to approximate by a particular measure. It is easily seen that with respect to rout...
Gary L. Miller, Peter C. Richter
Added 30 Jun 2010
Updated 30 Jun 2010
Type Conference
Year 2004
Where SPAA
Authors Gary L. Miller, Peter C. Richter
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