Vertex Sparsification in Trees
Lecture Notes in Computer Science(2016)
摘要
Given an unweighted tree T=(V,E) with terminals K ⊂ V, we show how to obtain a 2-quality vertex flow and cut sparsifier H with V_H = K. We prove that our result is essentially tight by providing a 2-o(1) lower-bound on the quality of any cut sparsifier for stars. In addition we give improved results for quasi-bipartite graphs. First, we show how to obtain a 2-quality flow sparsifier with V_H = K for such graphs. We then consider the other extreme and construct exact sparsifiers of size O(2^k), when the input graph is unweighted.
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关键词
Graph sparsification,Vertex flow sparsifiers,Trees
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