3 research outputs found
Vertex Sparsification and Oblivious Reductions
Given an undirected, capacitated graph and a set of terminals of size , we construct an undirected, capacitated graph for which the cut function approximates the value of every minimum cut separating any subset of terminals from the remaining terminals . We refer to this graph as a cut-sparsifier, and we prove that there are cut-sparsifiers that can approximate all these minimum cuts in to within an approximation factor that depends only polylogarithmically on , the number of terminals. We prove such cut-sparsifiers exist through a zero-sum game, and we construct such sparsifiers through oblivious routing guarantees. These results allow us to derive a more general theory of Steiner cut and flow problems, and allow us to obtain approximation algorithms with guarantees independent of the size of the graph for a number of graph partitioning, graph layout, and multicommodity flow problems for which such guarantees were previously unknown.Hertz Foundation (Fellowship)Hertz Foundation (Fellowship