标题：Unbalanced Graph Partitioning
作者：Li, Angsheng; Zhang, Peng
作者机构：[Zhang, Peng] Shandong Univ, Sch Comp Sci, Jinan 250101, Peoples R China.; [Li, Angsheng] Chinese Acad Sci, Inst Software, State Key Lab Comp Sci, B 更多
会议名称：21st Annual International Symposium on Algorithms and Computations (ISAAC)
会议日期：DEC 15-17, 2010
来源：ALGORITHMS AND COMPUTATION, PT I
摘要：We investigate the unbalanced cut problems. A cut (A, B) is called unbalanced if the size of its smaller side is at most k (called k-size) or exactly k (called Ek-size), where k is an input parameter. An s-t cut (A, B) is called unbalanced if its s-side is of k-size or Ek-size. We consider three types of unbalanced cut problems, in which the quality of a cut is measured with respect to the capacity, the sparsity, and the conductance, respectively.; We show that even if the input graph is restricted to be a tree, the Ek-Sparsest Cut problem (to find an Ek-size cut with the minimum sparsity) is still NP-hard. We give a bicriteria approximation algorithm for the k-Sparsest Cut problem (to find a k-size cut with the minimum sparsity), which outputs a cut whose sparsity is at most O(log n) times the optimum and whose smaller side has size at most O(log n)k. As a consequence, this leads to a (O(log n), O(log n))-approximation algorithm for the Min k-Conductance problem (to find a k-size cut with the minimum conductance). We also prove that the Min k-Size s-t Cut problem is NP-hard and give an O(log n)-approximation algorithm for it.