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Title:Cuts and connectivity in graphs and hypergraphs
Author(s):Xu, Chao
Director of Research:Chandrasekaran, Karthekeyan
Doctoral Committee Chair(s):Chekuri, Chandra
Doctoral Committee Member(s):Erickson, Jeff; Király, Tamás
Department / Program:Computer Science
Discipline:Computer Science
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):hypergraph
cuts
Abstract:In this thesis, we consider cut and connectivity problems on graphs, digraphs, hypergraphs and hedgegraphs. The main results are the following: - We introduce a faster algorithm for finding the reduced graph in element-connectivity computations. We also show its application to node separation. - We present several results on hypergraph cuts, including (a) a near linear time algorithm for finding a (2+epsilon)-approximate min-cut, (b) an algorithm to find a representation of all min-cuts in the same time as finding a single min-cut, (c) a sparse subgraph that preserves connectivity for hypergraphs and (d) a near linear-time hypergraph cut sparsifier. - We design the first randomized polynomial time algorithm for the hypergraph k-cut problem whose complexity has been open for over 20 years. The algorithm generalizes to hedgegraphs with constant span. - We address the complexity gap between global vs. fixed-terminal cuts problems in digraphs by presenting a 2-1/448 approximation algorithm for the global bicut problem.
Issue Date:2018-04-19
Type:Text
URI:http://hdl.handle.net/2142/101009
Rights Information:Copyright 2018 Chao Xu
Date Available in IDEALS:2018-09-04
Date Deposited:2018-05


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