2026-09-20T00:59:40Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/101009 2023-07-11 col_2142_5131 col_2142_10761 com_2142_5130 com_2142_10755 com_2142_234

Chandrasekaran, Karthekeyan Chekuri, Chandra Erickson, Jeff Király, Tamás Xu, Chao 2018-09-04T20:27:15Z 2018-09-04T20:27:15Z 2018-04-19 2018-05 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. Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-08-31 without embargo terms The student, Chao Xu, accepted the attached license on 2018-04-17 at 18:47. The student, Chao Xu, submitted this Dissertation for approval on 2018-04-17 at 19:10. This Dissertation was approved for publication on 2018-04-19 at 08:14. DSpace SAF Submission Ingestion Package generated from Vireo submission #12329 on 2018-08-31 at 17:13:28 Made available in DSpace on 2018-09-04T20:27:15Z (GMT). No. of bitstreams: 3 XU-DISSERTATION-2018.pdf: 1907636 bytes, checksum: 12735f8b0ae3dc3b174ff410dbc89f3f (MD5) LICENSE.txt: 4204 bytes, checksum: d21d95b24fed7b6cfa859e9dc0bc41cf (MD5) PROQUEST_LICENSE.txt: 4550 bytes, checksum: 172b33248e3ba90bd46f3d083efa6fc5 (MD5) Previous issue date: 2018-04-19 application/pdf http://hdl.handle.net/2142/101009 en Copyright 2018 Chao Xu hypergraph cuts Cuts and connectivity in graphs and hypergraphs text text Computer Science Computer Science University of Illinois at Urbana-Champaign Dissertation Ph.D.