Cuts and connectivity in graphs and hypergraphs

hypergraph;cuts

Xu, Chao

关键词: hypergraph;    cuts;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/101009/XU-DISSERTATION-2018.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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.