Director of Research (if dissertation) or Advisor (if thesis)
Doctoral Committee Chair(s)
Department of Study
Degree Granting Institution
University of Illinois at Urbana-Champaign
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.