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- Balabhaskar Balasundaram, Sergiy Butenko, Illya V. Hicks
- Operations Research
- 2011

This paper introduces and studies the maximum k-plex problem, which arises in social network analysis, but can also be used in several other important application areas, including wireless networks,â€¦ (More)

- Illya V. Hicks
- INFORMS Journal on Computing
- 2005

T is the second of two papers dealing with the relationship of branchwidth and planar graphs. Branchwidth and branch decompositions, introduced by Robertson and Seymour, have been shown to beâ€¦ (More)

- Illya V. Hicks
- INFORMS Journal on Computing
- 2005

T notion of branch decompositions and its related connectivity invariant for graphs, branchwidth, were introduced by Robertson and Seymour in their series of papers that proved Wagnerâ€™s conjecture.â€¦ (More)

Given a graph with non-negative edge weights, the MAXCUT problem is to partition the set of vertices into two subsets so that the sum of the weights of edges with endpoints in different subsets isâ€¦ (More)

- Benjamin McClosky, Illya V. Hicks
- J. Comb. Optim.
- 2012

The maximum clique problem provides a classic framework for detecting cohesive subgraphs. However, this approach can fail to detect much of the cohesive structure in a graph. To address this issue,â€¦ (More)

- Illya V. Hicks
- Networks
- 2005

Branch decomposition-based algorithms have been used in practical settings to solve some NP-hard problems like the travelling salesman problem (TSP) and general minor containment. The notions ofâ€¦ (More)

- Illya V. Hicks
- Networks
- 2004

Given a simple graph G, a simple connected graph H, and a branch decomposition of G of width k, we present a practical algorithm to test if H is a minor of G. The notion of branch decompositions andâ€¦ (More)

We describe three combinatorial branch-and-bound solvers for the maximum weight independent set problem. All use weighted clique covers to generate upper bounds, and all branch according to theâ€¦ (More)

- Benjamin McClosky, Illya V. Hicks
- SIAM J. Discrete Math.
- 2009

k-plexes are cohesive subgraphs which were introduced to relax the structure of cliques. A co-k-plex is the complement of a k-plex and is therefore similar to a stable set. This paper derives theâ€¦ (More)

- Susan Margulies, Jing Ma, Illya V. Hicks
- INFORMS Journal on Computing
- 2013

Branch-decompositions and Integer Programming S. Margulies Department of Computational and Applied Math, Rice University, Houston, Texas, {susan.margulies@rice.edu} J. Ma Department of Managementâ€¦ (More)