Illya V. Hicks


Branchwidth (and related) Papers

  1. 1.A Branch-Decomposition Algorithm for the p-Median Problem, with C. Fast

  2. 2.A Branch-and-Price-and-Cut Method for Computing an Optimal Bramble, with S. Sonuc and J.C. Smith, Discrete Optimization 18, 2015, 168-188 (preprint pdf)

  3. 3.  The Cunningham-Geelen Method in Practice:  Branch-decompositions and Integer Programming, with S. Margulies and J. Ma, INFORMS Journal on Computing 25(4), 2013, 599-610 pdf

  4. 4.  Branch Decomposition Heuristics for Linear Matroids, with J. Ma, S. Margulies, and E. Goins, Discrete Optimization 10(2), 2013, 102-119 pdf correction

  5. 5.  A Combinatorial Optimization Algorithm  for Solving the Branchwidth Problem, with E. Ulusal, and J. C. Smith, Computational Optimization and Applications 51(3), 2012, 1211-1229 pdf

  6. 6. The Branchwidth of Graphs and their Cycle Matroids, with N. McMurray, Journal of Combinatorial Theory Series B 97(5), 2007, 681-692 pdf

  7. 7. Graphs, Branchwidth, and Tangles! Oh My!, Networks 45(2), 2005, 55-60 pdf

  8. 8. Planar Branch Decompositions I: The Ratcatcher , INFORMS Journal on Computing 17(4), 2005, 402-412 pdf

  9. 9. Planar Branch Decompositions II: The Cycle Method , INFORMS Journal on Computing 17(4), 2005, 413-421 pdf

  10. 10. Branch Decompositions and Minor Containment , Networks 43(1), 2004, 1-9 ps Errantum

  11. 11.Branchwidth Heuristics, Congressus Numerantium 159, 2002, 31-50 ps pdf

Clique Generalization Papers

  1. 12.A Branch-and-Cut Method for Bilevel Interdiction on Cliques and Clique Relaxations, with T. Becker and J.C. Smith

  2. 13.On the k-Core Polytope, with C. Wood

  3. 14.The Maximum Co-2-plex Problem for {Bull, Claw}-free Graphs, with C. Wood

  4. 15.The Minimal k-Core Problem for Modeling k-assemblies, with C. Wood, Journal of Mathematical Neuroscience 5(14, 2015, 1-19

  5. 16.On the 2-club Polytope, with F. Pajouh and B. Balasundarm, Operations Research (to appear)

  6. 17. Combinatorial Branch-and-Bound for the Maximum Weight Independent Set Problem, with J. Warren (working paper) pdf

  7. 18. Co-2-plex Vertex Partitions, with B. McClosky and J. Arellano, Journal of Combinatorial Optimization 30(3), 2015, 729-746

  8. 19.  Combinatorial Algorithms for the Maximum k-plex Problem, with B. McClosky, Journal of Combinatorial Optimization 23(1), 2012, 29-49 pdf

  9. 20.   Clique Relaxations in Social Network Analysis: The Maximum k-plex Problem, with B. Balasundaram and S. Butenko, Operations Research 59(1), 2011, 133-142 pdf

  10. 21.  Co-2-plex Polynomials, with B. McClosky and A. Simms, Journal of Combinatorial Optimization 22(4), 2011, 640-650 pdf

  11. 22. The Co-2-plex Polytope and Integral Systems, with B. McClosky, SIAM Journal on Discrete Mathematics 23(3), 2009, 1135-1148 pdf

  12. 23. Composition of Stable Set Polyhedra, with B. McClosky, Operations Research Letters 36, 2008, 615-617 pdf

  13. 24.A Branch-and-Price Approach for the Maximum Weight Independent Set Problem, with J. Warren, D. Warrier, and W. Wilhelm, Networks 46(14), 2005, 198-209 pdf

Other Combinatorial Optimization Papers

  1. 25.Finding Optimal Hitting Sets for Random Walks on Networks, with D. Mikesell, F. Kenter, and F. Hunt

  2. 26.A Reduction of the Logspace Shortest Path Problem to Biconnected Graphs, with B. Brimkov

  3. 27.Memory Efficient Shortest Path Algorithms for Cactus Graphs, with B. Brimkov, Discrete Applied Mathematics (to appear)

  4. 28.Chromatic and Flow Polynomials of Generalized Vertex Join Graphs and Outerplanar Graphs, with B. Brimkov, Discrete Applied Mathematics (to appear)

  5. 29.An Algebraic Exploration of Dominating Sets and Vizing’s Conjecture, with S. Margulies, Electronic Journal of Combinatorics 19(2), 2012, P1 pdf

  6. 30. A Note on Total and Paired Domination of Cartesian Product Graphs, K. Choudhary and S. Margulies, Electronic Journal of Combinatorics 20(3), P25 pdf

  7. 31. A Note on Integer Domination of Cartesian Product Graphs, K. Choudhary and S. Margulies, Discrete Mathematics 338(7), 2015, 1239-1242 pdf

  8. 32.New Facets for the Planar Subgraph Polytope, Networks 51(2), 2008, 120-132 pdf

  9. 33. On Greedy Construction Heuristics for MAX CUT problem, with S. Kahruman, E. Kolotoğlu*, and S. Butenko, International Journal on Computational Science and Engineering 3(3), 2007, 211-218

  10. 34. Restricted b -factors in Bipartite Graphs and t- designs, with I. Arambula, Journal of Combinatorial Design 14(3), 2006, 169-182 pdf

Systems Engineering Papers

  1. 35. Degree of Redundancy of Linear Systems using Implicit Set Covering, with J. Arellano, IEEE Transactions on Automation Science and Engineering 99, 2013, 1-7 pdf

  2. 36.Scheduling the Adjuvant Endocrine Therapy for Early Stage Breast Cancer, with K. Diehl, S. Kahruman, E. Kolotoglu, and S. Butenko, Annals of Operations Research 196(1), 2012, 683-705 pdf

  3. 37. Service Restoration in Naval Shipboard Power Systems, with K. L. Butler- Purry and N. D. R. Sarma , IEE Proceedings Generation, Transmission and Distribution 151(1), 2004, 95-102 pdf

  4. 38. Optimization Procedures for Simultaneous Road Rehabilitation and Bridge Replacement Decisions in Highway Networks , with A. Garcia-Diaz and M. Bonyuet , Engineering Optimization 34(5), 2002, 445-459


 1) Branch and Tree Decomposition Techniques for Discrete Optimization, with A. M. C. A. Koster and E. Kolotoglu, Tutorials in Operations Research: INFORMS--New Orleans 2005, J. Cole Smith (ed), INFORMS, Hanover, MD pdf Errantum

2) Branchwidth and Branch Decompositions, Encyclopedia of Optimization, C. Floudas and P. Pardalos (eds.), Springer, New York, 2009

3) Branch-width and Tangles, with S. Oum, Wiley Encyclopedia of OR/MS, J. Cochran et al. (eds.), Wiley, New York, 2011

4) Graph and Network Theory:  Basic Concepts and Applications, with A. Garcia-Diaz, Wiley Encyclopedia of OR/MS, J. Cochran et al. (eds.), Wiley, New York, 2011

Research Projects

  1. 1)     A New Decomposition Approach for a Class of NP-hard Graph Problems , with W. E. Wilhelm, NSF DMI-0217265, $175K, 9/1/2002 -- 8/31/2005, ($24K REU)

  2. 2)   SGER: Branch Decomposition Techniques for Independence Systems, NSF DMI-0521209, $80K, 8/1/2005 -- 7/31/2006

  3. 3)    Innovative Techniques for Constructing Branch Decompositions, NSF DMS-0729251, $185K, 9/1/2006 -- 8/31/2009

  4. 4)     Branch Decomposition Techniques for Submodular Optimization, NSF CMMI-0926618, $250K, 8/1/2009 -- 7/31/2013

  5. 5)     SHF: Medium: Collaborative Research:  Marrying Program Analysis and Numerical Search, NSF CCF-1162076, with S. Chaudhuri, $600K, 9/1/2012 -- 8/31/2016

  6. 6)    Innovative Techniques to Optimally Distribute and Package Healthcare Services for Rural and Remote Areas, NSF CMMMI-1300477, $250K, 6/1/2013 --- 5/31/2016

  7. 7)    Collaborative Research:  Risk-Averse Cluster Detection in Network Models of Bigdata Under Measurement Uncertainty, NSF CMMMI-1404864, with B. Balasundaram (OK-State), $170K, 4/15/2014 -- 3/31/2017

  8. 8)    Techniques to Interdict and Monitor Cohesiveness in Dark Networks, NSF CMMI-1634550, $300K, 9/01/16 -- 8/31/19

Education and Outreach Projects

  1. 1)     Travel Support for Minority Students to Attend INFORMS Annual Meeting; October 24-27, 2004; Denver, CO NSF DMI-0440785, $4.75K, 9/1/2004 -- 8/31/ 2005

  2. 2)     Pathways to the Doctorate Research Assistantship Award 2005 , Texas A&M University, $25K, 9/1/2005 -- 8/31/2007

  3. 3)     Travel Support for Minority Students to Attend INFORMS Annual Meeting; November 13-16, 2005; New Orleans, LA, NSF DMI-0537840, $5K, 9/1/2005 -- 8/31/2006

  4. 4)    GAAN: Fellowships for Research in Industrial and Systems Engineering, with G.-A. Klutke and S. Cetinkaya, DoEd, Texas A&M, $380K, 9/1/2006 -- 8/31/2009

  5. 5)     BPC-DP:  Academic Mentoring Workshops for Underrepresented Participants, with V. Taylor (Texas A&M) and B. York (Portland St.), NSF CNS-0634272, Texas A&M, $388K,  3/1/2007 -- 2/28/2010

  6. 6)    Travel Support for Minority Students to Attend INFORMS Annual Meetings, NSF CMMI-0739996, $19K, 8/1/2007 -- 7/31/2011

  7. 7)    Travel Support for Minority Students Attending INFORMS Annual Meeetings, NSF CMMI-1130507, $18.9K, 7/20/2011 -- 7/19/2014

  8. 8)    Travel Support for Minority Students Attending INFORMS Annual Meeting, NSF CMMI-1536904, $18.9K, 9/1/2015 -- 8/31/2018



Name: Illya V. Hicks

Status: Married

Hometown: Waco, TX


Occupation: Professor

School: Computational and Applied Mathematics Department, Rice University

Location: Houston, TX


Computational and Applied Mathematics Department

Rice University

6100 Main St. - MS 134

Houston, TX 77005-1892

(office) 713-348-5667

(fax) 713-348-5318

Email me


My research interests are in combinatorial optimization, integer programming, graph theory and matroid theory. Some applications of interest are social networks, cancer treatment and network design. My current research is focused on using graph decomposition techniques to solve NP-complete problems. I teach courses related to discrete optimization.