Optimizing over the cut cone: A new polyhedral algorithm for the maximum-weight cut problem

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dc.contributor.advisorBixby, Robert E.en_US
dc.creatorSaigal, Sanjayen_US
dc.date.accessioned2009-06-03T23:59:15Zen_US
dc.date.available2009-06-03T23:59:15Zen_US
dc.date.issued1991en_US
dc.description.abstractPolyhedral cutting-plane algorithms for hard combinatorial problems have scored notable successes. However, computational research on the Maximum-Weight Cut Problem (MCP) on undirected graphs has been inconclusive. In 1988, Barahona suggested a new polyhedral algorithm that, given a good initial solution, attempts to prove optimality. If the initial cut is non-optimal, it is iteratively improved until optimal. The expected advantages are three-fold. If a good, fast heuristic is used, an optimal solution may be available. The algorithm can then prove optimality fast. Secondly, if time is a serious constraint, prematurely terminating the algorithm yields a cut at least as good as the original. Finally, since the algorithm nominally optimizes over the cut cone rather than the cut polytope, the underlying separation problem is very simple. This research explores Barahona's algorithm on a class of MCP instances arising in statistical mechanics. The graphs are toroidal grids, together with an additional universal vertex. By considering different integer programming formulations, it has been possible to design a fast algorithm that replaces optimization over the cut polytope by repeated optimization over the intersection of the cut cone and the unit cube. This latter polyhedron is shown to be equivalent to the multicut polytope, and its basic facet classes are identified. The final algorithm is successful in solving MCP instances over 70 x 70 grids, over 5 times bigger than previous algorithms. Substantial improvements in computation time have also been achieved.en_US
dc.format.extent120 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoThesis Math. Sci. 1991 Saigalen_US
dc.identifier.citationSaigal, Sanjay. "Optimizing over the cut cone: A new polyhedral algorithm for the maximum-weight cut problem." (1991) Diss., Rice University. <a href="https://hdl.handle.net/1911/16481">https://hdl.handle.net/1911/16481</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/16481en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectOperations researchen_US
dc.subjectMathematicsen_US
dc.titleOptimizing over the cut cone: A new polyhedral algorithm for the maximum-weight cut problemen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematical Sciencesen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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