In this paper a branch-and-cut algorithm, based on a formulation previously introduced by us, is proposed for the Graph Coloring Problem. Since colors are indistinguishable in graph coloring, there may typically exist...
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In this paper a branch-and-cut algorithm, based on a formulation previously introduced by us, is proposed for the Graph Coloring Problem. Since colors are indistinguishable in graph coloring, there may typically exist many different symmetrical colorings associated with a same number of colors. If solutions to an integer programming model of the problem exhibit that property, the branch-and-cut method tends to behave poorly even for small size graph coloring instances. Our model avoids, to certain extent, that bottleneck. Computational experience indicates that the results we obtain improve, in most cases, on those given by the well-known exact solution graph coloring algorithm Dsatur. (c) 2005 Elsevier B.V. All rights reserved.
The group Steiner tree problem consists of, given a graph G, a collection M of subsets of V (G) and a cost c(e) for each edge of G, finding a minimum-cost subtree that connects at least one vertex from each R is an el...
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The group Steiner tree problem consists of, given a graph G, a collection M of subsets of V (G) and a cost c(e) for each edge of G, finding a minimum-cost subtree that connects at least one vertex from each R is an element of R. It is a generalization of the well-known Steiner tree problem that arises naturally in the design of VLSI chips. In this paper, we study a polyhedron associated with this problem and some extended formulations. We give facet defining inequalities and explore the relationship between the group Steiner tree problem and other combinatorial optimization problems. (c) 2006 Elsevier B.V. All rights reserved.
Cell suppression is a widely used technique for protecting sensitive information in statistical data presented in tabular form. Previous works on the subject mainly concentrate on 2- and 3-dimensional tables whose ent...
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Cell suppression is a widely used technique for protecting sensitive information in statistical data presented in tabular form. Previous works on the subject mainly concentrate on 2- and 3-dimensional tables whose entries are subject to marginal totals. In this paper we address the problem of protecting sensitive data in a statistical table whose entries are linked by a generic system of linear constraints. This very general setting covers, among others, k-dimensional tables with marginals as well as the so-called hierarchical and linked tables that are very often used nowadays for disseminating statistical data. In particular, we address the optimization problem known in the literature as the (secondary) Cell Suppression Problem, in which the information loss due to suppression has to be minimized. We introduce a new integer linear programming model and outline an enumerative algorithm for its exact solution. The algorithm can also be used as a heuristic procedure to find near-optimal solutions. Extensive computational results on a test-bed of 1,160 real-world and randomly generated instances are presented, showing the effectiveness of the approach. In particular, we were able to solve to proven optimality 4-dimensional tables with marginals as well as linked tables of reasonable size (to our knowledge, tables of this kind were never solved optimally by previous authors).
branch and bound (BB) is the primary deterministic approach that has been applied successfully to solve mixed-integer nonlinear programming (MINLPs) problems in which the participating functions are nonconvex. Recentl...
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branch and bound (BB) is the primary deterministic approach that has been applied successfully to solve mixed-integer nonlinear programming (MINLPs) problems in which the participating functions are nonconvex. Recently, a decomposition algorithm was proposed to solve nonconvex MINLPs. In this work, a generalized branch and cut (GBC) algorithm is proposed and it is shown that both decomposition and BE algorithms are specific instances of the GBC algorithm with a certain set of heuristics. This provides a unified framework for comparing BE and decomposition algorithms. Finally, a set of heuristics which may be potentially more efficient computationally compared to all currently available deterministic algorithms is presented. (C) 2000 Elsevier Science Ltd. All rights reserved.
branch and bound (BB) is the primary deterministic approach that has been applied successfully to solve mixed-integer nonlinear programming (MINLPs) problems in which the participating functions are nonconvex. Recentl...
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branch and bound (BB) is the primary deterministic approach that has been applied successfully to solve mixed-integer nonlinear programming (MINLPs) problems in which the participating functions are nonconvex. Recently, a decomposition algorithm was proposed to solve nonconvex MINLPs. In this work, a generalized branch and cut (GBC) algorithm is proposed and it is shown that both decomposition and BE algorithms are specific instances of the GBC algorithm with a certain set of heuristics. This provides a unified framework for comparing BE and decomposition algorithms. Finally, a set of heuristics which may be potentially more efficient computationally compared to all currently available deterministic algorithms is presented. (C) 2000 Elsevier Science Ltd. All rights reserved.
Several branch-and-bound algorithms for the exact solution of the asymmetric traveling salesman problem (ATSP), based on the assignment problem (AP) relaxation, have been proposed in the literature. These algorithms p...
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Several branch-and-bound algorithms for the exact solution of the asymmetric traveling salesman problem (ATSP), based on the assignment problem (AP) relaxation, have been proposed in the literature. These algorithms perform very well for some instances (e.g., those with uniformly random integer costs), but very poorly for others. The aim of this paper is to evaluate the effectiveness of a branch-and-cut algorithm exploiting ATSP-specific facet-defining cuts, to be used to attack hard instances that cannot be solved by the AP-based procedures from the literature. We present new separation algorithms for some classes of facet-defining cuts, and a new variable-pricing technique for dealing with highly degenerate primal LP problems. A branch-and-cut algorithm based on these new results is designed and evaluated through computational analysis on several classes of both random and real-world instances. The outcome of the research is that, on hard instances, the branch-and-cut algorithm clearly outperforms the best AP-based algorithms from the literature.
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