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101
Fast Approximation Algorithms for Fractional Packing and Covering Problems
, 1995
"... This paper presents fast algorithms that find approximate solutions for a general class of problems, which we call fractional packing and covering problems. The only previously known algorithms for solving these problems are based on general linear programming techniques. The techniques developed ..."
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Cited by 232 (14 self)
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This paper presents fast algorithms that find approximate solutions for a general class of problems, which we call fractional packing and covering problems. The only previously known algorithms for solving these problems are based on general linear programming techniques. The techniques developed in this paper greatly outperform the general methods in many applications, and are extensions of a method previously applied to find approximate solutions to multicommodity flow problems. Our algorithm is a Lagrangean relaxation technique; an important aspect of our results is that we obtain a theoretical analysis of the running time of a Lagrangean relaxationbased algorithm. We give several applications of our algorithms. The new approach yields several orders of magnitude of improvement over the best previously known running times for algorithms for the scheduling of unrelated parallel machines in both the preemptive and the nonpreemptive models, for the job shop problem, for th...
Branchandprice: Column generation for solving huge integer programs
 Oper. Res
, 1998
"... We discuss formulations of integer programs with a huge number of variables and their solution by column generation methods, i.e., implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branchandbound tree. We present classes of models for which th ..."
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Cited by 211 (9 self)
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We discuss formulations of integer programs with a huge number of variables and their solution by column generation methods, i.e., implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branchandbound tree. We present classes of models for which this approach decomposes the problem, provides tighter LP relaxations, and eliminates symmetry. Wethen discuss computational issues and implementation of column generation, branchandbound algorithms, including special branching rules and e cient ways to solve the LP relaxation. We also discuss the relationship with Lagrangian duality. 1
An effective implementation of the linkernighan traveling salesman heuristic
 European Journal of Operational Research
, 2000
"... This report describes an implementation of the LinKernighan heuristic, one of the most successful methods for generating optimal or nearoptimal solutions for the symmetric traveling salesman problem. Computational tests show that the implementation is highly effective. It has found optimal solution ..."
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Cited by 120 (1 self)
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This report describes an implementation of the LinKernighan heuristic, one of the most successful methods for generating optimal or nearoptimal solutions for the symmetric traveling salesman problem. Computational tests show that the implementation is highly effective. It has found optimal solutions for all solved problem instances we have been able to obtain, including a 7397city problem (the largest nontrivial problem instance solved to optimality today). Furthermore, the algorithm has improved the best known solutions for a series of largescale problems with unknown optima, among these an 85900city problem. 1.
A Theoretician's Guide to the Experimental Analysis of Algorithms
, 1996
"... This paper presents an informal discussion of issues that arise when one attempts to analyze algorithms experimentally. It is based on lessons learned by the author over the course of more than a decade of experimentation, survey paper writing, refereeing, and lively discussions with other experimen ..."
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Cited by 76 (0 self)
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This paper presents an informal discussion of issues that arise when one attempts to analyze algorithms experimentally. It is based on lessons learned by the author over the course of more than a decade of experimentation, survey paper writing, refereeing, and lively discussions with other experimentalists. Although written from the perspective of a theoretical computer scientist, it is intended to be of use to researchers from all fields who want to study algorithms experimentally. It has two goals: first, to provide a useful guide to new experimentalists about how such work can best be performed and written up, and second, to challenge current researchers to think about whether their own work might be improved from a scientific point of view. With the latter purpose in mind, the author hopes that at least a few of his recommendations will be considered controversial.
Approximation Algorithms for Asymmetric TSP by Decomposing Directed Regular Multigraphs
 Proc. 44th Annual Symposium on Foundations of Computer Science (FOCS
, 2003
"... A directed multigraph is said to be dregular if the indegree and outdegree of every vertex is exactly d. By Hall’s theorem one can represent such a multigraph as a combination of at most n2 cycle covers each taken with an appropriate multiplicity. We prove that if the dregular multigraph does not ..."
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Cited by 51 (1 self)
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A directed multigraph is said to be dregular if the indegree and outdegree of every vertex is exactly d. By Hall’s theorem one can represent such a multigraph as a combination of at most n2 cycle covers each taken with an appropriate multiplicity. We prove that if the dregular multigraph does not contain more than ⌊d/2 ⌋ copies of any 2cycle then we can find a similar decomposition into n2 pairs of cycle covers where each 2cycle occurs in at most one component of each pair. Our proof is constructive and gives a polynomial algorithm to find such a decomposition. Since our applications only need one such a pair of cycle covers whose weight is at least the average weight of all pairs, we also give an alternative, simpler algorithm to extract a single such pair. This combinatorial theorem then comes handy in rounding a fractional solution of an LP relaxation of the maximum Traveling Salesman Problem (TSP) problem. The first stage of the rounding procedure obtains 2cycle covers that do not share a 2cycle with weight at least twice the weight of the optimal solution. Then we show how to extract a tour from the 2 cycle covers, whose weight is at least 2/3 of the weight of the longest tour. This improves upon the previous
Convex Nondifferentiable Optimization: A Survey Focussed On The Analytic Center Cutting Plane Method.
, 1999
"... We present a survey of nondifferentiable optimization problems and methods with special focus on the analytic center cutting plane method. We propose a selfcontained convergence analysis, that uses the formalism of the theory of selfconcordant functions, but for the main results, we give direct pr ..."
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Cited by 51 (2 self)
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We present a survey of nondifferentiable optimization problems and methods with special focus on the analytic center cutting plane method. We propose a selfcontained convergence analysis, that uses the formalism of the theory of selfconcordant functions, but for the main results, we give direct proofs based on the properties of the logarithmic function. We also provide an in depth analysis of two extensions that are very relevant to practical problems: the case of multiple cuts and the case of deep cuts. We further examine extensions to problems including feasible sets partially described by an explicit barrier function, and to the case of nonlinear cuts. Finally, we review several implementation issues and discuss some applications.
Chained LinKernighan for large traveling salesman problems
, 2000
"... We discuss several issues that arise in the implementation of Martin, Otto, and Felten's Chained LinKernighan heuristic for largescale traveling salesman problems. Computational results are presented for TSPLIB instances ranging in size from 11,849 cities up to 85,900 cities; for each of these ..."
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Cited by 47 (1 self)
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We discuss several issues that arise in the implementation of Martin, Otto, and Felten's Chained LinKernighan heuristic for largescale traveling salesman problems. Computational results are presented for TSPLIB instances ranging in size from 11,849 cities up to 85,900 cities; for each of these instances, solutions within 1% of the optimal value can be found in under 1 CPU minute on a 300 Mhz Pentium II workstation, and solutions within 0.5% of optimal can be found in under 10 CPU minutes. We also demonstrate the scalability of the heuristic, presenting results for randomly generated Euclidean instances having up to 25,000,000 cities. For the largest of these random instances, a tour within 1% of an estimate of the optimal value can be obtained in under 1 CPU day on a 64bit IBM RS6000 workstation.
A Matter of Degree: Improved Approximation Algorithms for DegreeBounded Minimum Spanning Trees
 SIAM JOURNAL ON COMPUTING
, 2000
"... ..."
Survivable networks, linear programming relaxations and the parsimonious property
, 1993
"... We consider the survivable network design problem the problem of designing, at minimum cost, a network with edgeconnectivity requirements. As special cases, this problem encompasses the Steiner tree problem, the traveling salesman problem and the kedgeconnected network design problem. We establ ..."
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Cited by 44 (12 self)
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We consider the survivable network design problem the problem of designing, at minimum cost, a network with edgeconnectivity requirements. As special cases, this problem encompasses the Steiner tree problem, the traveling salesman problem and the kedgeconnected network design problem. We establish a property, referred to as the parsimonious property, of the linear programming (LP) relaxation of a classical formulation for the problem. The parsimonious property has numerous consequences. For example, we derive various structural properties of these LP relaxations, we present some algorithmic improvements and we perform tight worstcase analyses of two heuristics for the survivable network design problem.
Relaxed Tours and Path Ejections for the Traveling Salesman Problem
, 1996
"... We describe an edge based ejection chain method to generate compound neighborhood structures for the Traveling Salesman Problem. These neighborhood structures enclose a special substructure which is not necessarily a Hamiltonian tour. Instead the neighborhood components are linked together to compos ..."
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Cited by 38 (9 self)
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We describe an edge based ejection chain method to generate compound neighborhood structures for the Traveling Salesman Problem. These neighborhood structures enclose a special substructure which is not necessarily a Hamiltonian tour. Instead the neighborhood components are linked together to compose successive levels of an ejection chain, and coordinated by a suitable reference structure to generate compound moves with outstanding proprieties. More precisely, such a substructure can be viewed as a relaxed tour, which allows solution transformations to be obtained without preserving the Hamiltonian property at each step. Furthermore, in the ejection chain process, the generation of substructures produces a variety of alternating paths for the selection of subsequent ejection moves as well as for the choice of the corresponding trial moves. Finally, we propose two algorithmic variants  a Preliminary and a Full Subpath Ejection Chain Method  based on this type of compound neighborhood...