Experiments with a Network Design Algorithm Using -approximate Linear Programs

We describe an upper-bound algorithm for multicommodity network design problems that relies on new results for approximately solving certain linear programs, and on the greedy heuristic for set-covering problems.

[1]  K. Onaga,et al.  On feasibility conditions of multicommodity flows in networks , 1971 .

[2]  Vasek Chvátal,et al.  A Greedy Heuristic for the Set-Covering Problem , 1979, Math. Oper. Res..

[3]  Martin E. Dyer,et al.  Linear Time Algorithms for Two- and Three-Variable Linear Programs , 1984, SIAM J. Comput..

[4]  Farhad Shahrokhi,et al.  On solving large maximum concurrent flow problems , 1987, CSC '87.

[5]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988 .

[6]  Thomas L. Magnanti,et al.  A Dual-Ascent Procedure for Large-Scale Uncapacitated Network Design , 1989, Oper. Res..

[7]  Prakash Mirchandani,et al.  Modeling and Solving the Capacitated Network Loading Problem , 1991 .

[8]  Philip N. Klein,et al.  Approximating Concurrent Flow with Unit Demands and Capacities: An Implementation , 1991, Network Flows And Matching.

[9]  Clifford Stein,et al.  Implementation of a Combinatorial Multicommodity Flow Algorithm , 1991, Network Flows And Matching.

[10]  Laurence A. Wolsey,et al.  Network Design with Divisible Capacities: Aggregated Flow and Knapsack Subproblems , 1992, IPCO.

[11]  Thomas L. Magnanti,et al.  The convex hull of two core capacitated network design problems , 1993, Math. Program..

[12]  M. Stoer,et al.  A polyhedral approach to multicommodity survivable network design , 1994 .

[13]  Jonathan Eckstein,et al.  Parallel Branch-and-Bound Algorithms for General Mixed Integer Programming on the CM-5 , 1994, SIAM J. Optim..

[14]  Leonid Khachiyan,et al.  Fast Approximation Schemes for Convex Programs with Many Blocks and Coupling Constraints , 1994, SIAM J. Optim..

[15]  Leonid Khachiyan,et al.  An exponential-function reduction method for block-angular convex programs , 1995, Networks.

[16]  Thomas L. Magnanti,et al.  Modeling and Solving the Two-Facility Capacitated Network Loading Problem , 1995, Oper. Res..

[17]  David R. Karger,et al.  Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity flows , 1995, STOC '95.

[18]  Fillia Makedon,et al.  Fast Approximation Algorithms for Multicommodity Flow Problems , 1995, J. Comput. Syst. Sci..

[19]  Éva Tardos,et al.  Fast Approximation Algorithms for Fractional Packing and Covering Problems , 1995, Math. Oper. Res..

[20]  Daniel Bienstock,et al.  Computational study of a family of mixed-integer quadratic programming problems , 1995, Math. Program..

[21]  Oktay Günlük,et al.  Capacitated Network Design - Polyhedral Structure and Computation , 1996, INFORMS J. Comput..

[22]  Daniel Bienstock,et al.  Development and implementation of heuristic algorithms for multicommodity flow problems , 1996 .

[23]  Francisco Barahona,et al.  Network Design Using Cut Inequalities , 1996, SIAM J. Optim..

[24]  Andrew V. Goldberg,et al.  An Implementation of a Combinatorial Approximation Algorithm for Minimum-Cost Multicommodity Flow , 1998, IPCO.

[25]  Antonio Sassano,et al.  A Lagrangian-based heuristic for large-scale set covering problems , 1998, Math. Program..

[26]  Oktay Günlük,et al.  Minimum cost capacity installation for multicommodity network flows , 1998, Math. Program..

[27]  L. A. Wolseyz.  Designing Private Line Networks , 1999 .

[28]  Prakash Mirchandani.  Projections of the capacitated network loading problem , 2000, Eur. J. Oper. Res..