Skip to main content

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 53))

  • 584 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C. Albrecht, Provably good global routing by a new approximation algorithm for multicommodity flow. In Proceedings of the International Conference on Physical Design (ISPD), San Diego, CA, (2000), 19–25.

    Google Scholar 

  2. D. Alevras, M. Grötschel and R Wessäly, Cost-efficient network synthesis from leased lines, Annals of Operations Research 76 (1998), 1–20.

    Article  MATH  Google Scholar 

  3. F. Barahona, Network design using cut inequalities, SIAM J. Opt. 6 (1996), 823–837.

    MathSciNet  MATH  Google Scholar 

  4. F. Barahona and R. Anbil, The Volume Algorithm: producing primal solutions with a subgradient method, Mathematical Programming 87(200), 385–399.

    Google Scholar 

  5. D. Bienstock, Experiments with a network design algorithm using ε-approximate linear programs (1996).

    Google Scholar 

  6. D. Bienstock, S. Chopra, O. Günlük and C. Tsai (1996), Minimum Cost Capacity Installation for Multicommodity Network Flows, Math. Programming 81 (1998), 177–199.

    MathSciNet  Google Scholar 

  7. D. Bienstock, G. Muratore, Strong inequalities for capacitated survivable network design problems, Math. Programming 89 (2000), 127–147.

    MathSciNet  MATH  Google Scholar 

  8. D. Bienstock, O. Raskina, Asymptotic analysis of the flow deviation method for the maximum concurrent flow problem (2000), to appear, Math. Programming.

    Google Scholar 

  9. R. Bixby, personal communication.

    Google Scholar 

  10. V. Chvatal, A greedy heuristic for the set-covering problem, Math. of Operations Research 4 (1979), 233–235.

    MathSciNet  MATH  Google Scholar 

  11. R. Cominetti and J.-P. Dussault, A stable exponential penalty algorithm with superlinear convergence, J. Optimization Theory and Applications 83:2 (1994).

    MathSciNet  Google Scholar 

  12. R. Cominetti and J. San Martín, Asymptotic analysis of the exponential penalty trajectory in linear programming, Mathematical Programming 67 (1994), 169–187.

    Article  MathSciNet  Google Scholar 

  13. R. Courant, Variational methods for the solution of problems of equilibrium and vibration, Bull. Amer. Math. Soc. 49 (1943), 1–43.

    Article  MathSciNet  MATH  Google Scholar 

  14. S.C. Dafermos and F.T. Sparrow, The traffic assignment problem for a general network, Journal of Research of the National Bureau of Standards-B, 73B (1969).

    Google Scholar 

  15. R. Daniel, personal communication.

    Google Scholar 

  16. G.B. Danzig and P. Wolfe, The decomposition algorithm for linear programming, Econometrica 29 (1961), 767–778.

    MathSciNet  Google Scholar 

  17. A.V. Fiacco and G.P. McCormick, Nonlinear Programming: Sequential Unconstrained Optimization Techniques, Wiley, New York (1968).

    Google Scholar 

  18. W. Feller, An introduction to probability theory and its applications, Wiley, New York (1966).

    MATH  Google Scholar 

  19. A. Frangioni and G. Gallo, A Bundle Type Dual-Ascent Approach to Linear Multicommodity Min Cost Flow Problems, INFORMS JOC 11 (1999) 370–393.

    MathSciNet  MATH  Google Scholar 

  20. J.-L. Goffin, J. Gondzio, R. Sarkissian and J.-P. Vial, Solving nonlinear multicommodity flow problems by the analytic center cutting plane method, Mathematical Programming 76 (1996) 131–154.

    MathSciNet  Google Scholar 

  21. ILOG CPLEX, Incline Village, NV.

    Google Scholar 

  22. L.K. Fleischer, Aproximating Fractional Multicommodity Flow Independent of the Number of Commodities, SIAM J. Disc. Math., 13 (2000), 505–520.

    MathSciNet  MATH  Google Scholar 

  23. M. Frank and P. Wolfe, An algorithm for quadratic programming, Naval Res. Logistics Quarterly 3 (1956), 149–154.

    MathSciNet  MATH  Google Scholar 

  24. N. Garg and J. Könemann, Faster and simpler algorithms for multicommodity flow and other fractional packing problems, Proc. 39th Ann. Symp. on Foundations of Comp. Sci. (1998) 300–309.

    Google Scholar 

  25. L. Fratta, M. Gerla and L. Kleinrock, The flow deviation method: an approach to store-and-forward communication network design, Networks 3 (1971), 97–133.

    MathSciNet  Google Scholar 

  26. A. Goldberg, J. Oldham, S. Plotkin and C. Stein, An Implementation of a Combinatorial Approximation Algorithm for Minimum Multicommodity Flow, IPCO 1988, R.E. Bixby, E.A. Boyd, R.Z. Rios-Mercado, eds., Lecture Notes in Computer Science 1412, Springer, Berlin, 338–352.

    Google Scholar 

  27. M.D. Grigoriadis and L.G. Khachiyan (1991), Fast approximation schemes for convex programs with many blocks and couping constraints, SIAM Journal on Optimization 4 (1994) 86–107.

    Article  MathSciNet  MATH  Google Scholar 

  28. M.D. Grigoriadis and L.G. Khachiyan, An exponential-function reduction method for block-angular convex programs, Networks 26 (1995) 59–68.

    MathSciNet  MATH  Google Scholar 

  29. M.D. Grigoriadis and L.G. Khachiyan, Approximate minimum-cost multicommodity flows in Õ(ε −2 KNM)time, Mathematical Programming 75 (1996), 477–482.

    Article  MathSciNet  Google Scholar 

  30. M.D. Grigoriadis and L.G. Khachiyan, Coordination complexity of parallel price-directive decomposition, Math. Oper. Res. 21 (1996) 321–340.

    MathSciNet  MATH  Google Scholar 

  31. G.H. Golub and C.F. Van Loan, Matrix Computations, The Johns Hopkins University Press, Baltimore and London (1996).

    MATH  Google Scholar 

  32. G. Karakostas, Faster Approximation Schemes for Fractional Multicommodity Flow Problems, Proc. 13th Ann. Symp. on Discrete Algorithms (2002).

    Google Scholar 

  33. P. Klein, S. Plotkin, C. Stein and E. Tardos, Faster approximation algorithms for the unit capacity concurrent flow problem with applications to routing and finding sparse cuts, Proc. 22nd Ann. ACM Symp. on Theory of Computing (1990), 310–321.

    Google Scholar 

  34. P. Klein and N. Young, On the number of iterations for Dantzig-Wolfe optimization and packing-covering approximation algorithms, Proceedings IPCO 1999, 320–327.

    Google Scholar 

  35. T. Leighton, F. Makedon, S. Plotkin, C. Stein, E. Tardos and S. Tragoudas, Fast approximation algorithms for multicommodity flow problems, Proc. 23nd Ann. ACM Symp. on Theory of Computing (1991), 101–111.

    Google Scholar 

  36. T. Leighton and S. Rao, An approximate max-flow min-cut theorem for uniform multicommodity flow problems with applications to approximation algorithms, Proc. FOCS 29 (1988), 422–431.

    Google Scholar 

  37. T. Leong, P. Shor and C. Stein, Implementation of a Combinatorial Multicommodity Flow Algorithm, DIMACS Series in Discrete mathematics and Theoretical Computer Science 12 (1993), 387–405.

    Google Scholar 

  38. C. Lemarechal, A. Nemirovskii and Y. Nesterov, New variants of bundle methods, Math. Programming 69 (1995), 111–148.

    MathSciNet  Google Scholar 

  39. N. Linial, E. London and Y. Rabinovich, The geometry of graphs and some of its algorithmic applications, Proc. FOCS 35 (1994), 577–591.

    Google Scholar 

  40. L. Lovász, On the ratio of optimal integral and fractional covers, Discrete Mathematics 13 (1975), 383–390.

    MathSciNet  MATH  Google Scholar 

  41. M. Luby and N. Nisan, A parallel approximation algorithm for positive linear programming, Proc. 24th Ann. ACM Symp. on Theory of Computing (1993), 448–457.

    Google Scholar 

  42. D. Luenberger, Introduction to Linear and Nonlinear Programming, Addison-Wesley, Menlo Park (1973).

    MATH  Google Scholar 

  43. T. Magnanti, P. Mirchandani and R. Vachani, Modeling and solving the capacitated network loading problem, Working Paper OR 239-91, MIT (1991).

    Google Scholar 

  44. T. Magnanti and Y. Wang, Polyhedral Properties of the Network Restoration Problem-with the Convex Hull of a Special Case (1997), to appear, Math. Programming.

    Google Scholar 

  45. K. Onaga and O.. Kokusho, On feasibility conditions of multicommodity flows in networks, IEEE Transactions on Circuit Theory, 18 (1971), 425–429.

    Article  Google Scholar 

  46. J.B. Orlin, A faster strongly polynomial minimum cost flow algorithm, Operations Research 41 (1993), 338–350.

    MathSciNet  MATH  Google Scholar 

  47. S. Plotkin and D. Karger, Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity flows, In Proceedings of the 27th Annual ACM Symposium on Theory of Computing, (1995), 18–25.

    Google Scholar 

  48. S. Plotkin, D.B. Shmoys and E. Tardos, Fast approximation algorithms for fractional packing and covering problems, Math. of Oper. Res. 20 (1995) 495–504. Extended abstract: Proc. 32nd Annual IEEE Symp. On Foundations of Computer Science, (1991), 495–504.

    MathSciNet  Google Scholar 

  49. T. Radzik, Fast deterministic approximation for the multicommodity flow problem, Proc. 6th ACM-SIAM Symp. on Discrete Algorithms (1995).

    Google Scholar 

  50. O. Raskina, Ph. D. Dissertation, Dept. of IEOR, Columbia University (2001).

    Google Scholar 

  51. R. Schneur, Scaling algorithms for multicommodity flow problems and network flow problems with side constraints, Ph.D. Thesis, MIT (1991).

    Google Scholar 

  52. A. Schrijver, Theory of Linear and Integer Programming, Wiley (1986).

    Google Scholar 

  53. F. Shahrokhi and D.W. Matula, The maximum concurrent flow problem, Journal of the ACM 37 (1991), 318–334.

    MathSciNet  Google Scholar 

  54. M. Stoer and G. Dahl, A polyhedral approach to multicommodity survivable network design, Numerische Mathematik 68 (1994), 149–167.

    Article  MathSciNet  MATH  Google Scholar 

  55. P.M. Vaidya, An algorithm for linear programming which requires O((((m + n)n 2 + (m + n)1.5 n)L) arithmetic operations, Math. Programming 47, 175–201.

    Google Scholar 

  56. L. Wolsey, An analysis of the greedy algorithm for the submodular set covering problem, Combinatorica 2 (1982), 385–393.

    MathSciNet  MATH  Google Scholar 

  57. S. Wright, Primal-Dual interior point methods, Siam (1997).

    Google Scholar 

  58. N. Young, Randomized rounding without solving the linear program, in Proc. 6th ACM-SIAM Symp. on Discrete Algorithms (1995), 170–178.

    Google Scholar 

  59. N. Young, Sequential and parallel algorithms for mixed packing and covering, to appear, Proc. 42nd Annual IEEE Symp. On Foundations of Computer Science(2001).

    Google Scholar 

Download references

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Kluwer Academic Publishers

About this chapter

Cite this chapter

(2002). Computational Experiments Using the Exponential Potential Function Framework. In: Potential Function Methods for Approximately Solving Linear Programming Problems. International Series in Operations Research & Management Science, vol 53. Springer, Boston, MA. https://doi.org/10.1007/0-306-47626-6_4

Download citation

  • DOI: https://doi.org/10.1007/0-306-47626-6_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4020-7173-7

  • Online ISBN: 978-0-306-47626-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics