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General Techniques for Combinatorial Approximation

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  • Sartaj Sahni

    (University of Minnesota, Minneapolis, Minnesota)

Abstract

This is a tutorial on general techniques for combinatorial approximation. In addition to covering known techniques, a new one is presented. These techniques generate fully polynomial time approximation schemes for a large number of NP-complete problems. Some of the problems they apply to are: 0-1 knapsack, integer knapsack, job sequencing with deadlines, minimizing weighted mean flow times, and optimal SPT schedules. We also present experimental results for the job sequencing with deadlines problem.

Suggested Citation

  • Sartaj Sahni, 1977. "General Techniques for Combinatorial Approximation," Operations Research, INFORMS, vol. 25(6), pages 920-936, December.
    • Handle: RePEc:inm:oropre:v:25:y:1977:i:6:p:920-936
    DOI: 10.1287/opre.25.6.920
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    Cited by:

    1. Halman, Nir & Kellerer, Hans & Strusevich, Vitaly A., 2018. "Approximation schemes for non-separable non-linear boolean programming problems under nested knapsack constraints," European Journal of Operational Research, Elsevier, vol. 270(2), pages 435-447.
    2. Dolgui, Alexandre & Kovalev, Sergey & Pesch, Erwin, 2015. "Approximate solution of a profit maximization constrained virtual business planning problem," Omega, Elsevier, vol. 57(PB), pages 212-216.
    3. Safer, Hershel M. & Orlin, James B., 1953-, 1995. "Fast approximation schemes for multi-criteria flow, knapsack, and scheduling problems," Working papers 3757-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    4. Tzafestas, Spyros & Triantafyllakis, Alekos, 1993. "Deterministic scheduling in computing and manufacturing systems: a survey of models and algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(5), pages 397-434.
    5. Perrot, F., 1979. "Zero-temperature equation of state of metals in the statistical model with density gradient correction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 98(3), pages 555-565.
    6. Imed Kacem & Hans Kellerer & Yann Lanuel, 2015. "Approximation algorithms for maximizing the weighted number of early jobs on a single machine with non-availability intervals," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 403-412, October.
    7. Aissi, Hassene & Bazgan, Cristina & Vanderpooten, Daniel, 2007. "Approximation of min-max and min-max regret versions of some combinatorial optimization problems," European Journal of Operational Research, Elsevier, vol. 179(2), pages 281-290, June.
    8. Cheng, T. C. Edwin & Gordon, Valery S. & Kovalyov, Mikhail Y., 1996. "Single machine scheduling with batch deliveries," European Journal of Operational Research, Elsevier, vol. 94(2), pages 277-283, October.
    9. Tomášek, M. & Mikoláš, V., 1979. "Remarks on the density functional approach to the inhomogeneous electron gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 95(3), pages 547-560.
    10. Aissi, Hassene & Bazgan, Cristina & Vanderpooten, Daniel, 2009. "Min-max and min-max regret versions of combinatorial optimization problems: A survey," European Journal of Operational Research, Elsevier, vol. 197(2), pages 427-438, September.
    11. Evgeny Gurevsky & Dmitry Kopelevich & Sergey Kovalev & Mikhail Y. Kovalyov, 2023. "Integer knapsack problems with profit functions of the same value range," 4OR, Springer, vol. 21(3), pages 405-419, September.
    12. Wei Ding & Guoliang Xue, 2014. "Minimum diameter cost-constrained Steiner trees," Journal of Combinatorial Optimization, Springer, vol. 27(1), pages 32-48, January.
    13. Safer, Hershel M. & Orlin, James B., 1953-, 1995. "Fast approximation schemes for multi-criteria combinatorial optimization," Working papers 3756-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.

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