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Approximation Algorithms for Scheduling and Packing Problems

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Book cover Approximation and Online Algorithms (WAOA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7164))

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Abstract

In this paper we present an overview about new approximation results for several optimization problems. During the last years we have worked on the design of approximation algorithms with a smaller approximation ratio and on the design of efficient polynomial time approximation schemes with a faster running time. We presented approximation algorithms with a smaller ratio for scheduling with fixed jobs and for two dimensional strip packing. On the other hand, we developed efficient approximation schemes with an improved running time for multiple knapsack and scheduling independent jobs on uniform processors.

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References

  1. Alon, N., Azar, Y., Woeginger, G.J., Yadid, T.: Approximation schemes for scheduling on parallel machines. Journal on Scheduling 1, 55–66 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bazgan, C.: Schémas d’approximation et complexité paramétrée. Technical Report, Université Paris-Sud (1995)

    Google Scholar 

  3. Caprara, A., Kellerer, H., Pferschy, U.: The multiple subset sum problem. SIAM Journal of Optimization 11, 308–319 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  4. Cesati, M., Trevisan, L.: On the efficiency of polynomial time approximation schemes. Information Processing Letters 64, 165–171 (1997)

    Article  MathSciNet  Google Scholar 

  5. Chekuri, C., Khanna, S.: A PTAS for the multiple knapsack problem. SIAM Journal on Computing 35, 713–728 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chen, B.: Tighter bounds for MULTIFIT scheduling on uniform processors. Discrete Applied Mathematics 31, 227–260 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  7. Coffman, E.G., Garey, M.R., Johnson, D.S.: An application of bin packing to multiprocessor scheduling. SIAM Journal on Computing 7, 1–17 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  8. Coffman, E.G., Garey, M.R., Johnson, D.S., Tarjan, R.E.: Performance Bounds for Level-Oriented Two-Dimensional Packing Algorithms. SIAM Journal on Computing 4, 808–826 (1980)

    Article  MathSciNet  Google Scholar 

  9. Diedrich, F., Jansen, K.: Improved approximation algorithms for scheduling with fixed jobs. In: Proceedings of Symposium on Discrete Algorithms, SODA, pp. 675–684 (2009)

    Google Scholar 

  10. Epstein, L., Sgall, J.: Approximation schemes for scheduling on uniformly related and identical parallel machines. Algorithmica 39, 43–57 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  11. Fellows, M.R.: Blow-Ups, Win/Win’s, and Crown Rules: Some New Directions in FPT. In: Bodlaender, H.L. (ed.) WG 2003. LNCS, vol. 2880, pp. 1–12. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  12. Friesen, D.K., Langston, M.A.: Bounds for multifit scheduling on uniform processors. SIAM Journal on Computing 12, 60–70 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  13. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-completeness. W.H. Freeman, San Francisco (1979)

    MATH  Google Scholar 

  14. Gonzales, T., Ibarra, O.H., Sahni, S.: Bounds for LPT schedules on uniform processors. SIAM Journal on Computing 6, 155–166 (1977)

    Article  MathSciNet  Google Scholar 

  15. Harren, R., Jansen, K., Prädel, L., van Stee, R.: A (5/3 + ε)-Approximation for Strip Packing. In: Dehne, F., Iacono, J., Sack, J.-R. (eds.) WADS 2011. LNCS, vol. 6844, pp. 475–487. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  16. Harren, R., van Stee, R.: Improved Absolute Approximation Ratios for Two-Dimensional Packing Problems. In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds.) APPROX 2009. LNCS, vol. 5687, pp. 177–189. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  17. Hochbaum, D.S.: Various notions of approximations: good, better, best, and more. In: Hochbaum, D.S. (ed.) Approximation Algorithms for NP-Hard Problems, Ch. 9, pp. 346–398. Prentice Hall (1997)

    Google Scholar 

  18. Hochbaum, D.S., Shmoys, D.B.: Using dual approximation algorithms for scheduling problems: practical and theoretical results. Journal of the ACM 34, 144–162 (1987)

    Article  MathSciNet  Google Scholar 

  19. Hochbaum, D.S., Shmoys, D.B.: A polynomial approximation scheme for scheduling on uniform processors: using the dual approximation approach. SIAM Journal on Computing 17, 539–551 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  20. Horowitz, R., Sahni, S.: Exact and approximate algorithms for scheduling non-identical processors. Journal of the ACM 23, 317–327 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  21. Hwang, H.-C., Lee, K., Chang, S.Y.: The effect of machine availability on the worst-case performance of LPT. Discrete Applied Mathematics 148, 49–61 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  22. Jansen, K.: Parameterized approximation scheme for the multiple knapsack problem. SIAM Journal on Computing 39, 1392–1412 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  23. Jansen, K.: An EPTAS for scheduling jobs on uniform processors: using an MILP relaxation with a constant number of integral variables. SIAM Journal on Discrete Mathematics 24, 457–485 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  24. Jansen, K.: A fast approximation scheme for the multiple knapsack problem. In: Proceedings of Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2012 (to appear, 2012)

    Google Scholar 

  25. Jansen, K., Prädel, L., Schwarz, U.M., Svensson, O.: Faster approximation algorithms for scheduling with fixed jobs. In: Proceedings of Conference of Computing: the Australasian Theory Symposium, CATS 2011, pp. 3–9 (2011)

    Google Scholar 

  26. Jansen, K., Robenek, C.: Scheduling Jobs on Identical and Uniform Processors Revisited. In: Solis-Oba, R., Persiano, G. (eds.) WAOA 2011. LNCS, vol. 7164, pp. 109–122. Springer, Heidelberg (2012)

    Google Scholar 

  27. Jansen, K., Thöle, R.: Approximation algorithms for scheduling parallel jobs. SIAM Journal on Computing 39, 3571–3615 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  28. Kellerer, H., Pferschy, U., Pisinger, D.: Knapsack Problems. Springer, Berlin (2004)

    MATH  Google Scholar 

  29. Lenstra, H.W.: Integer programming with a fixed number of variables. Mathematics of Operations Research 8, 538–548 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  30. Leung, J.: Bin packing with restricted piece sizes. Information Processing Letters 31, 145–149 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  31. Marx, D.: Parameterized complexity and approximation algorithms. The Computer Journal 51, 60–78 (2008)

    Article  Google Scholar 

  32. Megow, N., Möhring, R.H., Schulz, J.: Decision Support and Optimization in Shutdown and Turnaround Scheduling. Informs Journal on Computing 23, 189–204 (2011)

    Article  MathSciNet  Google Scholar 

  33. Scharbrodt, M., Steger, A., Weisser, H.: Approximability of scheduling with fixed jobs. Journal of Scheduling 2, 267–284 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  34. Scharbrodt, M.: Produktionsplanung in der Prozessindustrie: Modelle, effiziente Algorithmen und Umsetzung, Dissertation, Fakultät für Informatik, Technische Universität München (2000)

    Google Scholar 

  35. Scheithauer, G., Terno, J.: Theoretical investigations on the modified integer round-up property for the one-dimensional cutting stock problem. European Journal of Operational Research 20, 93–100 (1997)

    MathSciNet  MATH  Google Scholar 

  36. Schiermeyer, I.: Reverse-Fit: A 2-Optimal Algorithm for Packing Rectangles. In: van Leeuwen, J. (ed.) ESA 1994. LNCS, vol. 855, pp. 290–299. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  37. Sleator, D.D.: A 2.5 times optimal algorithm for packing in two dimensions. Information Processing Letters 10, 37–40 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  38. Steinberg, A.: A Strip-Packing Algorithm with Absolute Performance Bound 2. SIAM Journal on Computing 2, 401–409 (1997)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Institut für Informatik, Christian-Albrechts-Universität zu Kiel, 24098, Kiel, Germany

    Klaus Jansen

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  1. Klaus Jansen
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Editors and Affiliations

  1. Department of Computer Science, The University of Western Ontario, N6A 5B7, London, ON, Canada

    Roberto Solis-Oba

  2. Dipartimento di Informatica "Renato M. Capocelli", Università di Salerno, Via Ponte Don Melillo, 84081, Fisciano, SA, Italy

    Giuseppe Persiano

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Jansen, K. (2012). Approximation Algorithms for Scheduling and Packing Problems. In: Solis-Oba, R., Persiano, G. (eds) Approximation and Online Algorithms. WAOA 2011. Lecture Notes in Computer Science, vol 7164. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29116-6_1

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  • DOI: https://doi.org/10.1007/978-3-642-29116-6_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29115-9

  • Online ISBN: 978-3-642-29116-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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