SEA 2013: Experimental Algorithms pp 1-3 | Cite as

Algorithms and Linear Programming Relaxations for Scheduling Unrelated Parallel Machines

  • Martin Skutella
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7933)

Abstract

Since the early days of combinatorial optimization, algorithms and techniques from the closely related area of mathematical programming have played a pivotal role in solving combinatorial optimization problems. This holds both for ‘easy’ problems that can be solved efficiently in polynomial time, such as, e. g., the weighted matching problem [3], as well as for NP-hard problems whose solution might take exponential time in the worst case, such as, e. g., the traveling salesperson problem [1].

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Applegate, D.L., Bixby, R.E., Chvátal, V., Cook, W.J.: The Traveling Salesman Problem: A Computational Study. Princeton University Press (2006) Google Scholar
  2. 2.
    Dyer, M.E., Wolsey, L.A.: Formulating the single machine sequencing problem with release dates as a mixed integer program. Discrete Applied Mathematics 26, 255–270 (1990)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Edmonds, J.: Maximum matching and a polyhedron with 0,1-vertices. Journal of Research National Bureau of Standards Section B 69, 125–130 (1965)MathSciNetMATHGoogle Scholar
  4. 4.
    Goemans, M.X., Queyranne, M., Schulz, A.S., Skutella, M., Wang, Y.: Single machine scheduling with release dates. SIAM Journal on Discrete Mathematics 15, 165–192 (2002)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and approximation in deterministic sequencing and scheduling: A survey. Annals of Discrete Mathematics 5, 287–326 (1979)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Hall, L.A., Schulz, A.S., Shmoys, D.B., Wein, J.: Scheduling to minimize average completion time: Off-line and on-line approximation algorithms. Mathematics of Operations Research 22, 513–544 (1997)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Megow, N., Uetz, M., Vredeveld, T.: Models and algorithms for stochastic online scheduling. Mathematics of Operations Research 31(3), 513–525 (2006)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Möhring, R.H., Schulz, A.S., Uetz, M.: Approximation in stochastic scheduling: The power of LP-based priority policies. Journal of the ACM 46, 924–942 (1999)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Potts, C.N.: An algorithm for the single machine sequencing problem with precedence constraints. Mathematical Programming Studies 13, 78–87 (1980)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Queyranne, M.: Structure of a simple scheduling polyhedron. Mathematical Programming 58, 263–285 (1993)MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Schulz, A.S.: Stochastic online scheduling revisited. In: Yang, B., Du, D.-Z., Wang, C.A. (eds.) COCOA 2008. LNCS, vol. 5165, pp. 448–457. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Schulz, A.S., Skutella, M.: The power of α-points in preemptive single machine scheduling. Journal of Scheduling 5, 121–133 (2002)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Schulz, A.S., Skutella, M.: Scheduling unrelated machines by randomized rounding. SIAM Journal on Discrete Mathematics 15, 450–469 (2002)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Skutella, M.: Approximation and randomization in scheduling. PhD thesis, Technische Universität Berlin, Germany (1998)Google Scholar
  15. 15.
    Skutella, M.: Convex quadratic and semidefinite programming relaxations in scheduling. Journal of the ACM 48, 206–242 (2001)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Skutella, M., Sviridenko, M., Uetz, M.: Stochastic scheduling on unrelated machines (in preparation, 2013)Google Scholar
  17. 17.
    Skutella, M., Uetz, M.: Stochastic machine scheduling with precedence constraints. SIAM Journal on Computing 34, 788–802 (2005)MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Sviridenko, M., Wiese, A.: Approximating the configuration-LP for minimizing weighted sum of completion times on unrelated machines. In: Goemans, M., Correa, J. (eds.) IPCO 2013. LNCS, vol. 7801, pp. 387–398. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  19. 19.
    Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms. Cambridge University Press (2011)Google Scholar
  20. 20.
    Wolsey, L.A.: Mixed integer programming formulations for production planning and scheduling problems. Invited talk at the 12th International Symposium on Mathematical Programming. MIT, Cambridge (1985)Google Scholar
  21. 21.
    Wolsey, L.A.: Integer Programming. Wiley (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Martin Skutella
    • 1
  1. 1.Fakultät II – Mathematik und Naturwissenschaften, Institut für Mathematik, Sekr. MA 5-2Technische Universität BerlinBerlinGermany

Personalised recommendations