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].
Supported by the DFG Research Center Matheon “Mathematics for key technologies” in Berlin and by the DFG Focus Program 1307 within the project “Algorithm Engineering for Real-time Scheduling and Routing”.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Applegate, D.L., Bixby, R.E., Chvátal, V., Cook, W.J.: The Traveling Salesman Problem: A Computational Study. Princeton University Press (2006)
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)
Edmonds, J.: Maximum matching and a polyhedron with 0,1-vertices. Journal of Research National Bureau of Standards Section B 69, 125–130 (1965)
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)
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)
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)
Megow, N., Uetz, M., Vredeveld, T.: Models and algorithms for stochastic online scheduling. Mathematics of Operations Research 31(3), 513–525 (2006)
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)
Potts, C.N.: An algorithm for the single machine sequencing problem with precedence constraints. Mathematical Programming Studies 13, 78–87 (1980)
Queyranne, M.: Structure of a simple scheduling polyhedron. Mathematical Programming 58, 263–285 (1993)
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)
Schulz, A.S., Skutella, M.: The power of α-points in preemptive single machine scheduling. Journal of Scheduling 5, 121–133 (2002)
Schulz, A.S., Skutella, M.: Scheduling unrelated machines by randomized rounding. SIAM Journal on Discrete Mathematics 15, 450–469 (2002)
Skutella, M.: Approximation and randomization in scheduling. PhD thesis, Technische Universität Berlin, Germany (1998)
Skutella, M.: Convex quadratic and semidefinite programming relaxations in scheduling. Journal of the ACM 48, 206–242 (2001)
Skutella, M., Sviridenko, M., Uetz, M.: Stochastic scheduling on unrelated machines (in preparation, 2013)
Skutella, M., Uetz, M.: Stochastic machine scheduling with precedence constraints. SIAM Journal on Computing 34, 788–802 (2005)
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)
Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms. Cambridge University Press (2011)
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)
Wolsey, L.A.: Integer Programming. Wiley (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Skutella, M. (2013). Algorithms and Linear Programming Relaxations for Scheduling Unrelated Parallel Machines. In: Bonifaci, V., Demetrescu, C., Marchetti-Spaccamela, A. (eds) Experimental Algorithms. SEA 2013. Lecture Notes in Computer Science, vol 7933. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38527-8_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-38527-8_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38526-1
Online ISBN: 978-3-642-38527-8
eBook Packages: Computer ScienceComputer Science (R0)