Abstract
We consider scheduling problems over scenarios where the goal is to find a single assignment of the jobs to the machines which performs well over all possible scenarios. Each scenario is a subset of jobs that must be executed in that scenario and all scenarios are given explicitly. The two objectives that we consider are minimizing the maximum makespan over all scenarios and minimizing the sum of the makespans of all scenarios. For both versions, we give several approximation algorithms and lower bounds on their approximability. With this research into optimization problems over scenarios, we have opened a new and rich field of interesting problems.
This work was partially supported by EU-IRSES grant EUSACOU and Tinbergen Institute. EF was partially supported by projects PRH PICT 2009-119 and UBACYT 20020090100149. AvZ was partially supported by Suzann Wilson Matthews summer research award.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., Protasi, M.: Complexity and approximation: Combinatorial optimization problems and their approximability properties. Springer (1999)
Austrin, P., Guruswami, V., Håstad, J.: (2 + ε)-SAT is NP-hard. Electronic Colloquium on Computational Complexity, TR13-159 (2013)
Ben-Tal, A., Nemirovski, A.: Robust optimization–methodology and applications. Mathematical Programming 92(3), 453–480 (2002)
Bouyahia, Z., Bellalouna, M., Ghedira, K.: Load balancing a priori strategy for the probabilistic weighted flowtime problem. Comput. Ind. Eng. 64(1), 1–10 (2013)
Bouyahia, Z., Bellalouna, M., Jaillet, P., Ghedira, K.: A priori parallel machines scheduling. Comput. Ind. Eng. 58(3), 488–500 (2010), Supply, Production and Distribution Systems
Chekuri, C., Khanna, S.: On multidimensional packing problems. SIAM Journal on Computing 33(4), 837–851 (2004)
Epstein, L., Levin, A., Marchetti-Spaccamela, A., Megow, N., Mestre, J., Skutella, M., Stougie, L.: Universal sequencing on an unreliable machine. SIAM Journal on Computing 41, 565–586 (2012)
Feuerstein, E., Marchetti-Spaccamela, A., Schalekamp, F., Sitters, R., van der Ster, S., Stougie, L., van Zuylen, A.: Scheduling over scenarios on two machines. CoRR, abs/1404.4766 (2014)
Garey, M.R., Johnson, D.S.: Computers and Intractability; A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1990)
Goemans, M.X., Williamson, D.P.: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. ACM 42(6), 1115–1145 (1995)
Gupta, A., Pál, M., Ravi, R., Sinha, A.: Sampling and cost-sharing: Approximation algorithms for stochastic optimization problems. SIAM Journal on Computing 40(5), 1361–1401 (2011)
Håstad, J.: Some optimal inapproximability results. J. ACM 48(4), 798–859 (2001)
Jaillet, P.: A priori solution of a traveling salesman problem in which a random subset of the customers are visited. Oper. Res. 36(6), 929–936 (1988)
Karloff, H.J., Zwick, U.: A 7/8-approximation algorithm for MAX 3SAT? In: FOCS, pp. 406–415. IEEE Computer Society (1997)
Khot, S.: On the power of unique 2-prover 1-round games. In: Proceedings of 34th Annual ACM Symposium on Theory of Computing, pp. 767–775 (2002)
Khot, S., Kindler, G., Mossel, E., O’Donnell, R.: Optimal inapproximability results for MAX-CUT and other 2-variable CSPs? SIAM J. Comput. 37(1), 319–357 (2007)
Zhang, J., Ye, Y., Han, Q.: Improved approximations for max set splitting and max NAE SAT. Discrete Applied Mathematics 142(1-3), 133–149 (2004)
Zwick, U.: Outward rotations: A tool for rounding solutions of semidefinite programming relaxations, with applications to MAX CUT and other problems. In: STOC, pp. 679–687 (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Feuerstein, E. et al. (2014). Scheduling over Scenarios on Two Machines. In: Cai, Z., Zelikovsky, A., Bourgeois, A. (eds) Computing and Combinatorics. COCOON 2014. Lecture Notes in Computer Science, vol 8591. Springer, Cham. https://doi.org/10.1007/978-3-319-08783-2_48
Download citation
DOI: https://doi.org/10.1007/978-3-319-08783-2_48
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08782-5
Online ISBN: 978-3-319-08783-2
eBook Packages: Computer ScienceComputer Science (R0)