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Optimal Coordination Mechanisms for Multi-job Scheduling Games

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Algorithms - ESA 2014 (ESA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8737))

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Abstract

We consider the unrelated machine scheduling game in which players control subsets of jobs. Each player’s objective is to minimize the weighted sum of completion time of her jobs, while the social cost is the sum of players’ costs. The goal is to design simple processing policies in the machines with small coordination ratio, i.e., the implied equilibria are within a small factor of the optimal schedule. We work with a weaker equilibrium concept that includes that of Nash. We first prove that if machines order jobs according to their processing time to weight ratio, a.k.a. Smith-rule, then the coordination ratio is at most 4, moreover this is best possible among nonpreemptive policies. Then we establish our main result. We design a preemptive policy, externality, that extends Smith-rule by adding extra delays on the jobs accounting for the negative externality they impose on other players. For this policy we prove that the coordination ratio is 1 + φ ≈ 2.618, and complement this result by proving that this ratio is best possible even if we allow for randomization or full information. Finally, we establish that this externality policy induces a potential game and that an ε-equilibrium can be found in polynomial time. An interesting consequence of our results is that an ε −local optima of R| | ∑ w j C j for the jump (a.k.a. move) neighborhood can be found in polynomial time and are within a factor of 2.618 of the optimal solution. The latter constitutes the first direct application of purely game-theoretic ideas to the analysis of a well studied local search heuristic.

Research partially supported by the Millenium Nucleus Information and Coordination in Networks ICM/FIC P10-024F.

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References

  1. Abed, F., Huang, C.-C.: Preemptive coordination mechanisms for unrelated machines. In: Epstein, L., Ferragina, P. (eds.) ESA 2012. LNCS, vol. 7501, pp. 12–23. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  2. Azar, Y., Jain, K., Mirrokni, V.S. (Almost) Optimal coordination mechanisms for unrelated machine scheduling. In: SODA (2008)

    Google Scholar 

  3. Bhattacharyay, S., Imz, S., Kulkarnix, J., Munagala, K.: Coordination mechanisms from (almost) all scheduling policies. In: ITCS (2014)

    Google Scholar 

  4. Brueggemann, T., Hurink, J.L., Kern, W.: Quality of move-optimal schedules for minimizing total weighted completion time. Oper. Res. Lett. 34(5), 583–590 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bruno, J., Coffman, E.G., Sethi, R.: Scheduling independent tasks to reduce mean finishing time. Commun. ACM 17, 382–387 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  6. Caragiannis, I.: Efficient coordination mechanisms for unrelated machine scheduling. In: SODA (2009)

    Google Scholar 

  7. Chen, B., Potts, C.N., Woeginger, G.J.: A review of machine scheduling: Complexity, algorithms and approximability. In: Handbook of Combinatorial Optimization, vol. 3, Kluwer Academic Publishers (1998)

    Google Scholar 

  8. Caragiannis, I., Flammini, M., Kaklamanis, C., Kanellopoulos, P., Moscardelli, L.: Tight bounds for selfish and greedy load balancing. Algorithmica 61(3), 606–637 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  9. Christodoulou, G., Koutsoupias, E., Nanavati, A.: Coordination mechanisms. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 345–357. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  10. Cohen, J., Dürr, C., Thang, N.K.: Smooth inequalities and equilibrium inefficiency in scheduling games. In: Goldberg, P.W. (ed.) WINE 2012. LNCS, vol. 7695, pp. 350–363. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  11. Cole, R., Correa, J.R., Gkatzelis, V., Mirrokni, V.S., Olver Inner, N.: product spaces for MinSum coordination mechanisms. In: STOC (2011)

    Google Scholar 

  12. Cole, R., Correa, J.R., Gkatzelis, V., Mirrokni, V., Olver, N.: Decentralized utilitarian mechanisms for scheduling games. In: Game. Econ. Behav. (to appear)

    Google Scholar 

  13. Correa, J.R., Queyranne, M.: Efficiency of equilibria in restricted uniform machine scheduling with total weighted completion time as social cost. Naval Res. Logist. 59, 384–395 (2012)

    Article  MathSciNet  Google Scholar 

  14. Czumaj, A., Vöcking, B.: Tight bounds for worst-case equilibria. ACM T. Algo. 3 (2007)

    Google Scholar 

  15. Davis, E., Jaffe, J.M.: Algorithms for scheduling tasks on unrelated processors. J. ACM 28(4), 721–736 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  16. Dürr, C., Nguyen, K.T.: Non-clairvoyant scheduling games. In: Mavronicolas, M., Papadopoulou, V.G. (eds.) SAGT 2009. LNCS, vol. 5814, pp. 135–146. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  17. Farzad, B., Olver, N., Vetta, A.: A priority-based model of routing. Chic. J. Theor. Comput. (2008)

    Google Scholar 

  18. Finn, G., Horowitz, E.: A linear time approximation algorithm for multiprocessor scheduling. BIT 19, 312–320 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  19. Fleischer, L., Svitkina, Z.: Preference-constrained oriented matching. In: ANALCO (2010)

    Google Scholar 

  20. Heydenreich, B., Müller, R., Uetz, M.: Mechanism Design for Decentralized Online Machine Scheduling. Oper. Res. 58(2), 445–457 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  21. Hoogeveen, H., Schuurman, P., Woeginger, G.J.: Non-approximability results for scheduling problems with minsum criteria. In: Bixby, R.E., Boyd, E.A., Ríos-Mercado, R.Z. (eds.) IPCO 1998. LNCS, vol. 1412, p. 353. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  22. Hoeksma, R., Uetz, M.: The Price of Anarchy for Minsum Related Machine Scheduling. In: Solis-Oba, R., Persiano, G. (eds.) WAOA 2011. LNCS, vol. 7164, pp. 261–273. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  23. Horn, W.A.: Minimizing average flow time with parallel machines. Oper. Res. 21(3), 846–847 (1973)

    Article  MATH  Google Scholar 

  24. Ibarra, O.H., Kim, C.E.: Heuristic algorithms for scheduling independent tasks on nonidentical processors. J. ACM 24(2), 280–289 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  25. Immorlica, N., Li, L., Mirrokni, V.S., Schulz, A.S.: Coordination mechanisms for selfish scheduling. Theor. Comput. Sci. 410(17), 1589–1598 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  26. Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, p. 404. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  27. Lu, P., Yu, C.: Worst-Case Nash Equilibria in Restricted Routing. In: Papadimitriou, C., Zhang, S. (eds.) WINE 2008. LNCS, vol. 5385, pp. 231–238. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  28. Nash, J.: Equilibrium points in N-person games. PNAS 36, 48–49 (1950)

    Article  MATH  MathSciNet  Google Scholar 

  29. Potts, C.N., Strusevich, V.: Fifty years of scheduling: a survey of milestones. J Oper. Res. Society 60(1), 41–68 (2009)

    Article  Google Scholar 

  30. Rahn, M., Schäfer, G.: Bounding the inefficiency of altruism through social contribution games (2013) (manuscript )

    Google Scholar 

  31. Roughgarden, T.: Intrinsic robustness of the price of anarchy. In: STOC (2009)

    Google Scholar 

  32. Sahni, S., Cho, Y.: Bounds for list schedules on uniform processors. SIAM J. Comput. 9, 91–103 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  33. Schulz, A.S., Skutella, M.: Scheduling unrelated machines by randomized rounding. SIAM J. Discrete Math. 15(4), 450–469 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  34. Schuurman, P., Vredeveld, T.: Performance guarantees of local search for multiprocessor scheduling. In: Aardal, K., Gerards, B. (eds.) IPCO 2001. LNCS, vol. 2081, p. 370. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  35. Sethuraman, J., Squillante, M.S.: Optimal scheduling of multiclass parallel machines. In: SODA (1999)

    Google Scholar 

  36. Skutella, M.: Convex quadratic and semidefinite programming relaxations in scheduling. J. ACM 48(2), 206–242 (2001)

    Article  MathSciNet  Google Scholar 

  37. Skutella, M., Woeginger, G.J.: A ptas for minimizing the total weighted completion time on identical parallel machines. Math. Oper. Res. 25(1), 63–75 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  38. Smith, W.: Various optimizers for single stage production. Naval Res. Logist. Quart. 3(1-2), 59–66 (1956)

    Article  MathSciNet  Google Scholar 

  39. Vredeveld, T., Hurkens, C.: Experimental comparison of approximation algorithms for scheduling unrelated parallel machines. INFORMS J. Comput. 14, 175–189 (2002)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Germany

    Fidaa Abed

  2. Departamento de Ingenieria Industrial, Universidad de Chile, Chile

    José R. Correa

  3. Chalmers University of Technology, Sweden

    Chien-Chung Huang

Authors
  1. Fidaa Abed
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  2. José R. Correa
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  3. Chien-Chung Huang
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Editors and Affiliations

  1. Massachusetts Institute of Technology, Cambridge, MA, USA

    Andreas S. Schulz

  2. Karlsruhe Institute of Technology (KIT), Kaiserstruhe 12, 76131, Karlsruhe, Germany

    Dorothea Wagner

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Abed, F., Correa, J.R., Huang, CC. (2014). Optimal Coordination Mechanisms for Multi-job Scheduling Games. In: Schulz, A.S., Wagner, D. (eds) Algorithms - ESA 2014. ESA 2014. Lecture Notes in Computer Science, vol 8737. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44777-2_2

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  • DOI: https://doi.org/10.1007/978-3-662-44777-2_2

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