Asynchronous Coordination Under Preferences and Constraints

  • Armando Castañeda
  • Pierre Fraigniaud
  • Eli Gafni
  • Sergio Rajsbaum
  • Matthieu Roy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9988)

Abstract

Adaptive renaming can be viewed as a coordination task involving a set of asynchronous agents, each aiming at grabbing a single resource out of a set of resources Similarly, musical chairs is also defined as a coordination task involving a set of asynchronous agents, each aiming at picking one of a set of available resources, where every agent comes with an a priori preference for some resource. We foresee instances in which some combinations of resources are allowed, while others are disallowed.

We model these constraints as an undirected graph whose nodes represent the resources, and an edge between two resources indicates that these two resources cannot be used simultaneously. In other words, the sets of resources that are allowed are those which form independent sets.

We assume that each agent comes with an a priori preference for some resource. If an agent’s preference is not in conflict with the preferences of the other agents, then this preference can be grabbed by the agent. Otherwise, the agents must coordinate to resolve their conflicts, and potentially choose non preferred resources. We investigate the following problem: given a graph, what is the maximum number of agents that can be accommodated subject to non-altruistic behaviors of early arriving agents?

Just for cyclic constraints, the problem is surprisingly difficult. Indeed, we show that, intriguingly, the natural algorithm inspired from optimal solutions to adaptive renaming or musical chairs is sub-optimal for cycles, but proven to be at most 1 to the optimal. The main message of this paper is that finding optimal solutions to the coordination with constraints and preferences task requires to design “dynamic” algorithms, that is, algorithms of a completely different nature than the “static” algorithms used for, e.g., renaming.

References

  1. 1.
    Afek, Y., Attiya, H., Dolev, D., Gafni, E., Merritt, M., Shavit, N.: Atomic snapshots of shared memory. J. ACM 40(4), 873–890 (1993)CrossRefMATHGoogle Scholar
  2. 2.
    Afek, Y., Babichenko, Y., Feige, U., Gafni, E., Linial, N., Sudakov, B.: Oblivious collaboration. In: Peleg, D. (ed.) DISC 2011. LNCS, vol. 6950, pp. 489–504. Springer, Heidelberg (2011). doi:10.1007/978-3-642-24100-0_45 CrossRefGoogle Scholar
  3. 3.
    Afek, Y., Babichenko, Y., Feige, U., Gafni, E., Linial, N., Sudakov, B.: Musical chairs. SIAM J. Discrete Math. 28(3), 1578–1600 (2014)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Attiya, H., Bar-Noy, A., Dolev, D., Peleg, D., Reischuk, R.: Renaming in an asynchronous environment. J. ACM 37(3), 524–548 (1990)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Attiya, H., Welch, J.: Distributed Computing Fundamentals, Simulations, and Advanced Topics, 2nd edn. Wiley, New York (2004)MATHGoogle Scholar
  6. 6.
    Baker, B.S., Coffman Jr., E.G.: Mutual exclusion scheduling. Theor. Comput. Sci. 162(2), 225–243 (1996)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Bodlaender, H.L., Jansen, K.: Restrictions of graph partition problems. Part I. Theor. Comput. Sci. 148(1), 93–109 (1995)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Borowsky, E., Gafni, E.: Generalized FLP impossibility result for \(t\)-resilient asynchronous computations. In: Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing, STOC 1993, pp. 91–100. ACM, New York (1993)Google Scholar
  9. 9.
    Borowsky, E., Gafni, E.: Immediate atomic snapshots and fast renaming. In: Proceedings of the Twelfth Annual ACM Symposium on Principles of Distributed Computing, PODC 1993, pp. 41–51. ACM, New York (1993)Google Scholar
  10. 10.
    Castañeda, A., Rajsbaum, S., Raynal, M.: The renaming problem in shared memory systems: an introduction. Comput. Sci. Rev. 5(3), 229–251 (2011)CrossRefMATHGoogle Scholar
  11. 11.
    Even, G., Halldórsson, M.M., Kaplan, L., Ron, D.: Scheduling with conflicts: online and offline algorithms. J. Sched. 12(2), 199–224 (2009)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Flocchini, P., Prencipe, G., Santoro, N.: Distributed Computing by Oblivious Mobile Robots. Synthesis Lectures on Distributed Computing Theory. Morgan & Claypool Publishers, San Rafeal (2012)MATHGoogle Scholar
  13. 13.
    Gafni, E., Mostéfaoui, A., Raynal, M., Travers, C.: From adaptive renaming to set agreement. Theor. Comput. Sci. 410(14), 1328–1335 (2009). Structural Information and Communication Complexity (SIROCCO 2007)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Gafni, E., Rajsbaum, S.: Recursion in distributed computing. In: Dolev, S., Cobb, J., Fischer, M., Yung, M. (eds.) SSS 2010. LNCS, vol. 6366, pp. 362–376. Springer, Heidelberg (2010). doi:10.1007/978-3-642-16023-3_30 CrossRefGoogle Scholar
  15. 15.
    Garey, M.R., Graham, R.L.: Bounds for multiprocessor scheduling with resource constraints. SIAM J. Comput. 4(2), 187–200 (1975)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Halldórsson, M.M., Kortsarz, G., Proskurowski, A., Salman, R., Shachnai, H., Telle, J.A.: Multicoloring trees. Inf. Comput. 180(2), 113–129 (2003)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Herlihy, M., Kozlov, D., Rajsbaum, S.: Distributed Computing Through Combinatorial Topology. Morgan Kaufmann, San Francisco (2013)MATHGoogle Scholar
  18. 18.
    Herlihy, M., Shavit, N.: The topological structure of asynchronous computability. J. ACM 46(6), 858–923 (1999)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Raynal, M.: Concurrent Programming: Algorithms, Principles, and Foundations. Springer, Heidelberg (2013)CrossRefMATHGoogle Scholar
  20. 20.
    Saks, M., Zaharoglou, F.: Wait-free k-set agreement is impossible: the topology of public knowledge. SIAM J. Comput. 29(5), 1449–1483 (2000)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Armando Castañeda
    • 1
  • Pierre Fraigniaud
    • 2
  • Eli Gafni
    • 3
  • Sergio Rajsbaum
    • 1
  • Matthieu Roy
    • 4
  1. 1.Instituto de MatemáticasUNAMMéxico D.F.Mexico
  2. 2.CNRS, University Paris DiderotParisFrance
  3. 3.Computer Science DepartmentUCLALos AngelesUSA
  4. 4.LAAS-CNRS, Université de Toulouse, CNRSToulouseFrance

Personalised recommendations