Musical chairs

Yehuda Afek*, Yakov Babichenko, Uriel Feige, Eli Gafni, Nati Linial, Benny Sudakov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In the musical chairs game MC(n, m), a team of n players plays against an adversarial scheduler. The scheduler wins if the game proceeds indefinitely, while termination after a finite number of rounds is declared a win of the team. At each round of the game each player occupies one of the m available chairs. Termination (and a win of the team) is declared as soon as each player occupies a unique chair. Two players that simultaneously occupy the same chair are said to be in conflict. In other words, termination (and a win for the team) is reached as soon as there are no conflicts. The only means of communication throughout the game is this: At every round of the game, the scheduler selects an arbitrary nonempty set of players who are currently in conflict, and notifies each of them separately that it must move. A player who is thus notified changes its chair according to its deterministic program. As we show, for m ≥ 2n - 1 chairs the team has a winning strategy. Moreover, using topological arguments we show that this bound is tight. For m ≤ 2n - 2 the scheduler has a strategy that is guaranteed to make the game continue indefinitely and thus win. We also have some results on additional interesting questions.

Original languageAmerican English
Pages (from-to)1578-1600
Number of pages23
JournalSIAM Journal on Discrete Mathematics
Volume28
Issue number3
DOIs
StatePublished - 2014

Bibliographical note

Publisher Copyright:
© 2014 Society for Industrial and Applied Mathematics.

Keywords

  • Asynchronous computation
  • Distributed computing
  • Oblivious computing
  • Probabilistic analysis
  • Renaming

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