Exact and Approximate Algorithms for Scheduling Nonidentical Processors
Journal of the ACM (JACM)
Heuristic Algorithms for Scheduling Independent Tasks on Nonidentical Processors
Journal of the ACM (JACM)
Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Tight bounds for worst-case equilibria
ACM Transactions on Algorithms (TALG)
(Almost) optimal coordination mechanisms for unrelated machine scheduling
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Coordination mechanisms for selfish scheduling
Theoretical Computer Science
Intrinsic robustness of the price of anarchy
Proceedings of the forty-first annual ACM symposium on Theory of computing
Theoretical Computer Science
Price of anarchy in parallel processing
Information Processing Letters
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Inner product spaces for MinSum coordination mechanisms
Proceedings of the forty-third annual ACM symposium on Theory of computing
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We address the classical uniformly related machine scheduling problem with minsum objective. The problem is solvable in polynomial time by the algorithm of Horowitz and Sahni. In that solution, each machine sequences its jobs shortest first. However when jobs may choose the machine on which they are processed, while keeping the same sequencing rule per machine, the resulting Nash equilibria are in general not optimal. The price of anarchy measures this optimality gap. By means of a new characterization of the optimal solution, we show that the price of anarchy in this setting is bounded from above by 2. We also give a lower bound of e/(e−1)≈1.58. This complements recent results on the price of anarchy for the more general unrelated machine scheduling problem, where the price of anarchy equals 4. Interestingly, as Nash equilibria coincide with shortest processing time first (SPT) schedules, the same bounds hold for SPT schedules. Thereby, our work also fills a gap in the literature.