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New bounds for truthful scheduling on two unrelated selfish machines

Kuryatnikova,Olga
; 
Vera,J.C.
Abstract
We consider the minimum makespan problem for n tasks and two unrelated parallel selfish machines. Let Rn be the best approximation ratio of randomized monotone scale-free algorithms. This class contains the most efficient algorithms known for truthful scheduling on two machines. We propose a new Min − Max formulation for Rn, as well as upper and lower bounds on Rn based on this formulation. For the lower bound, we exploit pointwise approximations of cumulative distribution functions (CDFs). For the upper bound, we construct randomized algorithms using distributions with piecewise rational CDFs. Our method improves upon the existing bounds on Rn for small n. In particular, we obtain almost tight bounds for n = 2 showing that |R2 − 1.505996| < 10− 6.
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Publisher Copyright: © 2019, The Author(s).
Date
2020-02
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Tilburg University Research Output Collection
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Keywords
minimax optimization, truthful scheduling, approximation, piecewise functions, algorithmic mechanism design
Citation
Kuryatnikova, O & Vera, J C 2020, 'New bounds for truthful scheduling on two unrelated selfish machines', Theory of Computing Systems, vol. 64, no. 2, pp. 199-226. https://doi.org/10.1007/s00224-019-09927-x
URI
https://hdl.handle.net/20.500.14602/71708
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