Selfish, Local and Online Scheduling via Vector Fitting
Danish Kashaev

TL;DR
This paper introduces a unified dual fitting approach using semidefinite programming to analyze and bound the efficiency of various scheduling and congestion games, improving known bounds and extending results to broader settings.
Contribution
It presents a novel dual fitting technique that simplifies proofs and extends bounds for the price of anarchy and approximation ratios in scheduling and congestion games.
Findings
Extended coordination ratio bounds to congestion games.
Improved bounds for the price of anarchy in weighted affine congestion games.
Analyzed local search and online algorithms, achieving tight bounds and competitive ratios.
Abstract
We provide a dual fitting technique on a semidefinite program yielding simple proofs of tight bounds for the robust price of anarchy of several congestion and scheduling games under the sum of weighted completion times objective. The same approach also allows to bound the approximation ratio of local search algorithms and the competitive ratio of online algorithms for the scheduling problem . All of our results are obtained through a simple unified dual fitting argument on the same semidefinite programming relaxation, which can essentially be obtained through the first round of the Lasserre/Sum of Squares hierarchy. As our main application, we show that the known coordination ratio bounds of respectively and for the scheduling game under the coordination mechanisms Smith's Rule,…
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Taxonomy
TopicsAuction Theory and Applications · Game Theory and Applications · Game Theory and Voting Systems
