A note on the integrality gap of the configuration LP for restricted Santa Claus
Klaus Jansen,Lars Rohwedder +1 more
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A better analysis is presented that shows the integrality gap is not worse than $3 + 5/6 \approx 3.8333$ and is shown to be non-constructive since the local search has not been shown to terminate in polynomial time.About:
This article is published in Information Processing Letters.The article was published on 2020-12-01 and is currently open access. It has received 4 citations till now.read more
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The Submodular Santa Claus Problem in the Restricted Assignment Case
TL;DR: If $f$ is a monotone submodular function, the authors can in polynomial time compute an $O(\log\log(n)$-approximate solution, and this paper makes comparable progress for the sub modular variant.
Proceedings ArticleDOI
Online Algorithms for the Santa Claus Problem
TL;DR: In this article , the authors study the online version of the Santa Claus problem, where the items are not known in advance and have to be assigned to agents as they arrive over time.
Book ChapterDOI
Improved Integrality Gap in Max-Min Allocation: or Topology at the North Pole
Penny Haxell,T. Szab'o +1 more
TL;DR: In this paper , the integrality gap of the configuration LP was improved to $3.534 by replacing the combinatorial augmenting tree argument of Haxell with a topological argument.
References
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Proceedings ArticleDOI
The Santa Claus problem
Nikhil Bansal,Maxim Sviridenko +1 more
TL;DR: This work considers the following problem: The Santa Claus has n presents that he wants to distribute among m kids, each kid has an arbitrary value for each present, and develops an O(log log m/log log log m) approximation algorithm for the restricted assignment case of the problem when pij,0 (i.e. when present j has either value p j or 0 for each kid).
Journal ArticleDOI
Santa Claus Schedules Jobs On Unrelated Machines
TL;DR: The main result is a polynomial time algorithm that estimates the optimal makespan of the restricted assignment problem within a factor $33/17 + \epsilon \approx 1.9412 + \EPsilon$, where $\ep silon > 0$ is an arbitrarily small constant.
Journal ArticleDOI
Santa claus meets hypergraph matchings
TL;DR: This work proves that the integrality gap of the configuration LP is no worse than 1/4, and provides a local search algorithm which finds the corresponding allocation, but is nonconstructive in the sense that this algorithm is not known to converge to a local optimum in a polynomial number of steps.
Journal ArticleDOI
Combinatorial Algorithm for Restricted Max-Min Fair Allocation
TL;DR: In this article, a 13-approximation algorithm for the problem was proposed, which uses the Configuration-LP to estimate the value of the optimal allocation to within a factor of 4+ e. In contrast, the best known approximation algorithm has an unspecified large constant guarantee.
Journal ArticleDOI
Quasi-Polynomial Local Search for Restricted Max-Min Fair Allocation
Lukáš Poláček,Ola Svensson +1 more
TL;DR: In this paper, a quasi-polynomial approximation algorithm for the restricted max-min fair allocation problem was proposed, with a bound of 2O(n) to nO(log n).
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