The Santa Claus problem

Bansal, Nikhil; Sviridenko, Maxim

doi:10.1145/1132516.1132522

Cited by 207 publications

(335 citation statements)

References 12 publications

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“…The problem was studied by Bezáková and Dani [3] and Golovin [14] who obtained approximation algorithms that provably return a solution that is always a factor of O(n) within the optimal value. The problem was popularized by Bansal and Sviridenko [2] as the Santa Claus problem, where Santa Claus aims to distribute presents to the kids so as to maximize the happiness of the least happy kid. Subsequently, Asadpour and Saberi [1] presented an O( √ n log 3 n)-approximation algorithm for this problem.…”

Section: Related Workmentioning

confidence: 99%

On Low-Envy Truthful Allocations

Caragiannis

Kaklamanis

Kanellopoulos

et al. 2009

Algorithmic Decision Theory

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Abstract. We study the problem of allocating a set of indivisible items to players having additive utility functions over the items. We consider allocations in which no player envies the bundle of items allocated to the other players too much. We present a simple proof that deterministic truthful allocations do not minimize envy by characterizing the truthful mechanisms for two players and two items. Also, we present an analysis for uniformly random allocations which are naturally truthful in expectation. These results simplify or improve previous results of Lipton et al.

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Section: Related Workmentioning

confidence: 99%

On Low-Envy Truthful Allocations

Caragiannis

Kaklamanis

Kanellopoulos

et al. 2009

Algorithmic Decision Theory

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“…For n players and divisible chores, the price of proportionality is at most n and at least (n+1) 2 4n , and the price of equitability is n.…”

Section: Theoremmentioning

confidence: 99%

The Efficiency of Fair Division

Caragiannis

Kaklamanis

Kanellopoulos

et al. 2009

Lecture Notes in Computer Science

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Abstract. We study the impact of fairness on the efficiency of allocations. We consider three different notions of fairness, namely proportionality, envy-freeness, and equitability for allocations of divisible and indivisible goods and chores. We present a series of results on the price of fairness under the three different notions that quantify the efficiency loss in fair allocations compared to optimal ones. Most of our bounds are either exact or tight within constant factors. Our study is of an optimistic nature and aims to identify the potential of fairness in allocations.

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“…Bezàkovà and Dani [12] proposed a linear factor approximation algorithm for this problem, which is based on a linear programming relaxation and rounding; our rounding procedure is similar to the rounding procedure used in their paper. Bansal and Sviridenko [10] obtained a tighter approximation algorithm for the restricted assignment version of the problem, where each resource can be allocated to only a subset of the agents, and each such agent has the same utility for that resource. As of now, no FPTAS has been proposed for the Santa Claus problem with a fixed number of agents.…”

Section: Our Resultsmentioning

confidence: 99%

“…The authors also thank Retsef Levi for pointing out the work by Bansal and Sviridenko [10]. This research was supported by NSF awards #0426686 and #0700044, and by ONR grant N00014-08-1-0029.…”

Section: Acknowledgmentsmentioning

confidence: 90%

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A General Framework for Designing Approximation Schemes for Combinatorial Optimization Problems with Many Objectives Combined into One

Mittal

Schulz

2008

Lecture Notes in Computer Science

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Abstract. In this paper, we propose a general framework for designing fully polynomial time approximation schemes for combinatorial optimization problems, in which more than one objective function are combined into one using any norm. The main idea is to exploit the approximate Pareto-optimal frontier for multi-criteria optimization problems. Using this approach, we obtain an FPTAS for a novel resource allocation problem, for the problem of scheduling jobs on unrelated parallel machines, and for the Santa Claus problem, when the number of agents/machines is fixed, for any norm, including the l∞-norm. Moreover, either FPTAS can be implemented in a manner so that the space requirements are polynomial in all input parameters. We also give approximation algorithms and hardness results for the resource allocation problem when the number of agents is not fixed.

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The Santa Claus problem

Cited by 207 publications

References 12 publications

On Low-Envy Truthful Allocations

On Low-Envy Truthful Allocations

The Efficiency of Fair Division

A General Framework for Designing Approximation Schemes for Combinatorial Optimization Problems with Many Objectives Combined into One

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