Selfish Vector Packing

Leah Epstein; Elena Kleiman

doi:10.1007/978-3-662-48350-3_40

Selfish Vector Packing

Leah Epstein, Elena Kleiman

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We study the multidimensional vector packing problem with selfish items. An item is d-dimensional non-zero vector, whose rational components are in [0, 1], and a set of items can be packed into a bin if for any 1 ≤ i ≤ d, the sum of the i^th components of all items of this set does not exceed 1. Items share costs of bins proportionally to their ℓ₁- norms, and each item corresponds to a selfish player in the sense that it prefers to be packed into a bin minimizing its resulting cost. This defines a class of games called vector packing games. We show that any game in this class has a packing that is a strong equilibrium, and that the strong price of anarchy (and the strong price of stability) is logarithmic in d, and provide an algorithm that constructs such a packing. We also show improved and nearly tight lower and upper bounds of d + 0.657067 and d+0.657143 respectively, on the price of anarchy, exhibiting a difference between the multidimensional problem and the one dimensional problem, for which that price of anarchy is at most 1.6428.

Original language	English
Title of host publication	Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings
Editors	Nikhil Bansal, Irene Finocchi
Publisher	Springer Verlag
Pages	471-482
Number of pages	12
ISBN (Print)	9783662483497
DOIs	https://doi.org/10.1007/978-3-662-48350-3_40
State	Published - 2015
Event	23rd European Symposium on Algorithms, ESA 2015 - Patras, Greece Duration: 14 Sep 2015 → 16 Sep 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9294
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	23rd European Symposium on Algorithms, ESA 2015
Country/Territory	Greece
City	Patras
Period	14/09/15 → 16/09/15

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2015.

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-662-48350-3_40

Cite this

Epstein, L., & Kleiman, E. (2015). Selfish Vector Packing. In N. Bansal, & I. Finocchi (Eds.), Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings (pp. 471-482). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9294). Springer Verlag. https://doi.org/10.1007/978-3-662-48350-3_40

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title = "Selfish Vector Packing",

abstract = "We study the multidimensional vector packing problem with selfish items. An item is d-dimensional non-zero vector, whose rational components are in [0, 1], and a set of items can be packed into a bin if for any 1 ≤ i ≤ d, the sum of the ith components of all items of this set does not exceed 1. Items share costs of bins proportionally to their ℓ1- norms, and each item corresponds to a selfish player in the sense that it prefers to be packed into a bin minimizing its resulting cost. This defines a class of games called vector packing games. We show that any game in this class has a packing that is a strong equilibrium, and that the strong price of anarchy (and the strong price of stability) is logarithmic in d, and provide an algorithm that constructs such a packing. We also show improved and nearly tight lower and upper bounds of d + 0.657067 and d+0.657143 respectively, on the price of anarchy, exhibiting a difference between the multidimensional problem and the one dimensional problem, for which that price of anarchy is at most 1.6428.",

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doi = "10.1007/978-3-662-48350-3_40",

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Epstein, L & Kleiman, E 2015, Selfish Vector Packing. in N Bansal & I Finocchi (eds), Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9294, Springer Verlag, pp. 471-482, 23rd European Symposium on Algorithms, ESA 2015, Patras, Greece, 14/09/15. https://doi.org/10.1007/978-3-662-48350-3_40

Selfish Vector Packing. / Epstein, Leah; Kleiman, Elena.
Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings. ed. / Nikhil Bansal; Irene Finocchi. Springer Verlag, 2015. p. 471-482 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9294).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - We study the multidimensional vector packing problem with selfish items. An item is d-dimensional non-zero vector, whose rational components are in [0, 1], and a set of items can be packed into a bin if for any 1 ≤ i ≤ d, the sum of the ith components of all items of this set does not exceed 1. Items share costs of bins proportionally to their ℓ1- norms, and each item corresponds to a selfish player in the sense that it prefers to be packed into a bin minimizing its resulting cost. This defines a class of games called vector packing games. We show that any game in this class has a packing that is a strong equilibrium, and that the strong price of anarchy (and the strong price of stability) is logarithmic in d, and provide an algorithm that constructs such a packing. We also show improved and nearly tight lower and upper bounds of d + 0.657067 and d+0.657143 respectively, on the price of anarchy, exhibiting a difference between the multidimensional problem and the one dimensional problem, for which that price of anarchy is at most 1.6428.

AB - We study the multidimensional vector packing problem with selfish items. An item is d-dimensional non-zero vector, whose rational components are in [0, 1], and a set of items can be packed into a bin if for any 1 ≤ i ≤ d, the sum of the ith components of all items of this set does not exceed 1. Items share costs of bins proportionally to their ℓ1- norms, and each item corresponds to a selfish player in the sense that it prefers to be packed into a bin minimizing its resulting cost. This defines a class of games called vector packing games. We show that any game in this class has a packing that is a strong equilibrium, and that the strong price of anarchy (and the strong price of stability) is logarithmic in d, and provide an algorithm that constructs such a packing. We also show improved and nearly tight lower and upper bounds of d + 0.657067 and d+0.657143 respectively, on the price of anarchy, exhibiting a difference between the multidimensional problem and the one dimensional problem, for which that price of anarchy is at most 1.6428.

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ER -

Selfish Vector Packing

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