Selfish Vector Packing

Leah Epstein, Elena Kleiman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageEnglish
Title of host publicationAlgorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings
EditorsNikhil Bansal, Irene Finocchi
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783662483497
StatePublished - 2015
Event23rd European Symposium on Algorithms, ESA 2015 - Patras, Greece
Duration: 14 Sep 201516 Sep 2015

Publication series

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


Conference23rd European Symposium on Algorithms, ESA 2015

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2015.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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