TY - GEN
T1 - Selfish Vector Packing
AU - Epstein, Leah
AU - Kleiman, Elena
N1 - Publisher Copyright: © Springer-Verlag Berlin Heidelberg 2015.
PY - 2015
Y1 - 2015
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.
UR - http://www.scopus.com/inward/record.url?scp=84945583292&partnerID=8YFLogxK
U2 - https://doi.org/10.1007/978-3-662-48350-3_40
DO - https://doi.org/10.1007/978-3-662-48350-3_40
M3 - Conference contribution
SN - 9783662483497
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 471
EP - 482
BT - Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings
A2 - Bansal, Nikhil
A2 - Finocchi, Irene
PB - Springer Verlag
T2 - 23rd European Symposium on Algorithms, ESA 2015
Y2 - 14 September 2015 through 16 September 2015
ER -