Parametric packing of selfish items and the subset sum algorithm

Leah Epstein, Elena Kleiman, Julián Mestre

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


The subset sum algorithm is a natural heuristic for the classical Bin Packing problem: In each iteration, the algorithm finds among the unpacked items, a maximum size set of items that fits into a new bin. More than 35 years after its first mention in the literature, establishing the worst-case performance of this heuristic remains, surprisingly, an open problem. Due to their simplicity and intuitive appeal, greedy algorithms are the heuristics of choice of many practitioners. Therefore, better understanding simple greedy heuristics is, in general, an interesting topic in its own right. Very recently, Epstein and Kleiman (Proc. ESA 2008, pages 368-380) provided another incentive to study the subset sum algorithm by showing that the Strong Price of Anarchy of the game theoretic version of the Bin Packing problem is precisely the approximation ratio of this heuristic. In this paper we establish the exact approximation ratio of the subset sum algorithm, thus settling a long standing open problem. We generalize this result to the parametric variant of the Bin Packing problem where item sizes lie on the interval (0, α] for some α≤1, yielding tight bounds for the Strong Price of Anarchy for all α≤1. Finally, we study the pure Price of Anarchy of the parametric Bin Packing game for which we show nearly tight upper and lower bounds for all α≤1.

Original languageEnglish
Title of host publicationInternet and Network Economics - 5th International Workshop, WINE 2009, Proceedings
Number of pages12
StatePublished - 2009
Event5th International Workshop on Internet and Network Economics, WINE 2009 - Rome, Italy
Duration: 14 Dec 200918 Dec 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5929 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference5th International Workshop on Internet and Network Economics, WINE 2009

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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