A simple on-line bin-packing algorithm
Journal of the ACM (JACM)
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP
Journal of the ACM (JACM)
Selfish Routing and the Price of Anarchy
Selfish Routing and the Price of Anarchy
Tight bounds for worst-case equilibria
ACM Transactions on Algorithms (TALG)
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Bounds on multiprocessing anomalies and related packing algorithms
AFIPS '72 (Spring) Proceedings of the May 16-18, 1972, spring joint computer conference
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Modified subset sum heuristics for bin packing
Information Processing Letters
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
On the packing of selfish items
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Worst-case analysis of the subset sum algorithm for bin packing
Operations Research Letters
Strong price of anarchy for machine load balancing
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Online variable-sized bin packing with conflicts
Discrete Optimization
A note on a selfish bin packing problem
Journal of Global Optimization
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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, 驴] for some 驴 ≤ 1, yielding tight bounds for the Strong Price of Anarchy for all 驴 ≤ 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 驴 ≤ 1.