TY - GEN

T1 - Parametric packing of selfish items and the subset sum algorithm

AU - Epstein, Leah

AU - Kleiman, Elena

AU - Mestre, Julián

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=76649109640&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-10841-9_8

DO - 10.1007/978-3-642-10841-9_8

M3 - Conference contribution

AN - SCOPUS:76649109640

SN - 3642108407

SN - 9783642108402

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 67

EP - 78

BT - Internet and Network Economics - 5th International Workshop, WINE 2009, Proceedings

T2 - 5th International Workshop on Internet and Network Economics, WINE 2009

Y2 - 14 December 2009 through 18 December 2009

ER -