Back to Search
Start Over
Parametric Packing of Selfish Items and the Subset Sum Algorithm
- Source :
- Algorithmica. 74:177-207
- Publication Year :
- 2014
- Publisher :
- Springer Science and Business Media LLC, 2014.
-
Abstract
- 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, pp. 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 $$(0, \alpha ]$$(0,?] for some $$\alpha \le 1$$?≤1, yielding tight bounds for the Strong Price of Anarchy for all $$\alpha \le 1$$?≤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 $$\alpha \le 1$$?≤1.
- Subjects :
- FOS: Computer and information sciences
Computer Science::Computer Science and Game Theory
General Computer Science
Open problem
0211 other engineering and technologies
0102 computer and information sciences
02 engineering and technology
01 natural sciences
Upper and lower bounds
Combinatorics
Computer Science - Computer Science and Game Theory
Computer Science - Data Structures and Algorithms
Price of anarchy
Data Structures and Algorithms (cs.DS)
Greedy algorithm
Mathematics
021103 operations research
Bin packing problem
Heuristic
Applied Mathematics
Approximation algorithm
Computer Science Applications
010201 computation theory & mathematics
Subset sum problem
Algorithm
Computer Science and Game Theory (cs.GT)
Subjects
Details
- ISSN :
- 14320541 and 01784617
- Volume :
- 74
- Database :
- OpenAIRE
- Journal :
- Algorithmica
- Accession number :
- edsair.doi.dedup.....dc9125ea754ce1a10808968ef1bf0f6d