Linear time-approximation algorithms for bin packing

Authors:
Guochuan Zhang;Xiaoqiang Cai;C. K. Wong
Affiliations:
Department of Mathematics, Zhejiang University, Hangzhou 310027, People's Republic of China;Department of Systems Engineering & Engineering Management, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong;Department of Computer Science & Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong
Venue:
Operations Research Letters
Year:
2000

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Abstract

Simchi-Levi (Naval Res. Logist. 41 (1994) 579-585) proved that the famous bin packing algorithms FF and BF have an absolute worst-case ratio of no more than 74, and FFD and BFD have an absolute worst-case ratio of 32, respectively. These algorithms run in time O(nlogn). In this paper, we provide a linear time constant space (number of bins kept during the execution of the algorithm is constant) off-line approximation algorithms with absolute worst-case ratio 32. This result is best possible unless P=NP. Furthermore, we present a linear time constant space on-line algorithm and prove that the absolute worst-case ratio is 74.