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 7 4 , and FFD and BFD have an absolute worst-case ratio of 3 2 , respectively. These algorithms run in time O(n log n) . 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 3 2 . 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 7 4 .

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