论文信息 - Linear time-approximation algorithms for bin packing

Linear time-approximation algorithms for bin packing

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.

[1] G. S. Lueker,et al. Bin packing can be solved within 1 + ε in linear time , 1981 .

[2] David S. Johnson,et al. Near-optimal bin packing algorithms , 1973 .

[3] Jan Karel Lenstra,et al. Computing near-optimal schedules , 1995 .

[4] D. Simchi-Levi. New worst‐case results for the bin‐packing problem , 1994 .

[5] Jeffrey D. Ullman,et al. Worst-Case Performance Bounds for Simple One-Dimensional Packing Algorithms , 1974, SIAM J. Comput..

[6] David S. Johnson,et al. Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[7] Dorit S. Hochbaum,et al. Approximation Algorithms for NP-Hard Problems , 1996 .

[8] D. T. Lee,et al. A simple on-line bin-packing algorithm , 1985, JACM.

[9] D. T. Lee,et al. On-Line Bin Packing in Linear Time , 1989, J. Algorithms.

[10] Charles U. Martel. A linear time bin-packing algorithm , 1985 .

[11] Edward G. Coffman,et al. Approximation algorithms for bin packing: a survey , 1996 .