STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
On line bin packing with items of random size
Mathematics of Operations Research
On-line bin packing of items of random sizes, II
SIAM Journal on Computing
Markov chains, computer proofs, and average-case analysis of best fit bin packing
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Biased random walks, Lyapunov functions, and stochastic analysis of best fit bin packing
Journal of Algorithms
SIAM Journal on Discrete Mathematics
Sum-of-squares heuristics for bin packing and memory allocation
Journal of Experimental Algorithmics (JEA)
O((log n)2) time online approximation schemes for bin packing and subset sum problems
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
A dense hierarchy of sublinear time approximation schemes for bin packing
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
Proceedings of the 15th annual conference on Genetic and evolutionary computation
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This paper reports on experiments with a new on-line heuristic for one-dimensional bin packing whose average-case behavior is surprisingly robust. We restrict attention to the class of "discrete" distributions, i.e., ones in which the set of possible item sizes is finite (as is commonly the case in practical applications), and in which all sizes and probabilities are rational. It is known from [7] that for any such distribution the optimal expected waste grows either as Θ(n), Θ(√n), or O(1), Our new Sum of Squares algorithm (SS) appears to have roughly the same expected behavior in all three cases. This claim is experimentally evaluated using a newly-discovered, linear-programming-based algorithm that determines the optimal expected waste rate for any given discrete distribution in pseudopolynomial time (the best one can hope for given that the basic problem is NP-hard). Although SS appears to be essentially optimal when the expected optimal waste rate is sublinear, it is less impressive when the expected optimal waste rate is linear. The expected ratio of the number of bins used by SS to the optimal number appears to go to 1 asymptotically in the first case, whereas there are distributions for which it can be as high as 1.5 in the second. However, by modifying the algorithm slightly, using a single parameter that is tunable to the distribution in question (either by advanced knowledge or by on-line learning), we appear to be able to make the ratio go to 1 in all cases.