Optimal bin packing with items of random sizes
Mathematics of Operations Research
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
An improved lower bound for on-line bin packing algorithms
Information Processing Letters
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
Bin packing with discrete item sizes, part II: tight bounds on first fit
Random Structures & Algorithms - Special issue: average-case analysis of algorithms
Biased random walks, Lyapunov functions, and stochastic analysis of best fit bin packing
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Average-case analyses of first fit and random fit bin packing
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
SIAM Journal on Discrete Mathematics
Better approximation algorithms for bin covering
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Linear waste of best fit bin packing on skewed distributions
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Sum-of-squares heuristics for bin packing and memory allocation
Journal of Experimental Algorithmics (JEA)
Proceedings of the 15th annual conference on Genetic and evolutionary computation
A large-scale service system with packing constraints: minimizing the number of occupied servers
Proceedings of the ACM SIGMETRICS/international conference on Measurement and modeling of computer systems
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In this article we present a theoretical analysis of the online Sum-of-Squares algorithm (SS) for bin packing along with several new variants. SS is applicable to any instance of bin packing in which the bin capacity B and item sizes s(a) are integral (or can be scaled to be so), and runs in time O(nB). It performs remarkably well from an average case point of view: For any discrete distribution in which the optimal expected waste is sublinear, SS also has sublinear expected waste. For any discrete distribution where the optimal expected waste is bounded, SS has expected waste at most O(log n). We also discuss several interesting variants on SS, including a randomized O(nB log B)-time online algorithm SS* whose expected behavior is essentially optimal for all discrete distributions. Algorithm SS* depends on a new linear-programming-based pseudopolynomial-time algorithm for solving the NP-hard problem of determining, given a discrete distribution F, just what is the growth rate for the optimal expected waste.