On the sum-of-squares algorithm for bin packing
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
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SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
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ALENEX '99 Selected papers from the International Workshop on Algorithm Engineering and Experimentation
Windows scheduling as a restricted version of Bin Packing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
On the Sum-of-Squares algorithm for bin packing
Journal of the ACM (JACM)
Maximizing data locality in distributed systems
Journal of Computer and System Sciences
Sum-of-squares heuristics for bin packing and memory allocation
Journal of Experimental Algorithmics (JEA)
Windows scheduling as a restricted version of bin packing
ACM Transactions on Algorithms (TALG)
Dynamic bin packing of unit fractions items
Theoretical Computer Science
Dynamic bin packing of unit fractions items
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
A bounded item bin packing problem over discrete distribution
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
On dynamic bin packing: an improved lower bound and resource augmentation analysis
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Automating the packing heuristic design process with genetic programming
Evolutionary Computation
Two-dimensional bin packing with one-dimensional resource augmentation
Discrete Optimization
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We consider the one-dimensional bin packing problem with unit-capacity bins and item sizes chosen according to the discrete uniform distribution U{j,k}, $1 k,2/k,. . .,j/k} has probability 1/j of being chosen. Note that for fixed j,k as $m\rightarrow\infty$ the discrete distributions U{mj,mk} approach the continuous distribution U(0,j/k], where the item sizes are chosen uniformly from the interval (0,j/k]. We show that average-case behavior can differ substantially between the two types of distributions. In particular, for all j,k with jk-1, there exist on-line algorithms that have constant expected wasted space under U{j,k}, whereas no on-line algorithm has even o(n1/2) expected waste under U(0,u] for any $0 U{j,k} result is an application of a general theorem of Courcoubetis and Weber [C. Courcoubetis and R. R. Weber, Probab. Engrg. Inform. Sci., 4 (1990), pp. 447--460] that covers all discrete distributions. Under each such distribution, the optimal expected waste for a random list of n items must be either $\Theta (n)$, $\Theta (n^{1/2} )$, or O(1), depending on whether certain "perfect" packings exist. The perfect packing theorem needed for the U{j,k} distributions is an intriguing result of independent combinatorial interest, and its proof is a cornerstone of the paper.