Modeling and assessing inference exposure in encrypted databases
ACM Transactions on Information and System Security (TISSEC)
A Survey on Approximation Algorithms for Scheduling with Machine Unavailability
Algorithmics of Large and Complex Networks
Bin completion algorithms for multicontainer packing, knapsack, and covering problems
Journal of Artificial Intelligence Research
Approximation algorithms for scheduling with reservations
HiPC'07 Proceedings of the 14th international conference on High performance computing
Tight approximation algorithms for scheduling with fixed jobs and nonavailability
ACM Transactions on Algorithms (TALG)
Faster approximation algorithms for scheduling with fixed jobs
CATS '11 Proceedings of the Seventeenth Computing: The Australasian Theory Symposium - Volume 119
Faster approximation algorithms for scheduling with fixed jobs
CATS 2011 Proceedings of the Seventeenth Computing on The Australasian Theory Symposium - Volume 119
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The Multiple Subset Sum Problem (MSSP) is the variant of bin packing in which the number of bins is given and one would like to maximize the overall weight of the items packed in the bins. The problem is also a special case of the multiple knapsack problem in which all knapsacks have the same capacity and the item profits and weights coincide. Recently, polynomial time approximation schemes have been proposed for MSSP and its generalizations, see A. Caprara, H. Kellerer, and U. Pferschy (SIAM J. on Optimization, Vol. 11, pp. 308–319, 2000; Information Processing Letters, Vol. 73, pp. 111–118, 2000), C. Chekuri and S. Khanna (Proceedings of SODA 00, 2000, pp. 213–222), and H. Kellerer (Proceedings of APPROX, 1999, pp. 51–62). However, these schemes are only of theoretical interest, since they require either the solution of huge integer linear programs, or the enumeration of a huge number of possible solutions, for any reasonable value of required accuracy. In this paper, we present a polynomial-time 3/4-approximation algorithm which runs fast also in practice. Its running time is linear in the number of items and quadratic in the number of bins. The “core” of the algorithm is a procedure to pack triples of “large” items into the bins. As a byproduct of our analysis, we get the approximation guarantee for a natural greedy heuristic for the 3-Partitioning Problem.