Probabilistic bounds for dual bin-packing
Acta Informatica
On the Lagarias-Odlyzko algorithm for the subset sum problem
SIAM Journal on Computing
Probabilistic analysis of algorithms
Probabilistic analysis of algorithms
Probabilistic analysis of a heuristics for the dual bin packing problem
Information Processing Letters
Introduction to algorithms
Probabilistic recurrence relations
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Concrete Math
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Theory, Volume 1, Queueing Systems
Theory, Volume 1, Queueing Systems
Local restoration with multiple spanning trees in metro ethernet networks
IEEE/ACM Transactions on Networking (TON)
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Given a positive integer M, and a set S = {x1, x2, ..., xn} of positive integers, the maximum subset sum problem is to find a subset S' of S such that Σxεs'x is maximized under the constraint that the summation is no larger than M. In addition, the cardinality of S' is also a maximum among all subsets of S which achieve the maximum subset sum. This problem is known to be NP-hard. We analyze the average-case performance of a simple on-line approximation algorithm assuming that all integers in S are independent and have the same probabilty distribution. We develop a general methodology, i.e., using recurrence relations, to evaluate the expected values of the content and the cardinality of S' for any distribution. The maximum subset sum problem has important applications, especially in static job scheduling in multiprogrammed parallel systems. The algorithm studied can also be easily adapted for dynamic job scheduling in such systems.