On the Lagarias-Odlyzko algorithm for the subset sum problem
SIAM Journal on Computing
Probabilistic analysis of the multidimensional knapsack problem
Mathematics of Operations Research
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Average saving effects in enumerative methods for solving knapsack problems
Journal of Complexity
Improved low-density subset sum algorithms
Computational Complexity
Exponentially small bounds on the expected optimum of the partition and subset sum problems
Random Structures & Algorithms
Average-case analysis of off-line and on-line knapsack problems
Journal of Algorithms - Special issue on SODA '95 papers
Computing Partitions with Applications to the Knapsack Problem
Journal of the ACM (JACM)
Smoothed analysis of algorithms: why the simplex algorithm usually takes polynomial time
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On finding the exact solution of a zero-one knapsack problem
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Probabilistic analysis of knapsack core algorithms
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Computing equilibria for congestion games with (im)perfect information
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Typical properties of winners and losers in discrete optimization
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Random knapsack in expected polynomial time
Journal of Computer and System Sciences - Special issue: STOC 2003
Average-Case and Smoothed Competitive Analysis of the Multilevel Feedback Algorithm
Mathematics of Operations Research
Solving Medium-Density Subset Sum Problems in Expected Polynomial Time: An Enumeration Approach
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
Simple and efficient greedy algorithms for hamilton cycles in random intersection graphs
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Worst-case and average-case approximations by simple randomized search heuristics
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Solving medium-density subset sum problems in expected polynomial time
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Computers and Operations Research
Integer feasibility of random polytopes: random integer programs
Proceedings of the 5th conference on Innovations in theoretical computer science
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In this paper, we present the first average-case analysis proving an expected polynomial running time for an exact algorithm for the 0/1 knapsack problem. In particular, we prove, for various input distributions, that the number of dominating solutions (i.e., Pareto-optimal knapsack fillings) to this problem is polynomially bounded in the number of available items. An algorithm by Nemhauser and Ullmann can enumerate these solutions very efficiently so that a polynomial upper bound on the number of dominating solutions implies an algorithm with expected polynomial running time.The random input model underlying our analysis is very general and not restricted to a particular input distribution. We assume adversarial weights and randomly drawn profits (or vice versa). Our analysis covers general probability distributions with finite mean, and, in its most general form, can even handle different probability distributions for the profits of different items. This feature enables us to study the effects of correlations between profits and weights. Our analysis confirms and explains practical studies showing that so-called strongly correlated instances are harder to solve than weakly correlated ones.