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
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
Random knapsack in expected polynomial time
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
On the approximability of trade-offs and optimal access of Web sources
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
On finding the exact solution of a zero-one knapsack problem
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Solving random satisfiable 3CNF formulas in expected polynomial time
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Decision-making based on approximate and smoothed Pareto curves
Theoretical Computer Science
The Smoothed Number of Pareto Optimal Solutions in Bicriteria Integer Optimization
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Multi-objective problems in terms of relational algebra
RelMiCS'08/AKA'08 Proceedings of the 10th international conference on Relational and kleene algebra methods in computer science, and 5th international conference on Applications of kleene algebra
Algorithm engineering: bridging the gap between algorithm theory and practice
Algorithm engineering: bridging the gap between algorithm theory and practice
Pareto optimal solutions for smoothed analysts
Proceedings of the forty-third annual ACM symposium on Theory of computing
Lower bounds for the smoothed number of pareto optimal solutions
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Smoothed Analysis of the k-Means Method
Journal of the ACM (JACM)
Smoothed analysis of partitioning algorithms for Euclidean functionals
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Smoothed performance guarantees for local search
ESA'11 Proceedings of the 19th European conference on Algorithms
A universally-truthful approximation scheme for multi-unit auctions
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Decision making based on approximate and smoothed pareto curves
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Smoothed analysis of integer programming
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Smoothed analysis of integer programming
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
The smoothed analysis of algorithms
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Improved smoothed analysis of multiobjective optimization
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Reducing a target interval to a few exact queries
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Exact scalable sensitivity analysis for the next release problem
ACM Transactions on Software Engineering and Methodology (TOSEM)
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We present the first average-case analysis proving a polynomial upper bound on the expected running time of an exact algorithm for the 0/1 knapsack problem. In particular, we prove for various input distributions, that the number of Pareto-optimal knapsack fillings 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 Pareto-optimal solutions implies an algorithm with expected polynomial running time.The random input model underlying our analysis is quite 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.