Finding integer efficient solutions for bicriteria and tricriteria network flow problems using DINAS
Computers and Operations Research
Pareto Shortest Paths is Often Feasible in Practice
WAE '01 Proceedings of the 5th International Workshop on Algorithm Engineering
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
Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time
Journal of the ACM (JACM)
Random knapsack in expected polynomial time
Journal of Computer and System Sciences - Special issue: STOC 2003
Typical Properties of Winners and Losers [0.2ex] in Discrete Optimization
SIAM Journal on Computing
Efficiently computing succinct trade-off curves
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
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
Pareto optimal solutions for smoothed analysts
Proceedings of the forty-third annual ACM symposium on Theory of computing
Path trading: fast algorithms, smoothed analysis, and hardness results
SEA'11 Proceedings of the 10th international conference on Experimental algorithms
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
A universally-truthful approximation scheme for multi-unit auctions
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Improved smoothed analysis of multiobjective optimization
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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A well established heuristic approach for solving various bicriteria optimization problems is to enumerate the set of Pareto optimal solutions, typically using some kind of dynamic programming approach. The heuristics following this principle are often successful in practice. Their running time, however, depends on the number of enumerated solutions, which can be exponential in the worst case.In this paper, we prove an almost tight bound on the expected number of Pareto optimal solutions for general bicriteria integer optimization problems in the framework of smoothed analysis. Our analysis is based on a semi-random input model in which an adversary can specify an input which is subsequently slightly perturbed at random, e. g., using a Gaussian or uniform distribution.Our results directly imply tight polynomial bounds on the expected running time of the Nemhauser/Ullmann heuristic for the 0/1 knapsack problem. Furthermore, we can significantly improve the known results on the running time of heuristics for the bounded knapsack problem and for the bicriteria shortest path problem. Finally, our results also enable us to improve and simplify the previously known analysis of the smoothed complexity of integer programming.