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
Smoothed analysis of partitioning algorithms for Euclidean functionals
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Improved smoothed analysis of multiobjective optimization
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Randomized mechanisms for multi-unit auctions
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
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We prove that the number of Pareto-optimal solutions in any multiobjective binary optimization problem with a finite number of linear objective functions is polynomial in the model of smoothed analysis. This resolves a conjecture of Rene Beier. Moreover, we give polynomial bounds on all finite moments of the number of Pareto-optimal solutions, which yields the first non-trivial concentration bound for this quantity. Using our new technique, we give a complete characterization of polynomial smoothed complexity for binary optimization problems, which strengthens an earlier result due to Beier and Vöcking.