On the Size of Weights for Threshold Gates
SIAM Journal on Discrete Mathematics
Anti-Hadamard matrices, coin weighing, threshold gates, and indecomposable hypergraphs
Journal of Combinatorial Theory Series A
Minimum spanning trees made easier via multi-objective optimization
Natural Computing: an international journal
Randomized local search, evolutionary algorithms, and the minimum spanning tree problem
Theoretical Computer Science
Approximating covering problems by randomized search heuristics using multi-objective models
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Evolutionary algorithms and matroid optimization problems
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Computing minimum cuts by randomized search heuristics
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Runtime analysis of the (1+1) evolutionary algorithm on strings over finite alphabets
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
Black-box complexities of combinatorial problems
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Black-box complexities of combinatorial problems
Theoretical Computer Science
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Runtime analyses of randomized search heuristics for combinatorial optimization problems often depend on the size of the largest weight. We consider replacing the given set of weights with smaller weights such that the behavior of the randomized search heuristic does not change. Upper bounds on the size of the new, equivalent weights allow us to obtain upper bounds on the expected runtime of such randomized search heuristics independent of the size of the actual weights. Furthermore we give lower bounds on the largest weights for worst-case instances. Finally we present some experimental results, including examples for worst-case instances.