Polynomial approximation algorithms for the TSP and the QAP with a factorial domination number
Discrete Applied Mathematics
Domination analysis of some heuristics for the traveling salesman problem
Discrete Applied Mathematics
Linear Time Dynamic-Programming Algorithms for New Classes of Restricted TSPs: A Computational Study
INFORMS Journal on Computing
Domination analysis of combinatorial optimization problems
Discrete Applied Mathematics
Algorithms with large domination ratio
Journal of Algorithms
Combinatorial dominance guarantees for problems with infeasible solutions
ACM Transactions on Algorithms (TALG)
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
TSP tour domination and Hamilton cycle decompositions of regular digraphs
Operations Research Letters
Domination analysis of algorithms for bipartite boolean quadratic programs
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
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Gutin et al. [G. Gutin, A. Yeo, Polynomial approximation algorithms for the TSP and the QAP with a factorial domination number, Discrete Applied Mathematics 119 (1-2) (2002) 107-116] proved that, in the ATSP problem, a tour of weight not exceeding the weight of an average tour is of dominance ratio at least 1/(n-1) for all n6. (Tours with this property can be easily obtained.) In [N. Alon, G. Gutin, M. Krivelevich, Algorithms with large domination ratio, Journal on Algorithms 50 (2004) 118-131; G. Gutin, A. Vainshtein, A. Yeo, Domination analysis of combinatorial optimization problems, Discrete Applied Mathematics 129 (2-3) (2003) 513-520; G. Gutin, A. Yeo, Polynomial approximation algorithms for the TSP and the QAP with a factorial domination number, Discrete Applied Mathematics 119 (1-2) (2002) 107-116], algorithms with large dominance ratio were provided for Max Cut, Maxr-Sat, ATSP, and other problems. All these algorithms share a common property - they provide solutions of quality guaranteed to be not worse than the average solution value. In this paper we show that, in general, this property by itself does not necessarily ensure a good performance in terms of dominance. Specifically, we show that for the MaxSat problem, algorithms with this property might perform poorly in terms of dominance.