Modern heuristic techniques for combinatorial problems
Modern heuristic techniques for combinatorial problems
Modern heuristic techniques for combinatorial problems
New results on the computation of median orders
Proceedings of an international symposium on Graphs and combinatorics
Local Search in Combinatorial Optimization
Local Search in Combinatorial Optimization
How to Choose According to Partial Evaluations?
IPMU'94 Selected papers from the 5th International Conference on Processing and Management of Uncertainty in Knowledge-Based Systems, Advances in Intelligent Computing
Preference aggregation in group recommender systems for committee decision-making
Proceedings of the third ACM conference on Recommender systems
Learning linear ordering problems for better translation
EMNLP '09 Proceedings of the 2009 Conference on Empirical Methods in Natural Language Processing: Volume 2 - Volume 2
Note: A tournament of order 14 with disjoint Banks and Slater sets
Discrete Applied Mathematics
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The linear ordering problem consists in finding a linear order at minimum remoteness from a weighted tournament T, the remoteness being the sum of the weights of the arcs that we must reverse in T to transform it into a linear order. This problem, also known as the search of a median order, or of a maximum acyclic subdigraph, or of a maximum consistent set, or of a minimum feedback arc set, is NP-hard; when all the weights of T are equal to 1, the linear ordering problem is the same as Slater's problem. In this paper, we describe the principles and the results of an exact method designed to solve the linear ordering problem for any weighted tournament. This method, of which the corresponding software is freely available at the URL address http://www.enst.fr/~charon/tournament/median.html, is based upon a branch-and-bound search with a Lagrangean relaxation as the evaluation function and a noising method for computing the initial bound. Other components are designed to reduce the BB-search-tree.