Exact solution of large-scale, asymmetric traveling salesman problems
ACM Transactions on Mathematical Software (TOMS)
Phase Transitions and Backbones of 3-SAT and Maximum 3-SAT
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Backbones in optimization and approximation
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Cut-and-solve: an iterative search strategy for combinatorial optimization problems
Artificial Intelligence
Phase transitions and backbones of the asymmetric traveling salesman problem
Journal of Artificial Intelligence Research
The backbone of the travelling salesperson
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Cut-and-solve: An iterative search strategy for combinatorial optimization problems
Artificial Intelligence
Improving the efficiency of Helsgaun's Lin-Kernighan Heuristic for the symmetric TSP
CAAN'07 Proceedings of the 4th conference on Combinatorial and algorithmic aspects of networking
A backbone-based co-evolutionary heuristic for partial MAX-SAT
EA'05 Proceedings of the 7th international conference on Artificial Evolution
Extracting elite pairwise constraints for clustering
Neurocomputing
A backbone based TSP heuristic for large instances
Journal of Heuristics
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Backbone variables are the elements that are common to all optimal solutions of a problem instance. We call variables that are absent from every optimal solution fat variables. Identification of backbone and fat variables is a valuable asset when attempting to solve complex problems. In this paper, we demonstrate a method for identifying backbones and fat. Our method is based on an intuitive concept, which we refer to as limit crossing. Limit crossing occurs when we force the lower bound of a graph problem to exceed the upper bound by applying the lower-bound function to a constrained version of the graph. A desirable feature of this procedure is that it uses approximation functions to derive exact information about optimal solutions. In this paper, we prove the validity of the limit-crossing concept as well as other related properties. Then we exploit limit crossing and devise a pre-processing tool for discovering backbone and fat arcs for various instances of the Asymmetric Traveling Salesman Problem (ATSP). Our experimental results demonstrate the power of the limit-crossing method. We compare our pre-processor with the Carpaneto, Dell'Amico, and Toth pre-processor for several different classes of ATSP instances and reveal dramatic performance improvements.