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A feasible family of paths in a connected graph G is a family that contains at least one path between any pair of vertices in G. Any feasible path family defines a convexity on G. Well-known instances are: the geodesics, the induced paths, and all paths. We propose a more general approach for such 'path properties'. We survey a number of results from this… (More)

The simple plant location problem is a well-studied problem in combinatorial optimization. It is one of deciding where to locate a set of plants so that a set of clients can be supplied by them at the minimum cost. This problem often appears as a subproblem in other combinatorial problems. Several branch and bound techniques have been developed to solve… (More)

In this paper we use arc tolerances, instead of arc costs, to improve Branch-and-Bound type algorithms for the Asymmetric Trav-eling Salesman Problem (ATSP). We derive new tighter lower bounds based on exact and approximate bottleneck upper tolerance values of the Assignment Problem (AP). It is shown that branching by tolerances provides a more rational… (More)

The Data Correcting Algorithm is a branch and bound algorithm in which the data of a given problem instance is 'corrected' at each branching in such a way that the new instance will be as close as possible to a polynomially solvable instance and the result satisfies an acceptable accuracy (the difference between optimal and current solution). In this paper… (More)

The selection of entries to be included/excluded in Branch and Bound algorithms is usually done on the basis of cost values. We consider the class of Depth First Search algorithms, and we propose to use upper tolerances to guide the search for optimal solutions. In spite of the fact that it needs time to calculate tolerances, our computational experiments… (More)