Mathematical Programming Manuscript No. Traveling Salesman Games with the Monge Property ?
نویسنده
چکیده
Several works indicate the relationship between well-solved combinatorial optimization problems and the core non-emptiness of cooperative games associated with them. In this paper, we consider the core of symmetric traveling salesman games and relate it with well-solved cases of traveling salesman problems. We show that the core of a traveling salesman game in which the distance matrix is a symmetric Monge matrix is non-empty. Also we show that a traveling salesman game in which the distance matrix is a Kalmanson matrix is submodular. Moreover, we show that the problem of testing the core non-emptiness of a given traveling salesman game is NP-hard.
منابع مشابه
Traveling salesman games with the Monge property
Several works have indicated the relationships between polynomially solvable combinatorial optimization problems and the core non-emptiness of cooperative games associated with them, and between intractable combinatorial optimization problems and the hardness of the problem to decide the core non-emptiness of the associated games. In this paper, we study the core of a traveling salesman game, w...
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