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This paper is motivated by operating self service transport systems that flourish nowadays. In cities where such systems have been set up with bikes, trucks travel to maintain a suitable number of bikes per station. It is natural to study a version of the C-delivery TSP defined by Chalasani and Motwani in which, unlike their definition, C is part of the… (More)

We study the weighted circuit constraint in the context of constraint programming. It appears as a substructure in many practical applications, particularly routing problems. We propose a domain filtering algorithm for the weighted circuit constraint that is based on the 1-tree relaxation of Held and Karp. In addition, we study domain filtering based on an… (More)

We introduce an algorithm which solves mean payoff games in polynomial time on average, assuming the distribution of the games satisfies a flip invariance property on the set of actions associated with every state. The algorithm is a tropical analogue of the shadow-vertex simplex algorithm, which solves mean payoff games via linear feasibility problems over… (More)

We develop a tropical analogue of the simplex algorithm for linear programming. In particular, we obtain a combinatorial algorithm to perform one tropical pivoting step, including the computation of reduced costs, in O(n(m + n)) time, where m is the number of constraints and n is the dimension. 1. Introduction. The tropical semiring (T, ⊕,) is the set T = R… (More)

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