Abstract
In this paper, we consider the ordered TSP, a variant of the traveling salesman problem with precedence constraints, where the precedence constraints are such that a given subset of vertices has to be visited in some prescribed linear order. We give improved algorithms for the ordered TSP: For the metric case, we present a polynomial-time algorithm that guarantees an approximation ratio of 2.5-2/k, where k is the number of ordered vertices. For near-metric input instances satisfying a @b-relaxed triangle inequality, we improve the ratio to k@b^l^o^g^^2^(^@?^3^k^/^2^@?^+^1^).
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