The on-line asymmetric traveling salesman problem

The On-line Asymmetric Traveling Salesman Problem

We consider two on-line versions of the asymmetric traveling salesman problem with triangle inequality. For the homing version, in which the salesman is required to return in the city where it started from, we give a 3+ √ 5 2 -competitive algorithm and prove that this is best possible. For the nomadic version, the on-line analogue of the shortest asymmetric hamiltonian path problem, we show tha...

Asymmetric Traveling Salesman Problem

The asymmetric traveling salesman problem (ATSP) is one of the most fundamental problems in combinatorial optimization. An instance of ATSP is a directed complete graph G = (V,E) with edge weights w : E → N that satisfy the triangle inequality, i. e., w(a, c) ≤ w(a, b) +w(b, c) for all distinct vertices a, b, c ∈ V . The goal is to find a Hamiltonian cycle of minimum weight. The weight of a Ham...

The Asymmetric Traveling Salesman Problem

The Asymmetric Quadratic Traveling Salesman Problem

The quadratic traveling salesman problem asks for a tour of min-imal costs where the costs are associated with each two arcs that are traversedin succession. This structure arises, e. g., if the succession of two arcs representsthe costs of loading processes in transport networks or a switch between dif-ferent technologies in communication networks. Based on a quadratic integer<...

On the Integrality Ratio for the Asymmetric Traveling Salesman Problem

We improve the lower bound on the integrality ratio of the Held-Karp bound for asymmetric TSP with triangle inequality from 4/3 to 2. 1. Introduction. The traveling salesman problem (TSP)—the problem of finding a minimum cost tour through a set of cities—is the most celebrated combinatorial optimization problem. It is often used as a testbed for novel ideas, as was the case for Adleman's molecu...