On the Maximum Scatter TSP

. We study the problem of computing a Hamiltonian tour (cycle) or path on a set of points in order to maximize the minimum edge length in the tour or path. This "maximum scatter" TSP is closely related to the bottleneck TSP, and is motivated by applications in manufacturing (e.g., sequencing of rivet operations) and medical imaging. In this paper, we give the first algorithmic study of these problems, including complexity results, approximation algorithms, and exact algorithms for special cases. In an attempt to model more accurately the real problems that arise in practice, we also generalize the basic problem to consider a more general measure of "scatter" in which points on a tour or path should be far not only from their immediate predecessor and successor, but also from other near-neighbors along the tour or path. Key words. traveling salesperson problem, maximum scatter TSP, bottleneck TSP, Hamiltonian cycle/path, approximation algorithms, matching, optimization, Posa conjecture..