Summary: On the Maximum Scatter TSP \Lambda
Esther M. Arkin y YiJen Chiang z Joseph S. B. Mitchell x
Steven S. Skiena -- TaeCheon Yang k
December 27, 1996
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 nearneighbors along the tour or path.
Keywords: maximum scatter TSP, Hamiltonian cycle/path, approximation algorithms, opti
\Lambda An extended abstract of this paper will be presented at the 8th ACMSIAM Symposium on Discrete Algorithms,
New Orleans, Louisiana, January, 1997.
y Department of Applied Mathematics and Statistics, SUNY Stony Brook, NY 117943600; firstname.lastname@example.org.
Supported in part by NSF Grant CCR9504192.