Operations, Information and Decisions Papers
Document Type
Conference Paper
Date of this Version
6-1992
Publication Source
Proceeding SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Start Page
344
Last Page
349
DOI
10.1145/142675.142745
Abstract
It is proved that there are constants c1, c2, and c3 such that for any set S of n points in the unit square and for any minimum-lengths of T of S (1) the sum of squares of the edge lengths of T is bounded by c1 log n, (2) the sum of edge lengths of any subset E of T is bounded by c2|E|1/2, and (3) the number of edges having length t or greater in T is at most c3/t2. The second and third bounds are independent of the number of points in S, as well as their locations. Extensions to dimensions d>2 are also sketched. The presence of the logarithmic term in (1) is engaging because such a term is not needed in the case of the minimum spanning tree and several analogous problems, and, furthermore, we know that there always exists some tour of S (which perhaps does not have minimal length) for which the sum of squared edges is bounded independently of n.
Recommended Citation
Snyder, T. L., & Steele, J. M. (1992). A Priori Inequalities for the Euclidean Traveling Salesman. Proceeding SCG '92 Proceedings of the eighth annual symposium on Computational geometry, 344-349. http://dx.doi.org/10.1145/142675.142745
Date Posted: 27 November 2017