Probabilistic Analysis of Edge Elimination for Euclidean TSP
成果类型：
Article; Early Access
署名作者：
Zhong, Xianghui
署名单位：
University of Bonn
刊物名称：
MATHEMATICS OF OPERATIONS RESEARCH
ISSN/ISSBN：
0364-765X
DOI：
10.1287/moor.2020.0299
发表日期：
2025
关键词：
摘要：
One way to speed up the calculation of optimal traveling salesman problem tours in practice is eliminating edges that are certainly not in the optimal tour as a preprocessing step. In order to do so, several edge elimination approaches have been proposed in the past. In this work, we investigate two of them in the scenario where the input consists of n independently distributed random points in the two-dimensional unit square with density function bounded from above and below by arbitrary positive constants. We show that after the edge elimination procedure of Hougardy and Schroeder, the expected number of remaining edges is Theta(n), whereas after the nonrecursive part of Jonker and Volgenant, the expected number of remaining edges is Theta(n2).