Scholarlink

Given a weighted graph for TSP, a corresponding frequency graph is computed using the optimal paths with given endpoints (optimal paths for short). The edges in optimal Hamiltonian cycle (OHC) show special frequencies much bigger than those of most other edges. The average frequencies for edges and paths in OHC are studied as a frequency graph is computed based upon the frequency quadrilaterals or optimal 4-vertex paths. The lower frequency bounds for an OHC edge, two and three immediate OHC edges are proven to be 35/9, 22/3 and 35/3, respectively in the worst average case. Moreover, the average frequency for all OHC edges is bigger than 4 and it is bigger than 13/3 for big and large TSP. These findings are verified with experimental results.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

The Frequency Bounds for Travelling Salesman Problem Based on Frequency Quadrilaterals

  • 会议论文

  • 发表日期：

    2025年

查看全文
  • Yong Wang,
  • WenFa Zheng

摘要

Given a weighted graph for TSP, a corresponding frequency graph is computed using the optimal paths with given endpoints (optimal paths for short). The edges in optimal Hamiltonian cycle (OHC) show special frequencies much bigger than those of most other edges. The average frequencies for edges and paths in OHC are studied as a frequency graph is computed based upon the frequency quadrilaterals or optimal 4-vertex paths. The lower frequency bounds for an OHC edge, two and three immediate OHC edges are proven to be 35/9, 22/3 and 35/3, respectively in the worst average case. Moreover, the average frequency for all OHC edges is bigger than 4 and it is bigger than 13/3 for big and large TSP. These findings are verified with experimental results.