TSP using divide and conquer

Question

I'm solving traveling salesman problem in different ways. I've already solved it using backtracking and greedy algorithms. Now I have to solve it using divide and conquer. I understand how divide and conquer works but I can't understand how I can apply it to this problem. I tried looking for something in google but found almost nothing. I'd be vary grateful to hear some advices. Thank you.

Answer 1

The reason is probably, that TSP is not easily partitioned into independent sub-problems. This is a prerequisite to apply a divide and conquer strategy.

The paper Multilevel Graph Partitioning Scheme to Solve Traveling Salesman Problem describes how to use multilevel graph partitioning. To reduce the overall complexity, a K-Means clustering/partitioning algorithm is used to divide the TSP into multiple parts. In a second stage, each partition is solved separately. As a final step, the combined solution is improved by applying the Lin Kernighan heuristic.