A Quick Method to Compute Sparse Graphs for Traveling Salesman Problem Using Random Frequency Quadrilaterals

Abstract

Traveling salesman problem (TSP) is extensively studied in combinatorial optimization and computer science. This paper gives a quick method to compute sparse graphs for TSP based on random frequency quadrilaterals so as to reduce the TSP on the complete graph to the TSP on the sparse graph. When we choose N frequency quadrilaterals containing an edge e to compute its total frequency, the frequency of e in the optimal Hamiltonian cycle will be bigger than that of most of the other edges. We fix N to compute the frequency of each edge and the computation time of the quick method is O(n²). We suggest two frequency thresholds to trim the edges with frequency below the two frequency thresholds and generate the sparse graphs. The experimental results show we compute the sparse graphs for these TSP instances.