Filomat 2018 Volume 32, Issue 5, Pages: 1697-1702
https://doi.org/10.2298/FIL1805697W
Full text ( 226 KB)
A quick method to compute sparse graphs for traveling salesman problem using random frequency quadrilaterals
Wang Yong
Traveling salesman problem (TSP) is extensively studied in combinatorial
optimization and computer science. This paper gives a quick method to
compute the sparse graphs for TSP based on the random frequency
quadrilaterals so as to reduce the TSP on the complete graph to the TSP on
the sparse graphs. 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 the frequency below the two frequency thresholds and generate the
sparse graphs for TSP. The experimental results show we compute the sparse
graphs for these TSP instances in the TSPLIB.
Keywords: traveling salesman problem, sparse graph, frequency quadrilateral