Travelling salesman problem on dilute lattices : visit to a fraction of cities

2014 We study the travelling salesman problem on dilute lattices where the cities are represented by random lattice sites, occupied with concentration p, and the salesman intends to visit a finite fraction f of the total number of cities. The variation of the average optimal travel distance per city L (p, f) against f are investigated here for various values of p. The values of the normalised travel distance per city 03A9 (p, f ) = ~pL (p,f) are shown to be bounded within 03A9E (1,f) = 03A9c(1,f) = 1 for all f and 03A9E (0,0) ~ 0.54, 03A9E (0, 1) ~ 0.75 for Euclidean (E) metric and CC (0, 0) = (4/03C0) 03A9E (0,0) ~ 0.65 and 03A9C (0,1)~(4/03C0) 03A9E (0,1) ~ 0, 95 for Cartesian (C) metric. J. Phys. France 50 (1989) 255-261 1er FEVRIER 1989, : Classification Physics Abstracts 05.50 The travelling salesman problem (TSP), where, given the intercity distances, the salesman has to find out the shortest route for visiting N specified cities at least once, is a well known NP-complete optimisation problem: NP-completeness meaning that all known deterministic algorithims for finding the optimal route require computational Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01989005003025500