**Combinatorial and Discrete Geometry: Sheet K**

Prepared by:

Joseph Malkevitch

Department of Mathematics and Computer Studies

York College (CUNY)

Jamaica, New York 11451

email: joeyc@cunyvm.cuny.edu

web page: http://www.york.cuny.edu/~malk

1. i. Use A. Nearest neighbor B. Sorted edges in attempting to get a relatively good or optimal solution to the TSP problems below. ii. Are any of the solutions you get optimal? Use Home = 0 as the start of your tour.

Since nearest neighbor can be computed so easily, try finding the nearest neighbor tour from each of the vertices of the graph in turn. Do you get the same tour each time? What idea does this suggest about finding a method which might find a near optimal tour for a TSP quickly?