Optimal random matchings, tours, and spanning trees in hierarchically separated trees

Béla Csaba, Thomas A. Plick, Ali Shokoufandeh
2013 Theoretical Computer Science  
We derive tight bounds on the expected weights of several combinatorial optimization problems for random point sets of size n distributed among the leaves of a balanced hierarchically separated tree. We consider monochromatic and bichromatic versions of the minimum matching, minimum spanning tree, and traveling salesman problems. We also present tight concentration results for the monochromatic problems.
doi:10.1016/j.tcs.2013.05.021 fatcat:lfi5mslmybatznghne53d7kc6e