English

Optimal Random Matchings, Tours, and Spanning Trees in Hierarchically Separated Trees

Discrete Mathematics 2013-07-29 v1 Combinatorics

Abstract

We derive tight bounds on the expected weights of several combinatorial optimization problems for random point sets of size nn distributed among the leaves of a balanced hierarchically separated tree. We consider {\it monochromatic} and {\it bichromatic} versions of the minimum matching, minimum spanning tree, and traveling salesman problems. We also present tight concentration results for the monochromatic problems.

Keywords

Cite

@article{arxiv.1307.6939,
  title  = {Optimal Random Matchings, Tours, and Spanning Trees in Hierarchically Separated Trees},
  author = {Béla Csaba and Thomas A. Plick and Ali Shokoufandeh},
  journal= {arXiv preprint arXiv:1307.6939},
  year   = {2013}
}

Comments

24 pages, to appear in TCS

R2 v1 2026-06-22T00:58:13.265Z