Divide and conquer is almost optimal for the bounded-hop MST problem on random euclidean instances

  • Authors:
  • Andrea E. F. Clementi;Miriam Di Ianni;Angelo Monti;Massimo Lauria;Gianluca Rossi;Riccardo Silvestri

  • Affiliations:
  • Dipartimento di Matematica, Università degli Studi di Roma“Tor Vergata”, Roma, Italy;Dipartimento di Matematica, Università degli Studi di Roma“Tor Vergata”, Roma, Italy;Dipartimento di Informatica, Università degli Studi di Roma “La Sapienza”, Roma, Italy;Dipartimento di Informatica, Università degli Studi di Roma “La Sapienza”, Roma, Italy;Dipartimento di Matematica, Università degli Studi di Roma“Tor Vergata”, Roma, Italy;Dipartimento di Informatica, Università degli Studi di Roma “La Sapienza”, Roma, Italy

  • Venue:
  • SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
  • Year:
  • 2005

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Abstract

The d-Dim h-hops MST problem is defined as follows: Given a set S of points in the d-dimensional Euclidean space and s ∈ S, find a minimum-cost spanning tree for S rooted at s with height at most h. We investigate the problem for any constants h and d 0. We prove the first non trivial lower bound on the solution cost for almost all Euclidean instances (i.e. the lower-bound holds with high probability). Then we introduce an easy-to-implement, very fast divide and conquer heuristic and we prove that its solution cost matches the lower bound.