Lower bounds for testing Euclidean Minimum Spanning Trees

Oren Ben-Zwi, Oded Lachish, Ilan Newman

Research output: Contribution to journalArticlepeer-review

Abstract

The Euclidean Minimum Spanning Tree problem is to decide whether a given graph G = (P, E) on a set of points in the two-dimensional plane is a minimum spanning tree with respect to the Euclidean distance. Czumaj et al. [A. Czumaj, C. Sohler, M. Ziegler, Testing Euclidean Minimum Spanning Trees in the plane, Unpublished, Part II of ESA 2000 paper, downloaded from http://web.njit.edu/~czumaj/] gave a 1-sided-error non-adaptive property-tester for this task of query complexity over(O, ̃) (sqrt(n)). We show that every non-adaptive (not necessarily 1-sided-error) property-tester for this task has a query complexity of Ω (sqrt(n)), implying that the test in [A. Czumaj, C. Sohler, M. Ziegler, Testing Euclidean Minimum Spanning Trees in the plane, Unpublished, Part II of ESA 2000 paper, downloaded from http://web.njit.edu/~czumaj/] is of asymptotically optimal complexity. We further prove that every adaptive property-tester has query complexity of Ω (n1 / 3). Those lower bounds hold even when the input graph is promised to be a bounded degree tree.

Original languageEnglish
Pages (from-to)219-225
Number of pages7
JournalInformation Processing Letters
Volume102
Issue number6
DOIs
StatePublished - 15 Jun 2007

Bibliographical note

Funding Information:
✩ Research supported in part by grant 55/03 from the Israel Science Foundation. * Corresponding author. E-mail addresses: [email protected] (O. Ben-Zwi), [email protected] (O. Lachish), [email protected] (I. Newman).

Keywords

  • Computational geometry
  • Graph algorithms
  • Randomized algorithms

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications

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