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 [A. Czumaj, C. Sohler, M. Ziegler, Testing Euclidean Minimum Spanning Trees in the plane, Unpublished, Part II of ESA 2000 paper, downloaded from http://web.njit.edu/~czumaj/] gave a 1-sided-error non-adaptive property-tester for this task of query complexity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implying that the test in [A. Czumaj, C. Sohler, M. Ziegler, Testing Euclidean Minimum Spanning Trees in the plane, Unpublished, Part II of ESA 2000 paper, downloaded from http://web.njit.edu/~czumaj/] is of asymptotically optimal complexity.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.
Bibliographical noteFunding Information:
✩ Research supported in part by grant 55/03 from the Israel Science Foundation. * Corresponding author. E-mail addresses: firstname.lastname@example.org (O. Ben-Zwi), email@example.com (O. Lachish), firstname.lastname@example.org (I. Newman).
- Computational geometry
- Graph algorithms
- Randomized algorithms
ASJC Scopus subject areas
- Theoretical Computer Science
- Signal Processing
- Information Systems
- Computer Science Applications