Lower bounds for testing Euclidean Minimum Spanning Trees
نویسندگان
چکیده
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, Sohler, and Ziegler [2] gave a 1-sided-error non-adaptive property-tester for this task of query complexity Õ( √ n). We show that every non-adaptive (not necessarily 1-sided-error) property-tester for this task has a query complexity of Ω( √ n), thus, [2] test is of best complexity. We further prove that every adaptive property-tester has query complexity of Ω(n). Those lower bounds hold even when the input graph is promised to be a bounded degree tree.
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عنوان ژورنال:
- Inf. Process. Lett.
دوره 102 شماره
صفحات -
تاریخ انتشار 2007