Approximating the weight of the Euclidean minimum spanning tree in sublinear time

被引：45

作者：

Czumaj, A ^{[1
]}

Ergün, F

Fortnow, L

Magen, A

Newman, I

Rubinfeld, R

Sohler, C

机构：

[1] New Jersey Inst Technol, Dept Comp Sci, Newark, NJ 07102 USA

[2] Simon Fraser Univ, Sch Comp Sci, Burnaby, BC V5A 1S6, Canada

[3] NEC Res, Princeton, NJ 08540 USA

[4] Univ Chicago, Dept Comp Sci, Chicago, IL 60637 USA

[5] Univ Toronto, Dept Comp Sci, Toronto, ON M5S 3G4, Canada

[6] Univ Haifa, Dept Comp Sci, IL-31999 Haifa, Israel

[7] MIT, CSAIL, Cambridge, MA 02139 USA

[8] Univ Paderborn, Heinz Nixdorf Inst, D-33102 Paderborn, Germany

[9] Univ Paderborn, Fac Comp Sci Elect Engn & Math, D-33102 Paderborn, Germany

来源：

SIAM JOURNAL ON COMPUTING | 2005年 / 35卷 / 01期

关键词：

sublinear algorithms; minimum spanning tree;

D O I：

10.1137/S0097539703435297

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We consider the problem of computing the weight of a Euclidean minimum spanning tree for a set of n points in R-d. We focus on the setting where the input point set is supported by certain basic ( and commonly used) geometric data structures that can provide efficient access to the input in a structured way. We present an algorithm that estimates with high probability the weight of a Euclidean minimum spanning tree of a set of points to within 1+epsilon using only (O) over tilde(root n poly(1/epsilon)) queries for constant d. The algorithm assumes that the input is supported by a minimal bounding cube enclosing it, by orthogonal range queries, and by cone approximate nearest neighbor queries.

引用

页码：91 / 109

页数：19

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