Performance Evaluation: Ball-Tree and KD-Tree in the
context of MST
Hazarath Munaga
1,1
, Venkata Jarugumalli
1
1
Dept. of Information Technology
University College of Engineering
JNTUK, A.P. India
{hazarath.munaga, venkata.jarugumalli}@gmail.com
Abstract. Now a day’s many algorithms are invented / being inventing to find
the solution for Euclidean Minimum Spanning Tree (EMST) problem, as its
applicability is increasing in much wide range of fields containing spatial /
spatio – temporal data viz. astronomy which consists of millions of spatial data.
To solve this problem, we are presenting a technique by adopting the dual tree
algorithm for finding efficient EMST and experimented on a variety of real
time and synthetic datasets. This paper presents the observed experimental
observations and the efficiency of the dual tree framework, in the context of kd-
tree and ball-tree on spatial datasets of different dimensions.
Keywords: Euclidean Minimum Spanning Tree (EMST), dual Tree, kd-tree,
ball-tree
1 Introduction
Minimum Spanning Tree (hereinafter, MST) is the one of the oldest and most
thoroughly studied problem in computational geometry [1]. The Minimum-weight
Spanning Tree or simply MST problem is one of the well-known optimization
problems for finding minimum weighted spanning tree for both undirected and
directed graphs. MST have many applications in computer design, communication,
transportation and some other problems that can apply directly/indirectly are wireless
network connectivity, clustering and classification of different data namely spatial
data. In literature, several authors proposed a variety of greedy algorithms [2, 3, 4].
The general drawback with these greedy algorithms is that these cannot handle large
amount of data and performance bottleneck will happened and later some more
advanced algorithms are developed to solve this problem [5]. In this paper, authors
evaluated the performance of dual tree algorithmic framework [6] using single linkage
clustering [7] and compared the performance of the dual tree framework in the
context of kd-tree and ball-tree. As per the Ref. [8] theoretically single-linkage
clustering provides optimal clusters.
1
Dr MHM Krishna Prasad, Associate Professor & Head
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