Harish R
M170481CS
EFFICIENT COMPUTATION OF MINIMUM SPANNING TREE OF A SET OF
POINTS IN A PLANE
Problem Specification:
Given a set of points in a 2-dimensional plane, a minimum spanning tree is a tree that
connects all the points such that there exists only one path between any pair of vertices. If Prim's
algorithm or Kruskal's algorithm is used, construction of minimum spanning tree takes O(n 2) time
which is not efficient for large values of n.
The base paper [1] describes an algorithm that constructs delaunay triangulation as a
sub-procedure which takes O(n log n) as its running time which is the bottleneck for the overall time
complexity of the algorithm. In this project, I attempt to solve this problem by using 1) a sweepline
algorithm or 2) by using a randomized algorithm to construct delaunay triangulations faster and check
whether the time complexity can be improved.
Input:
X and Y co-ordinates of a set of points in a 2-dimensional euclidean plane
Output:
A minimum spanning tree that connects all the points
Diagrams:
References:
[1] Ge Hong-mei, Xu Chao, Yu Ben-cheng, Design and Analysis of Minimum Spanning Tree in
Euclidean Plane, International Conference on Computational and Information Sciences (2013).
