Exploring the parallel implementations of the three classical MST algorithms

Minimum spanning tree (MST) is one among the most studied combinatorial problems with practical applications in VLSI layout and routing, wireless communication and distributed networks, current problems in biology and medicine such as cancer detection, medical imaging, and proteomics, and national security and bioterrorism[1]. Since Minimum Spanning Tree (MST) is one of the well-known classical graph problems it finds its application in various fields and many attempts are being done to improve the speed of MST using parallel computing. Most of the previous attempts made were either too complicated to implement or they perform well only on special graphs with regular structure. The widespread adaption of multicore platforms and GPU's has offered the opportunity to explore new implementation techniques for many algorithms that were originally designed for uniprocessors. By formulating new parallel schemes, the programmers would be able to exploit the multiple hardware frameworks offered in today's platforms in a more efficient way. A category of problems among the most challenging to parallelize are the ones that exhibit inherently sequential characteristics. The discovery of the Single Source Shortest Path or the composition of the Minimum Spanning Forest of a given graph falls into this category. This paper is a survey on the different parallel MST algorithms that are implemented on Multicore architectures.