Encyclopedia of Algorithms

2008 Edition
| Editors: Ming-Yang Kao

Parallel Connectivity and Minimum Spanning Trees

2001; Chong, Han, Lam
  • Tak-Wah Lam
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30162-4_280

Keywords and Synonyms

EREW PRAM algorithms for finding connected components and minimum spanning trees     

Problem Definition

Given a weighted undirected graph G with n vertices and m edges, compute a minimum spanning tree (or spanning forest) of G on a parallel random access machine (PRAM) without concurrent write capability.

A minimum spanning tree of a graph is a spanning tree with the smallest possible sum of edge weights. Parallel random access machine (PRAM) is an abstract model for designing parallel algorithms and understanding the power of parallelism. In this model, processors (each being a random access machine) work in a synchronous manner and communicate through a shared memory. PARM can be further classified according to whether it is allowed for more than one processor to read and write into the same shared memory location simultaneously. The strongest model is CRCW (concurrent-read, concurrent-write) PRAM, and the weakest is EREW (exclusive-read,...

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Recommended Reading

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    Pettie, S. Ramachandran, V.: An Optimal Minimum Spanning Tree Algorithm. J. ACM 49(1), 16–34 (2002)MathSciNetGoogle Scholar
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    Pettie, S., Ramachandran, V.: A randomized time-work optimal parallel algorithm for finding a minimum spanning forest. SIAM J. Comput. 31(6), 1879–1895 (2002)MathSciNetGoogle Scholar
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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Tak-Wah Lam
    • 1
  1. 1.Department of Computer ScienceUniversity of Hong KongHong KongChina