### Abstract

A processor array with a reconfigurable bus system is a parallel computation model that consists of a processor array and a reconfigurable bus system. In this paper, a constant-time algorithm is proposed on this model for finding the cycles in an undirected graph. We can use this algorithm to decide whether a specified edge belongs to the minimum spanning tree of the graph or not. This cycle-finding algorithm is designed on a two-dimensional n × n processor array with a reconfigurable bus system, where n is the number of vertices in the graph. Based on this cycle-finding algorithm, the minimum spanning tree problem and the spanning tree problem can be solved in O(1) time by using fewer processors than before, O(n × m × n) and O(n^{3}) processors respectively. This is a substantial improvement over previous known results. Moreover, we also propose two constant-time algorithms for solving the minimum spanning tree verification problem and spanning tree verification problem by using O(n^{3}) and O(n^{2}) processors, respectively.

Original language | English |
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Pages (from-to) | 174-186 |

Number of pages | 13 |

Journal | Computer Journal |

Volume | 45 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2002 May 2 |

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### ASJC Scopus subject areas

- Computer Science(all)

### Cite this

**Constant-time algorithms for minimum spanning tree and related problems on processor array with reconfigurable bus systems.** / Pan, Tien Tai; Lin, Shun Shii.

Research output: Contribution to journal › Article

*Computer Journal*, vol. 45, no. 2, pp. 174-186. https://doi.org/10.1093/comjnl/45.2.174

}

TY - JOUR

T1 - Constant-time algorithms for minimum spanning tree and related problems on processor array with reconfigurable bus systems

AU - Pan, Tien Tai

AU - Lin, Shun Shii

PY - 2002/5/2

Y1 - 2002/5/2

N2 - A processor array with a reconfigurable bus system is a parallel computation model that consists of a processor array and a reconfigurable bus system. In this paper, a constant-time algorithm is proposed on this model for finding the cycles in an undirected graph. We can use this algorithm to decide whether a specified edge belongs to the minimum spanning tree of the graph or not. This cycle-finding algorithm is designed on a two-dimensional n × n processor array with a reconfigurable bus system, where n is the number of vertices in the graph. Based on this cycle-finding algorithm, the minimum spanning tree problem and the spanning tree problem can be solved in O(1) time by using fewer processors than before, O(n × m × n) and O(n3) processors respectively. This is a substantial improvement over previous known results. Moreover, we also propose two constant-time algorithms for solving the minimum spanning tree verification problem and spanning tree verification problem by using O(n3) and O(n2) processors, respectively.

AB - A processor array with a reconfigurable bus system is a parallel computation model that consists of a processor array and a reconfigurable bus system. In this paper, a constant-time algorithm is proposed on this model for finding the cycles in an undirected graph. We can use this algorithm to decide whether a specified edge belongs to the minimum spanning tree of the graph or not. This cycle-finding algorithm is designed on a two-dimensional n × n processor array with a reconfigurable bus system, where n is the number of vertices in the graph. Based on this cycle-finding algorithm, the minimum spanning tree problem and the spanning tree problem can be solved in O(1) time by using fewer processors than before, O(n × m × n) and O(n3) processors respectively. This is a substantial improvement over previous known results. Moreover, we also propose two constant-time algorithms for solving the minimum spanning tree verification problem and spanning tree verification problem by using O(n3) and O(n2) processors, respectively.

UR - http://www.scopus.com/inward/record.url?scp=0036240611&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036240611&partnerID=8YFLogxK

U2 - 10.1093/comjnl/45.2.174

DO - 10.1093/comjnl/45.2.174

M3 - Article

AN - SCOPUS:0036240611

VL - 45

SP - 174

EP - 186

JO - Computer Journal

JF - Computer Journal

SN - 0010-4620

IS - 2

ER -