IEICE TRANSACTIONS on Fundamentals
An Optimal Parallel Algorithm for Constructing a Spanning Forest on Trapezoid Graphs
Summary :
Given a simple graph G with n vertices, m edges and k connected components. The spanning forest problem is to find a spanning tree for each connected component of G. This problem has applications to the electrical power demand problem, computer network design, circuit analysis, etc. An optimal parallel algorithm for finding a spanning tree on the trapezoid graph is given by Bera et al., it takes O(log n) time with O(n/log n) processors on the EREW (Exclusive-Read Exclusive-Write) PRAM. Bera et al.'s algorithm is very simple and elegant. Moreover, it can correctly construct a spanning tree when the graph is connected. However, their algorithm can not accept a disconnected graph as an input. Applying their algorithm to a disconnected graph, Concurrent-Write occurs once for each connected component, thus this can not be achieved on EREW PRAM. In this paper we present an O(log n) time parallel algorithm with O(n/log n) processors for constructing a spanning forest on trapezoid graph G on EREW PRAM even if G is a disconnected graph.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E91-A No.9 pp.2296-2300
- Publication Date
- 2008/09/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1093/ietfec/e91-a.9.2296
- Type of Manuscript
- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
- Category
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Hirotoshi HONMA, Shigeru MASUYAMA, "An Optimal Parallel Algorithm for Constructing a Spanning Forest on Trapezoid Graphs" in IEICE TRANSACTIONS on Fundamentals,
vol. E91-A, no. 9, pp. 2296-2300, September 2008, doi: 10.1093/ietfec/e91-a.9.2296.
Abstract: Given a simple graph G with n vertices, m edges and k connected components. The spanning forest problem is to find a spanning tree for each connected component of G. This problem has applications to the electrical power demand problem, computer network design, circuit analysis, etc. An optimal parallel algorithm for finding a spanning tree on the trapezoid graph is given by Bera et al., it takes O(log n) time with O(n/log n) processors on the EREW (Exclusive-Read Exclusive-Write) PRAM. Bera et al.'s algorithm is very simple and elegant. Moreover, it can correctly construct a spanning tree when the graph is connected. However, their algorithm can not accept a disconnected graph as an input. Applying their algorithm to a disconnected graph, Concurrent-Write occurs once for each connected component, thus this can not be achieved on EREW PRAM. In this paper we present an O(log n) time parallel algorithm with O(n/log n) processors for constructing a spanning forest on trapezoid graph G on EREW PRAM even if G is a disconnected graph.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e91-a.9.2296/_p
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@ARTICLE{e91-a_9_2296,
author={Hirotoshi HONMA, Shigeru MASUYAMA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={An Optimal Parallel Algorithm for Constructing a Spanning Forest on Trapezoid Graphs},
year={2008},
volume={E91-A},
number={9},
pages={2296-2300},
abstract={Given a simple graph G with n vertices, m edges and k connected components. The spanning forest problem is to find a spanning tree for each connected component of G. This problem has applications to the electrical power demand problem, computer network design, circuit analysis, etc. An optimal parallel algorithm for finding a spanning tree on the trapezoid graph is given by Bera et al., it takes O(log n) time with O(n/log n) processors on the EREW (Exclusive-Read Exclusive-Write) PRAM. Bera et al.'s algorithm is very simple and elegant. Moreover, it can correctly construct a spanning tree when the graph is connected. However, their algorithm can not accept a disconnected graph as an input. Applying their algorithm to a disconnected graph, Concurrent-Write occurs once for each connected component, thus this can not be achieved on EREW PRAM. In this paper we present an O(log n) time parallel algorithm with O(n/log n) processors for constructing a spanning forest on trapezoid graph G on EREW PRAM even if G is a disconnected graph.},
keywords={},
doi={10.1093/ietfec/e91-a.9.2296},
ISSN={1745-1337},
month={September},}
Copy
TY - JOUR
TI - An Optimal Parallel Algorithm for Constructing a Spanning Forest on Trapezoid Graphs
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2296
EP - 2300
AU - Hirotoshi HONMA
AU - Shigeru MASUYAMA
PY - 2008
DO - 10.1093/ietfec/e91-a.9.2296
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E91-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2008
AB - Given a simple graph G with n vertices, m edges and k connected components. The spanning forest problem is to find a spanning tree for each connected component of G. This problem has applications to the electrical power demand problem, computer network design, circuit analysis, etc. An optimal parallel algorithm for finding a spanning tree on the trapezoid graph is given by Bera et al., it takes O(log n) time with O(n/log n) processors on the EREW (Exclusive-Read Exclusive-Write) PRAM. Bera et al.'s algorithm is very simple and elegant. Moreover, it can correctly construct a spanning tree when the graph is connected. However, their algorithm can not accept a disconnected graph as an input. Applying their algorithm to a disconnected graph, Concurrent-Write occurs once for each connected component, thus this can not be achieved on EREW PRAM. In this paper we present an O(log n) time parallel algorithm with O(n/log n) processors for constructing a spanning forest on trapezoid graph G on EREW PRAM even if G is a disconnected graph.
ER -
English
