## Minimum-Cost Spanning Tree as a Path-Finding Problem (1994)

Venue: | Information Processing Letters |

Citations: | 18 - 0 self |

### BibTeX

@ARTICLE{Maggs94minimum-costspanning,

author = {Bruce M. Maggs and Serge A. Plotkin},

title = {Minimum-Cost Spanning Tree as a Path-Finding Problem},

journal = {Information Processing Letters},

year = {1994},

volume = {26},

pages = {291--293}

}

### Years of Citing Articles

### OpenURL

### Abstract

In this paper we show that minimum-cost spanning tree is a special case of the closed semiring path-finding problem. This observation gives us a non-recursive algorithm for finding minimumcost spanning trees on mesh-connected computers that has the same asymptotic running time but is much simpler than the previous recursive algorithms.

### Citations

2446 | The Design and Analysis of Computer Algorithms - Aho, Hopcroft, et al. - 1974 |

603 | Data Structures and Networks Algorithms - Tarjan - 1983 |

374 |
Representation of events in nerve nets and finite automata
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(Show Context)
Citation Context ... of the closed semiring path-finding problem [1, sections 5.6--5.9]. For a graph of n vertices, the path-finding problem can be solved sequentially in O(n 3 ) steps by a dynamic programming algorithm =-=[7, 12]-=- of which the algorithms of Floyd [5] and Warshall [15] are special cases. This dynamic programming algorithm has a well known O(n) step implementation on an n \Theta n mesh-connected computer [2, 3, ... |

351 |
Algorithm 97: Shortest path
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- 1962
(Show Context)
Citation Context ...lem [1, sections 5.6--5.9]. For a graph of n vertices, the path-finding problem can be solved sequentially in O(n 3 ) steps by a dynamic programming algorithm [7, 12] of which the algorithms of Floyd =-=[5]-=- and Warshall [15] are special cases. This dynamic programming algorithm has a well known O(n) step implementation on an n \Theta n mesh-connected computer [2, 3, 4, 6, 13]. Previously known minimum-c... |

200 | A theorem on boolean matrices
- Warshall
- 1962
(Show Context)
Citation Context ...5.6--5.9]. For a graph of n vertices, the path-finding problem can be solved sequentially in O(n 3 ) steps by a dynamic programming algorithm [7, 12] of which the algorithms of Floyd [5] and Warshall =-=[15]-=- are special cases. This dynamic programming algorithm has a well known O(n) step implementation on an n \Theta n mesh-connected computer [2, 3, 4, 6, 13]. Previously known minimum-cost spanning tree ... |

153 |
Optimizing Synchronous Systems
- Leiserson, Saxe
- 1983
(Show Context)
Citation Context ...w can broadcast a value to the other elements of the row in a single step. This type of broadcast can be simulated by a mesh without this capability by slowing the algorithm down by a constant factor =-=[8, 9, 10]-=-. The algorithm proceeds as follows. We assume that the input graph is given in the form of a matrix of edge costs C 0 which enters row-by-row through the top of the mesh. Matrix row i is modified as ... |

113 |
Optimizing synchronous circuitry by retiming
- Leiserson, Rose, et al.
- 1983
(Show Context)
Citation Context ...w can broadcast a value to the other elements of the row in a single step. This type of broadcast can be simulated by a mesh without this capability by slowing the algorithm down by a constant factor =-=[8, 9, 10]-=-. The algorithm proceeds as follows. We assume that the input graph is given in the form of a matrix of edge costs C 0 which enters row-by-row through the top of the mesh. Matrix row i is modified as ... |

94 |
Regular Expressions and State Graphs for Automata
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- 1960
(Show Context)
Citation Context ... of the closed semiring path-finding problem [1, sections 5.6--5.9]. For a graph of n vertices, the path-finding problem can be solved sequentially in O(n 3 ) steps by a dynamic programming algorithm =-=[7, 12]-=- of which the algorithms of Floyd [5] and Warshall [15] are special cases. This dynamic programming algorithm has a well known O(n) step implementation on an n \Theta n mesh-connected computer [2, 3, ... |

92 |
Parallel matrix and graph algorithms
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(Show Context)
Citation Context ...[7, 12] of which the algorithms of Floyd [5] and Warshall [15] are special cases. This dynamic programming algorithm has a well known O(n) step implementation on an n \Theta n mesh-connected computer =-=[2, 3, 4, 6, 13]-=-. Previously known minimum-cost spanning tree algorithms for the mesh [2, 11] are based on the recursive algorithm of Boruvka (also attributed to Sollin) [14, pp. 71--83], which is complicated to impl... |

34 |
Direct VLSI implementation of combinatorial algorithms
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(Show Context)
Citation Context ...[7, 12] of which the algorithms of Floyd [5] and Warshall [15] are special cases. This dynamic programming algorithm has a well known O(n) step implementation on an n \Theta n mesh-connected computer =-=[2, 3, 4, 6, 13]-=-. Previously known minimum-cost spanning tree algorithms for the mesh [2, 11] are based on the recursive algorithm of Boruvka (also attributed to Sollin) [14, pp. 71--83], which is complicated to impl... |

17 |
Graph problems on a mesh-connected processor array
- Atallah, Kosaraju
- 1984
(Show Context)
Citation Context ...[7, 12] of which the algorithms of Floyd [5] and Warshall [15] are special cases. This dynamic programming algorithm has a well known O(n) step implementation on an n \Theta n mesh-connected computer =-=[2, 3, 4, 6, 13]-=-. Previously known minimum-cost spanning tree algorithms for the mesh [2, 11] are based on the recursive algorithm of Boruvka (also attributed to Sollin) [14, pp. 71--83], which is complicated to impl... |

9 |
Cellular Arrays for the Solution of Graph Problems
- Levitt, Kautz
- 1972
(Show Context)
Citation Context ... dynamic programming algorithm has a well known O(n) step implementation on an n \Theta n mesh-connected computer [2, 3, 4, 6, 13]. Previously known minimum-cost spanning tree algorithms for the mesh =-=[2, 11]-=- are based on the recursive algorithm of Boruvka (also attributed to Sollin) [14, pp. 71--83], which is complicated to implement. For example, the algorithm of [2] achieves O(n) steps by reducing the ... |

7 |
The parallel recognition of classes of graphs
- Scoy
- 1980
(Show Context)
Citation Context |

2 |
An Implementation of Warshall's Algorithm for Transitive Closure on a Cellular Computer
- Christopher
- 1973
(Show Context)
Citation Context |

1 |
Introduction to the Theory of Networks, Parallel Computation and VLSI Design. Unpublished manuscript
- Leighton
(Show Context)
Citation Context ...w can broadcast a value to the other elements of the row in a single step. This type of broadcast can be simulated by a mesh without this capability by slowing the algorithm down by a constant factor =-=[8, 9, 10]-=-. The algorithm proceeds as follows. We assume that the input graph is given in the form of a matrix of edge costs C 0 which enters row-by-row through the top of the mesh. Matrix row i is modified as ... |