## A new algorithm for the recognition of series parallel graphs (1995)

Venue: | CWI - Centrum voor Wiskunde en Informatica |

Citations: | 7 - 0 self |

### BibTeX

@TECHREPORT{Schoenmakers95anew,

author = {Berry Schoenmakers},

title = {A new algorithm for the recognition of series parallel graphs},

institution = {CWI - Centrum voor Wiskunde en Informatica},

year = {1995}

}

### OpenURL

### Abstract

In this paper we develop a new linear-time algorithm for the recognition of series parallel graphs. The algorithm is based on a succinct representation of series parallel graphs for which the presence of an arc can be tested in constant time; space utilization is linear in the number of vertices. We show how to compute such a representation in linear time from a breadth-first spanning tree. Furthermore, we present a precise condition for the existence of such succinct representations in general, which is, for instance, satisfied by planar graphs.

### Citations

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Citation Context ... to the computation of a maximum matching for a certain bipartite graph with O(n) edges. (A maximum matching can be computed in O((m + n) √ n) time for bipartite graphs of n vertices and m edges, see =-=[6]-=-.) Given a graph G, the bipartite (undirected) graph G ′ = (V ′ , E ′ ) is constructed as follows. The vertex set V ′ consists of c copies of each vertex of G on the one hand, and one copy of each arc... |

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Citation Context ...tion. 1 Introduction The class of series parallel graphs forms a subset of the class of directed multigraphs with a single source and sink. A common definition of this class is as follows (see, e.g., =-=[3, 4, 10]-=-). The graph consisting of two vertices s and t, say, connected by an arc (s, t) is the basic series parallel graph; vertex s is the source and vertex t is the sink. Compound series parallel graphs ca... |

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Citation Context ...tion. 1 Introduction The class of series parallel graphs forms a subset of the class of directed multigraphs with a single source and sink. A common definition of this class is as follows (see, e.g., =-=[3, 4, 10]-=-). The graph consisting of two vertices s and t, say, connected by an arc (s, t) is the basic series parallel graph; vertex s is the source and vertex t is the sink. Compound series parallel graphs ca... |

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Citation Context ...tion. 1 Introduction The class of series parallel graphs forms a subset of the class of directed multigraphs with a single source and sink. A common definition of this class is as follows (see, e.g., =-=[3, 4, 10]-=-). The graph consisting of two vertices s and t, say, connected by an arc (s, t) is the basic series parallel graph; vertex s is the source and vertex t is the sink. Compound series parallel graphs ca... |

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Citation Context ...ted multigraph G, the recognition problem is to determine whether G is series parallel or not. This problem has received quite some attention and several 1slinear-time solutions are known (see, e.g., =-=[9, 10, 11]-=-). Also some parallel recognition algorithms have been presented [5, 4]. Our algorithm compares favourably in simplicity with these known algorithms. For instance, compared to [9, 10], the use of poin... |

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Citation Context ...s parallel or not. This problem has received quite some attention and several 1slinear-time solutions are known (see, e.g., [9, 10, 11]). Also some parallel recognition algorithms have been presented =-=[5, 4]-=-. Our algorithm compares favourably in simplicity with these known algorithms. For instance, compared to [9, 10], the use of pointers is less pronounced. The algorithm is based on a succinct represent... |

2 |
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Citation Context ...ted multigraph G, the recognition problem is to determine whether G is series parallel or not. This problem has received quite some attention and several 1slinear-time solutions are known (see, e.g., =-=[9, 10, 11]-=-). Also some parallel recognition algorithms have been presented [5, 4]. Our algorithm compares favourably in simplicity with these known algorithms. For instance, compared to [9, 10], the use of poin... |