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International Workshop on Graph-Theoretic Concepts in Computer Science

WG 1994: Graph-Theoretic Concepts in Computer Science pp 269–281Cite as

Measuring the distance to series-parallelity by path expressions

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 903))

Abstract

Many graph and network problems are easily solved in the special case of series-parallel networks, but are highly intractable in the general case. This paper considers two complexity measures of two-terminal directed acyclic graphs (st-dags) describing the “distance” of an st-dag from series-parallelity. The two complexity measures are the factoring complexity ψ(G) and the reduction complexity μ(G). Bein, Kamburowski, and Stallmann [3] have shown that ψ(G)≤μ(G)≤n−3, where G is an st-dag with n nodes. They conjectured that ψ(G)=μ(G). This paper gives a proof for this conjecture.

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Authors and Affiliations

  1. Fachbereich Mathematik, TU Berlin, Sekr. MA 6-1, Strasse des 17. Juni 136, D-10623, Berlin

    Valeska Naumann

Authors
  1. Valeska Naumann
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Ernst W. Mayr Gunther Schmidt Gottfried Tinhofer

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© 1995 Springer-Verlag Berlin Heidelberg

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Naumann, V. (1995). Measuring the distance to series-parallelity by path expressions. In: Mayr, E.W., Schmidt, G., Tinhofer, G. (eds) Graph-Theoretic Concepts in Computer Science. WG 1994. Lecture Notes in Computer Science, vol 903. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59071-4_54

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  • DOI: https://doi.org/10.1007/3-540-59071-4_54

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59071-2

  • Online ISBN: 978-3-540-49183-5

  • eBook Packages: Springer Book Archive

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