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Efficient algorithms for a mixed k-partition problem of graphs without specifying bases

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Graph-Theoretic Concepts in Computer Science (WG 1994)

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

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Abstract

This paper describes efficient algorithms for partitioning a k-edge-connected graph into k edge-disjoint connected subgraphs, each of which has a specified number of elements(vertices and edges). If each subgraph contains the specified element (called base), we call this problem the mixed k-partition problem with bases(called k-PART-WB), otherwise we call it the mixed k-partition problem without bases (called k-PART-WOB). In this paper, we show that k-PART-WB always has a solution for every k-edge-connected graph and we consider the problem without bases and we obtain the following results: (1)for any k≥2, k-PART-WOB can be solved in O(∥V∥√∥V∥log2∥V∥+∥E∥) time for every 4-edge-connected graph G=(V,E), (2)3-PART-WOB can be solved in O(∥V∥2) for every 2-edge-connected graph G=(V,E) and (3)4-PART-WOB can be solved in O(∥E∥2) for every 3-edge-connected graph G=(V,E).

Partially supported by the Grant-in-Aid of Scientific Research of the Ministry of Education, Science and Culture of Japan under Grant: (C)05680271 and the Okawa Institute of Information and Telecommunication(94-11).

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Authors and Affiliations

  1. Nagoya Institute of Technology, Gokiso-cho, Syowa-ku, 466, Nagoya, Japan

    Koichi Wada, Akinari Takaki & Kimio Kawaguchi

Authors
  1. Koichi Wada
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  2. Akinari Takaki
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  3. Kimio Kawaguchi
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Ernst W. Mayr Gunther Schmidt Gottfried Tinhofer

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© 1995 Springer-Verlag Berlin Heidelberg

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Wada, K., Takaki, A., Kawaguchi, K. (1995). Efficient algorithms for a mixed k-partition problem of graphs without specifying bases. 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_58

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  • DOI: https://doi.org/10.1007/3-540-59071-4_58

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59071-2

  • Online ISBN: 978-3-540-49183-5

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