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International Symposium on Parameterized and Exact Computation

IPEC 2010: Parameterized and Exact Computation pp 228–238Cite as

Proper Interval Vertex Deletion

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6478))

Abstract

Deleting a minimum number of vertices from a graph to obtain a proper interval graph is an NP-complete problem. At WG 2010 van Bevern et al. gave an O((14k + 14)k + 1 kn 6) time algorithm by combining iterative compression, branching, and a greedy algorithm. We show that there exists a simple greedy O(n + m) time algorithm that solves the Proper Interval Vertex Deletion problem on \(\{claw,net,\allowbreak tent,\allowbreak C_4,C_5,C_6\}\)-free graphs. Combining this with branching on the forbidden structures \(claw,net,tent,\allowbreak C_4,C_5,\) and C 6 enables us to get an O(kn 6 6k) time algorithm for Proper Interval Vertex Deletion, where k is the number of deleted vertices.

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Authors and Affiliations

  1. Department of Informatics, University of Bergen, N-5020, Bergen, Norway

    Yngve Villanger

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  1. Yngve Villanger
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Editors and Affiliations

  1. The Institute of Mathematical Sciences, Chennai, India

    Venkatesh Raman

  2. The Institute of Mathematical Sciences, 600113, Chennai, India

    Saket Saurabh

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Villanger, Y. (2010). Proper Interval Vertex Deletion. In: Raman, V., Saurabh, S. (eds) Parameterized and Exact Computation. IPEC 2010. Lecture Notes in Computer Science, vol 6478. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17493-3_22

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  • DOI: https://doi.org/10.1007/978-3-642-17493-3_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17492-6

  • Online ISBN: 978-3-642-17493-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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