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On Minimum Circular Arrangement

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STACS 2004 (STACS 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2996))

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Abstract

Motivated by a scheduling problem encountered in multicast environments, we study a vertex labelling problem, called Minimum Circular Arrangement (MCA), that requires one to find an embedding of a given weighted directed graph into a discrete circle which minimizes the total weighted arc length. Its decision version is already known to be NP-complete when restricted to sparse weighted instances. We prove that the decision version of even un-weighted MCA is NP-complete in case of sparse as well as dense graphs.

We also consider complementary version of MCA, called MaxCA. We prove that it is MAX-SNP[π] complete and, therefore, has no PTAS unless P=NP. A similar proof technique shows that MCA is MAX-SNP[π]-Hard and hence admits no PTAS as well. Then we prove a conditional lower bound of \(\sqrt{2} - \epsilon\) for MCA approximation under some hardness assumptions, and conclude with a PTAS for MCA on dense instances.

Full version of the paper is available online [12].

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, University of Chicago, Chicago, Illinois, USA

    Murali K Ganapathy

  2. Tata Research Development and Design Centre, Pune, Maharashtra, India

    Sachin P Lodha

Authors
  1. Murali K Ganapathy
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  2. Sachin P Lodha
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Editor information

Editors and Affiliations

  1. Universität Stuttgart, FMI, Germany

    Volker Diekert

  2. LIAFA and the University of Paris 7, Denis Diderot,  

    Michel Habib

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Ganapathy, M.K., Lodha, S.P. (2004). On Minimum Circular Arrangement. In: Diekert, V., Habib, M. (eds) STACS 2004. STACS 2004. Lecture Notes in Computer Science, vol 2996. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24749-4_35

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  • DOI: https://doi.org/10.1007/978-3-540-24749-4_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21236-2

  • Online ISBN: 978-3-540-24749-4

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