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Approximating the Rainbow – Better Lower and Upper Bounds

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Computing and Combinatorics (COCOON 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7434))

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Abstract

In this paper we study the minimum rainbow subgraph problem, motivated by applications in bioinformatics. The input of the problem consists of an undirected graph where each edge is coloured with one of the p possible colors. The goal is to find a subgraph of minimum order (i.e. minimum number of vertices) which has precisely one edge from each color class.

In this paper we show a \(\max(\sqrt{2p}, \min_q(q + \frac{\Delta}{e^{p q^2/\Delta n}}))\)-approximation algorithm using LP rounding, where Δ is the maximum degree in the input graph. In particular, this is a \(\max(\sqrt{2n}, \sqrt{2\Delta\ln{\Delta}})\)-approximation algorithm. On the other hand we prove that there exists a constant c such that the minimum rainbow subgraph problem does not have a cln Δ-approximation, unless NP ⊆ TIME(n O(loglogn)).

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Authors and Affiliations

  1. Department of Communications & Networking, Aalto University School of Electrical Engineering, Aalto, Finland

    Alexandru Popa

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  1. Alexandru Popa
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Editor information

Editors and Affiliations

  1. School of IT, University of Sydney, Building J12, 2006, Sydney, NSW, Australia

    Joachim Gudmundsson , Julián Mestre  & Taso Viglas ,  & 

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Popa, A. (2012). Approximating the Rainbow – Better Lower and Upper Bounds. In: Gudmundsson, J., Mestre, J., Viglas, T. (eds) Computing and Combinatorics. COCOON 2012. Lecture Notes in Computer Science, vol 7434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32241-9_17

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  • DOI: https://doi.org/10.1007/978-3-642-32241-9_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32240-2

  • Online ISBN: 978-3-642-32241-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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