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Improved Parameterized Algorithms for Network Query Problems

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Parameterized and Exact Computation (IPEC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8894))

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Abstract

In the Partial Information Network Query (PINQ) problem, we are given a host graph \(H\), and a pattern \(\mathcal P\) whose topology is partially known. We seek a subgraph of \(H\) that resembles \(\mathcal{P}\). PINQ is a generalization of Subgraph Isomorphism, where the topology of \(\mathcal P\) is known, and Graph Motif, where the topology of \(\mathcal P\) is unknown. This generalization has important applications to bioinformatics, since it addresses the major challenge of analyzing biological networks in the absence of certain topological data. In this paper, we use a non-standard part-algebraic/part-combinatorial hybridization strategy to develop an exact parameterized algorithm as well as an FPT-approximation scheme for PINQ, allowing near resemblance between \(H\) and \(\mathcal P\). We thus unify and significantly improve previous results related to network queries.

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Notes

  1. 1.

    The notation \(O^*\) hides factors polynomial in the input size.

  2. 2.

    Indeed, without the cycle requirement, Clique is the special case where \(t=k\), \(I_F=I_A=D=0\), \(\varDelta (p,h)=0\) for all \(p\in V_i, 1\le i\le t\) and \(h\in V\), and \(w(e)=1\) for all \(e\in E\).

  3. 3.

    If such solution exists, we can simply reject the input.

  4. 4.

    This can be also viewed as applying the color coding technique [1] using only two colors.

  5. 5.

    For such solutions, the time gained by handling \(A\) in a manner similar to \(P_A\) prevails the time required for the preceding selection step.

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Authors and Affiliations

  1. Department of Computer Science, Technion, 32000, Haifa, Israel

    Ron Y. Pinter, Hadas Shachnai & Meirav Zehavi

Authors
  1. Ron Y. Pinter
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  2. Hadas Shachnai
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  3. Meirav Zehavi
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Correspondence to Meirav Zehavi .

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Editors and Affiliations

  1. Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland

    Marek Cygan

  2. University of Bergen, Bergen, Norway

    Pinar Heggernes

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Pinter, R.Y., Shachnai, H., Zehavi, M. (2014). Improved Parameterized Algorithms for Network Query Problems. In: Cygan, M., Heggernes, P. (eds) Parameterized and Exact Computation. IPEC 2014. Lecture Notes in Computer Science(), vol 8894. Springer, Cham. https://doi.org/10.1007/978-3-319-13524-3_25

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  • DOI: https://doi.org/10.1007/978-3-319-13524-3_25

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