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On positive-influence target-domination

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Abstract

Consider a graph \(G=(V,E)\) and a vertex subset \(A \subseteq V\). A vertex v is positive-influence dominated by A if either v is in A or at least half the number of neighbors of v belong to A. For a target vertex subset \(S \subseteq V\), a vertex subset A is a positive-influence target-dominating set for target set S if every vertex in S is positive-influence dominated by A. Given a graph G and a target vertex subset S, the positive-influence target-dominating set (PITD) problem is to find the minimum positive-influence dominating set for target S. In this paper, we show two results: (1) The PITD problem has a polynomial-time \((1 + \log \lceil \frac{3}{2} \Delta \rceil )\)-approximation in general graphs where \(\Delta \) is the maximum vertex-degree of the input graph. (2) For target set S with \(|S|=\Omega (|V|)\), the PITD problem has a polynomial-time O(1)-approximation in power-law graphs.

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Acknowledgments

Authors wish to thank referees for their insightful comments.

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Authors and Affiliations

  1. Department of Computer Science, University of Texas at Dallas, Richardson, TX, 75080, USA

    Guangmo Tong, Weili Wu & Ding-Zhu Du

  2. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611, USA

    Panos M. Pardalos

  3. Laboratory of Algorithms and Technologies for Networks Analysis (LATNA), National Research University, Higher School of Economics, 20 Myasnitskaya st., Moscow, 101000, Russia

    Panos M. Pardalos

  4. Division of Algorithms and Technologies for Networks Analysis, Faculty of Information Technology, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Ding-Zhu Du

Authors
  1. Guangmo Tong
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  2. Weili Wu
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  3. Panos M. Pardalos
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  4. Ding-Zhu Du
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Correspondence to Ding-Zhu Du.

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Tong, G., Wu, W., Pardalos, P.M. et al. On positive-influence target-domination. Optim Lett 11, 419–427 (2017). https://doi.org/10.1007/s11590-015-0938-8

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  • DOI: https://doi.org/10.1007/s11590-015-0938-8

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