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International Conference on Contemporary Computing

IC3 2011: Contemporary Computing pp 57–68Cite as

Some Observations on Algorithms for Computing Minimum Independent Dominating Set

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 168))

Abstract

In this paper, we present some observations on the various algorithms proposed to find a Minimum Independent Dominating Set (MIDS). MIDS is proven to be an NP-hard problem. We compared an exact algorithm based on intelligent subset enumeration with another exact algorithm based on matching in graphs. We found that the former performs better than the latter for small graphs despite having a worse asymptotic complexity. There is only one Polynomial Time Approximation Scheme (PTAS) proposed in literature for computing MIDS which works for polynomially bounded growth graphs. We observed that changing the ε value in the PTAS reduces the running time quite drastically but does not increase the cardinality returned significantly. We compared the cardinality of the IDS returned by various heuristics for grid, unit disk graph and general graph topologies. The results show that the highest degree heuristic returns the best cardinality amongst all these algorithms in literature for all graphs except grid graphs for which the inter-dominator 3-hop distance heuristic performs better. To the best of our knowledge, this is the first empirical study where the exact, PTAS and heuristic solutions to the MIDS problem have been compared in terms of the quality of the solution returned as well as provide insights into the behavior of these approaches for various types of graphs.

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Authors and Affiliations

  1. Department of Computer and Information Sciences, University of Hyderabad, Gachibowli, Hyderabad, 500046, India

    Anupama Potluri & Atul Negi

Authors
  1. Anupama Potluri
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  2. Atul Negi
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Editor information

Editors and Affiliations

  1. Iowa State University and IIT Bombay, India, 329 Durham, Ames, IA 5001, Iowa, USA

    Srinivas Aluru

  2. Indian Statistical Institute, 203 B.T. Road, 700 108, Kolkata, West Bengal, India

    Sanghamitra Bandyopadhyay

  3. The Ohio State University, 3190 Graves Hall, 333 W 10th Ave, 43210, Columbus, OH, USA

    Umit V. Catalyurek

  4. Department of Computing Science, Chalmers University, Rännvagen 6B, 412 96, Göteborg, Sweden

    Devdatt P. Dubhashi

  5. Dept. of Electrical and Computer Engineering, Iowa State University, 329 Durham, IA 50011, Ames, USA

    Phillip H. Jones

  6. TASSL, Dept. of Electrical & Computer Engineering, Rutgers, The State University of New Jersey, Brett Road, NJ 08854-8058, Piscataway, USA

    Manish Parashar

  7. School of Computer Engineering, Nanyang Technological University, N4-02a-32 Nanyang Ave, 639798, Singapore

    Bertil Schmidt

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© 2011 Springer-Verlag Berlin Heidelberg

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Potluri, A., Negi, A. (2011). Some Observations on Algorithms for Computing Minimum Independent Dominating Set. In: Aluru, S., et al. Contemporary Computing. IC3 2011. Communications in Computer and Information Science, vol 168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22606-9_10

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  • DOI: https://doi.org/10.1007/978-3-642-22606-9_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22605-2

  • Online ISBN: 978-3-642-22606-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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