Skip to main content
SpringerLink
Log in

GRASP for connected dominating set problems

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

The minimum connected dominating set problem, a variant of the classical minimum dominating set problem, is a very significant NP-hard combinatorial optimization problem with a number of applications. To address this problem, a greedy randomized adaptive search procedure (GRASP) that incorporates a novel local search procedure based on greedy function and tabu strategy is proposed. Firstly, the greedy function is proposed to define the score of each vertex so that our algorithm could obtain different possible optimal solutions. Secondly, a tabu strategy is introduced to prevent the search trapping into the local minimum and avoid the cycling problems. The proposed algorithm is evaluated against several state-of-art algorithms on a large collection of benchmark instances. The experimental results prove that GRASP performs better than its competitors in most benchmark instances.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Berge C (1973) Graphs and hypergraphs[M]. North-Holland Publishing Company, Amsterdam

    MATH  Google Scholar 

  2. Liu CL (1968) Introduction to combinatorial mathematics[M]. McGraw-Hill, New York

    MATH  Google Scholar 

  3. Di Benedetto CA (2010) Diffusion of innovation. Wiley, Chichester

    Google Scholar 

  4. Valente TW (1995) Network models of the diffusion of innovations. Hampton Press, Cresskill

    Google Scholar 

  5. Domingos P, Richardson M (2001) Mining the network value of customers. In: Proceedings of the seventh ACM SIGKDD international conference on knowledge discovery and data mining. ACM, pp 57–66

  6. Goldenberg J, Libai B, Muller E (2001) Using complex systems analysis to advance marketing theory development: modeling heterogeneity effects on new product growth through stochastic cellular automata. Acad Mark Sci Rev 9(3):1–18

    Google Scholar 

  7. Asavathiratham C, Roy S, Lesieutre B et al (2001) The influence model. Control Syst IEEE 21(6):52–64

    Article  Google Scholar 

  8. Cooper C, Klasing R, Zito M (2005) Lower bounds and algorithms for dominating sets in web graphs. Internet Math 2(3):275–300

    Article  MathSciNet  MATH  Google Scholar 

  9. Eubank S, Guclu H, Kumar VSA et al (2004) Modelling disease outbreaks in realistic urban social networks. Nature 429(6988):180–184

    Article  Google Scholar 

  10. Stanley EA (2006) Social networks and mathematical modeling. Connections 27(1):43–49

    Google Scholar 

  11. Garey M, Johnson DS (1979) Computers and intractability, a guide to the theory of NP—completeness. Freeman, San Francisco

    MATH  Google Scholar 

  12. Ruan L, Du H, Jia X, Wu W, Li Y, Ko KI (2004) A greedy approximation for minimum connected dominating sets. Theor Comput Sci 329(1–3):325–330

    Article  MathSciNet  MATH  Google Scholar 

  13. Cheng X, Ding M, Chen D (2004) An approximation algorithm for connected dominating set in ad hoc networks. In: Proceedings of the international workshop on theoretical aspects of wireless ad hoc, sensor and peer-to-peer networks (TAWN)

  14. Min M, Du H, Jia X, Huang CX, Huang SCH, Wu W (2006) Improving construction for connected dominating set with Steiner tree in wireless sensor networks. J Glob Optim 35(1):111–119

    Article  MathSciNet  MATH  Google Scholar 

  15. Guha S, Khuller S (1998) Approximation algorithms for connected dominating sets. Algorithmica 20(4):374–387

    Article  MathSciNet  MATH  Google Scholar 

  16. Butenko S, Cheng X, Oliveira C, Pardalos P (2004) A new heuristic for the minimum connected dominating set problem on ad hoc wireless networks. In: Butenko S (Ed) Recent developments in cooperative control and optimization. Kluwer Academic Publishers, New York, pp 61–73

  17. Butenko S, Oliveira C, Pardalos P (2003) A new algorithm for the minimum connected dominating set problem on ad hoc wireless networks. In: CCCT’03. International Institute of Informatics and Systematics (IIIS), pp 39–44

  18. Gendron B, Lucena A, da Cunha AS et al (2014) Benders decomposition, branch-and-cut, and hybrid algorithms for the minimum connected dominating set problem. INFORMS J Comput 26(4):645–657

    Article  MathSciNet  MATH  Google Scholar 

  19. Misra R, Mandal C (2010) Minimum connected dominating set using a collaborative cover heuristic for ad hoc sensor networks. IEEE Trans Parallel Distrib Syst 21(3):292–302

    Article  Google Scholar 

  20. Morgan M, Grout V (2007) Metaheuristics for wireless network optimisation. In: The third advanced international conference on telecommunications, AICT 2007, p 15, May 2007

  21. He H, Zhu Z, Makinen E (2009) A neural network model to minimize the connected dominating set for self-configuration of wireless sensor networks. IEEE Trans Neural Netw 20(6):973–982

    Article  Google Scholar 

  22. Downey RG, Fellows MR, McCartin C, Rosamond FA (2008) Parameterized approximation of dominating set problems. Inf Process Lett 109(1):68–70

    Article  MathSciNet  MATH  Google Scholar 

  23. Jovanovic R, Tuba M (2013) Ant colony optimization algorithm with pheromone correction strategy for the minimum connected dominating set problem. Comput Sci Inf Syst 10(1):133–149

    Article  Google Scholar 

  24. Nimisha TS, Ramalakshmi R (2015) Energy efficient connected dominating set construction using ant colony optimization technique in wireless sensor network. In: Innovations in information, embedded and communication systems (ICIIECS), 2015 international conference on IEEE, 2015, pp 1–5

  25. Feo TA, Resende MGC (1989) A probabilistic heuristic for a computationally difficult set covering problem. Oper Res Lett 8:67–71

    Article  MathSciNet  MATH  Google Scholar 

  26. Feo TA, Resende MGC (1995) Greedy randomized adaptive search procedures. J Glob Optim 6:109–133

    Article  MathSciNet  MATH  Google Scholar 

  27. Resende MGC, Ribeiro CC (2002) Greedy randomized adaptive search procedures. In: Glover F, Kochenberger G (eds) Handbook of metaheuristics. Kluwer Academic Publishers, Norwell, pp 219–249

    Google Scholar 

  28. Resende MGC, Ribeiro CC (2010) Greedy randomized adaptive search procedures: advances and applications. In: Gendreau M, Potvin J-Y (eds) Handbook of metaheuristics, 2nd edn. Springer, Berlin

    Google Scholar 

  29. Festa P, Resende MGC (2002) GRASP: an annotated bibliography. In: Ribeiro CC, Hansen P (eds) Essays and surveys on metaheuristics. Kluwer Academic Publishers, Boston, pp 325–367

    Chapter  Google Scholar 

  30. Festa P, Resende MGC (2009) An annotated bibliography of GRASP—Part I: algorithms. Int Trans Oper Res 16:1–24

    Article  MathSciNet  MATH  Google Scholar 

  31. Festa P, Resende MGC (2009) An annotated bibliography of GRASP—Part II: applications. Int Trans Oper Res 16(2):131–172

    Article  MathSciNet  MATH  Google Scholar 

  32. Wang Y, Li R, Zhou Y, Yin M (2016) A path cost-based GRASP for minimum independent dominating set problem. Neural Comput Appl. doi:10.1007/s00521-016-2324-6

    Google Scholar 

  33. Ho CK, Singh YP, Ewe HT (2006) An enhanced ant colony optimization metaheuristic for the minimum dominating set problem. Appl Artif Intell 20(10):881–903

    Article  Google Scholar 

  34. Zhou Y, Zhang H, Li R, Wang J (2016) Two local search algorithms for partition vertex cover problem. J Comput Theor Nanosci 13:743–751

    Article  Google Scholar 

  35. Li X, Zhang J, Yin M (2014) Animal migration optimization: an optimization algorithm inspired by animal migration behavior. Neural Comput Appl 24(7–8):1867–1877

    Article  Google Scholar 

  36. Li X, Wang J, Yin M (2014) Enhancing the performance of cuckoo search algorithm using orthogonal learning method. Neural Comput Appl 24(6):1233–1247

    Article  Google Scholar 

  37. Li X, Yin M (2014) Self adaptive constrained Artificial Bee Colony for constrained numerical optimization. Neural Comput Appl 24(3–4):723–734

    Article  Google Scholar 

  38. Wang Y, Cai S, Yin M (2016) Two efficient local search algorithms for maximum weight clique problem. In: AAAI2016

  39. Wang Y, Yin M, Ouyang D, Zhang L (2016) A novel local search algorithm with configuration checking and scoring mechanism for the set k-covering problem. Int Trans Oper Res. doi:10.1111/itor.12280

    Google Scholar 

  40. Glover F (1989) Tabu search—part I. ORSA J Comput 1(3):190–206

    Article  MATH  Google Scholar 

  41. Li R, Hu S, Wang Y, Yin M (2016) A local search algorithm with tabu strategy and perturbation mechanism for generalized vertex cover problem. Neural Comput Appl. doi:10.1007/s00521-015-2172-9

    Google Scholar 

  42. Zhang X, Li X, Wang J (2016) Local search algorithm with path relinking for single batch-processing machine scheduling problem. Neural Comput Appl. doi:10.1007/s00521-016-2339-z

    Google Scholar 

  43. Li R, Hu S, Wang J (2015) The community structure of the constraint satisfaction problem instances of model RB. J Comput Theor Nanosci 12:6088–6093

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported in part by National Natural Science Foundation of China under Grant Nos. (61403077, 61402070, 61403076, 61370156) and Program for New Century Excellent Talents in University (NCET-13-0724).

Author information

Authors and Affiliations

  1. School of Computer Science and Information Technology, Northeast Normal University, Changchun, 130024, China

    Ruizhi Li, Shuli Hu, Yupeng Zhou & Minghao Yin

  2. College of Information Science and Technology, Dalian Maritime University, Dalian, 116026, China

    Jian Gao

  3. Key Lab of Symbol Computation and Knowledge Engineer of Ministry of Education, Jilin University, Changchun, China

    Yiyuan Wang

Authors
  1. Ruizhi Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shuli Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jian Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yupeng Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yiyuan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Minghao Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Minghao Yin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, R., Hu, S., Gao, J. et al. GRASP for connected dominating set problems. Neural Comput & Applic 28 (Suppl 1), 1059–1067 (2017). https://doi.org/10.1007/s00521-016-2429-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-016-2429-y

Keywords

Search

Navigation