NuCDS: An Efficient Local Search Algorithm for Minimum Connected Dominating Set

Bohan Li
Bohan Li
Xindi Zhang
Xindi Zhang
Jinkun Lin
Jinkun Lin
Christian Blum
Christian Blum

IJCAI, pp. 1503-1510, 2020.

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Keywords:
minimum dominating setconnected dominating setmassive graphminimum dominating set problemwireless networkMore(12+)
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We proposed two new algorithmic components, namely the hybrid dynamic connectivity maintenance heuristic and the safety-based vertex selection heuristic, for minimum connected dominating set

Abstract:

The minimum connected dominating set (MCDS) problem is an important extension of the minimum dominating set problem, with wide applications, especially in wireless networks. Despite its practical importance, there are few works on solving MCDS for massive graphs, mainly due to the complexity of maintaining connectivity. In this paper, we ...More

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Introduction
  • The minimum dominating set (MDS) problem is to find a dominating set with the minimum number of vertices in the given graph.
  • An important generalization of MDS is the minimum connected dominating set (MCDS) problem, whose goal is to find a minimum size dominating set that forms a connected subgraph in the given graph.
  • An important application of MCDS is generating a virtual backbone in wireless networks such as mobile ad hoc networks [Al-Karaki and Kamal, 2008], wireless sensors networks [Misra and Mandal, 2009] and vehicular ad hoc networks [Chinnasamy et al, 2019].
  • Several exact algorithms [Fomin et al, 2008; Simonetti et
Highlights
  • Given an undirected connected graph G = (V, E), a set D ⊆ V is called a dominating set if each vertex in V either belongs to D or is adjacent to at least one vertex from D
  • In order to solve the performance bottleneck problem caused by the connectivity constraint of minimum connected dominating set, we introduce a hybrid dynamic connectivity maintenance method (HDC for short)
  • But we report the average run time when all algorithms obtain the same minimal and average values in Figure 2, which shows the effectiveness of NuCDS
  • We proposed two new algorithmic components, namely the hybrid dynamic connectivity maintenance heuristic and the safety-based vertex selection heuristic, for minimum connected dominating set
  • We conducted extensive benchmarks to evaluate the performance of NuCDS and the experimental results showed that our algorithm significantly outperforms its competitors on almost all the instances of any size
  • Three modified versions of NuCDS are proposed to verify the effectiveness of HDC and saf ety, especially on massive graphs
Results
  • Most instances of classical benchmarks are so easy that all algorithms obtain the same solution quality very quickly
  • The authors ignore these instances, but the authors report the average run time when all algorithms obtain the same minimal and average values in Figure 2, which shows the effectiveness of NuCDS.
  • NuCDS can solve all these 118 instances within the time limit, while MSLS, ACO-efficient, ACO-RVNS and RNS-TS can only solve 45, 48, 18, and 26 instances, respectively.
  • The excellent results of NuCDS on massive graphs can mainly be attributed to the power of the HDC heuristic
Conclusion
  • The authors proposed two new algorithmic components, namely the hybrid dynamic connectivity maintenance heuristic and the safety-based vertex selection heuristic, for MCDS.
  • Both components were used to develop an efficient local search algorithm named NuCDS.
  • As shown in Table 4, three modified versions of NuCDS are proposed to verify the effectiveness of HDC and saf ety, especially on massive graphs.
  • The authors compared NuCDS with NuCDS1 to show the effectiveness of saf ety, and with
Summary
  • Introduction:

    The minimum dominating set (MDS) problem is to find a dominating set with the minimum number of vertices in the given graph.
  • An important generalization of MDS is the minimum connected dominating set (MCDS) problem, whose goal is to find a minimum size dominating set that forms a connected subgraph in the given graph.
  • An important application of MCDS is generating a virtual backbone in wireless networks such as mobile ad hoc networks [Al-Karaki and Kamal, 2008], wireless sensors networks [Misra and Mandal, 2009] and vehicular ad hoc networks [Chinnasamy et al, 2019].
  • Several exact algorithms [Fomin et al, 2008; Simonetti et
  • Results:

    Most instances of classical benchmarks are so easy that all algorithms obtain the same solution quality very quickly
  • The authors ignore these instances, but the authors report the average run time when all algorithms obtain the same minimal and average values in Figure 2, which shows the effectiveness of NuCDS.
  • NuCDS can solve all these 118 instances within the time limit, while MSLS, ACO-efficient, ACO-RVNS and RNS-TS can only solve 45, 48, 18, and 26 instances, respectively.
  • The excellent results of NuCDS on massive graphs can mainly be attributed to the power of the HDC heuristic
  • Conclusion:

    The authors proposed two new algorithmic components, namely the hybrid dynamic connectivity maintenance heuristic and the safety-based vertex selection heuristic, for MCDS.
  • Both components were used to develop an efficient local search algorithm named NuCDS.
  • As shown in Table 4, three modified versions of NuCDS are proposed to verify the effectiveness of HDC and saf ety, especially on massive graphs.
  • The authors compared NuCDS with NuCDS1 to show the effectiveness of saf ety, and with
Tables
  • Table1: Results of NuCDS, MSLS, ACO-efficient, ACO-RVNS and RNS-TS on classical benchmarks
  • Table2: Results on SNAP and DIMACS10 benchmarks. To save space, we denote ACO-RVNS and RNS-TS as ACO and RNS
  • Table3: Results on the NDR benchmarks. To save space, we denote ACO-efficient and ACO-RVNS as ACOe and ACO, respectively. Moreover, since min and avg of all competitors are no better than that of NuCDS on all instances, we only report min of competitors
  • Table4: Three modified versions of NuCDS, where ”+” indicates that the version uses the corresponding strategy while ”-” means not
  • Table5: Comparing NuCDS with three modified versions on massive graphs. #Better and #Worse respectively represent the number of instances where NuCDS achieves better and worse result
Download tables as Excel
Related work
  • Because of its NP-hardness, much of the research effort in the past decade concerned with solving MCDS has focused on heuristics with the aim of obtaining a good solution within a reasonable time. Two algorithms called MCDS/SA and MCDS/TS based on simulated annealing and tabu search were proposed [Morgan and Grout, 2007]. Hedar and Ismail [2012] designed a simulated annealing algorithm with stochastic local search for MCDS. Later, Jovanovic and Tuba [2013] designed an ant colony optimization algorithm with a so-called pheromone correction strategy. A greedy random adaptive search procedure that incorporated a local search procedure based on a greedy function and tabu search was described in [Li et al, 2017]. Wu et al [2017] used a restricted swap-based neighborhood to improve the tabu search procedure, resulting in the RNS-TS algorithm. Two metaheuristics based on genetic algorithms and simulated annealing were designed to solve MCDS [Hedar et al, 2019]. Li et al [2019] presented a multi-start local search algorithm called MSLS based on three mechanisms including a vertex score, configuration checking, and vertex flipping. Finally, a meta-heuristic algorithm called ACO-RVNS [Bouamama et al, 2019] was proposed, based on ant colony optimization and reduced variable neighborhood search. Experiments show that, for classic graphs with fewer than 5000 vertices, RNS-TS, MSLS, and ACO-RVNS obtain similar state-of-theart performance.
Funding
  • This work was supported by Beijing Academy of Artificial Intelligence (BAAI), Youth Innovation Promotion Association, Chinese Academy of Sciences [No 2017150], and NSFC Grant 61806050
Reference
  • [Al-Karaki and Kamal, 2008] Jamal N Al-Karaki and Ahmed E Kamal. Efficient virtual-backbone routing in mobile ad hoc networks. Computer Networks, 52(2):327–350, 2008.
    Google ScholarLocate open access versionFindings
  • [Bouamama et al., 2019] Salim Bouamama, Christian Blum, and Jean-Guillaume Fages. An algorithm based on ant colony optimization for the minimum connected dominating set problem. Applied Soft Computing, 80:672–686, 2019.
    Google ScholarLocate open access versionFindings
  • [Cai and Su, 2013] Shaowei Cai and Kaile Su. Local search for boolean satisfiability with configuration checking and subscore. Artificial Intelligence, 204:75–98, 2013.
    Google ScholarLocate open access versionFindings
  • [Cai, 2015] Shaowei Cai. Balance between complexity and quality: Local search for minimum vertex cover in massive graphs. In Twenty-Fourth International Joint Conference on Artificial Intelligence, pages 747–753, 2015.
    Google ScholarLocate open access versionFindings
  • [Cheng et al., 2003] Xiuzhen Cheng, Xiao Huang, Deying Li, Weili Wu, and Ding-Zhu Du. A polynomial-time approximation scheme for the minimum-connected dominating set in ad hoc wireless networks. Networks: An International Journal, 42(4):202–208, 2003.
    Google ScholarLocate open access versionFindings
  • [Chinnasamy et al., 2019] A Chinnasamy, B Sivakumar, P Selvakumari, and A Suresh. Minimum connected dominating set based rsu allocation for smartcloud vehicles in vanet. Cluster Computing, 22(5):12795–12804, 2019.
    Google ScholarLocate open access versionFindings
  • [Erdem et al., 2009] Esra Erdem, Fangzhen Lin, and Torsten Schaub, editors. Proceedings of 10th International Conference on Logic Programming and Nonmonotonic Reasoning, volume 5753 of Lecture Notes in Computer Science, 2009.
    Google ScholarLocate open access versionFindings
  • [Fan and Watson, 2012] Neng Fan and Jean-Paul Watson. Solving the connected dominating set problem and power dominating set problem by integer programming. In International conference on combinatorial optimization and applications, pages 371–383, 2012.
    Google ScholarLocate open access versionFindings
  • [Fernau et al., 2011] Henning Fernau, Joachim Kneis, Dieter Kratsch, Alexander Langer, Mathieu Liedloff, Daniel Raible, and Peter Rossmanith. An exact algorithm for the maximum leaf spanning tree problem. Theoretical Computer Science, 412(45):6290–6302, 2011.
    Google ScholarLocate open access versionFindings
  • [Fomin et al., 2008] Fedor V Fomin, Fabrizio Grandoni, and Dieter Kratsch. Solving connected dominating set faster than 2 n. Algorithmica, 52(2):153–166, 2008.
    Google ScholarLocate open access versionFindings
  • [Gendron et al., 2014] Bernard Gendron, Abilio Lucena, Alexandre Salles da Cunha, and Luidi Simonetti. Benders decomposition, branch-and-cut, and hybrid algorithms for the minimum connected dominating set problem. INFORMS Journal on Computing, 26(4):645–657, 2014.
    Google ScholarLocate open access versionFindings
  • [Glover and Laguna, 1998] Fred Glover and Manuel Laguna. Tabu search. In Handbook of combinatorial optimization, pages 2093– 2229.
    Google ScholarLocate open access versionFindings
  • [Hedar and Ismail, 2012] Abdel-Rahman Hedar and Rashad Ismail. Simulated annealing with stochastic local search for minimum dominating set problem. International Journal of Machine Learning and Cybernetics, 3(2):97–109, 2012.
    Google ScholarLocate open access versionFindings
  • [Hedar et al., 2019] Abdel-Rahman Hedar, Rashad Ismail, Gamal A El-Sayed, and Khalid M Jamil Khayyat. Two metaheuristics designed to solve the minimum connected dominating set problem for wireless networks design and management. Journal of Network and Systems Management, 27(3):647–687, 2019.
    Google ScholarLocate open access versionFindings
  • [Hopcroft and Tarjan, 1973] John Hopcroft and Robert Tarjan. Algorithm 447: efficient algorithms for graph manipulation. Communications of the ACM, 16(6):372–378, 1973.
    Google ScholarLocate open access versionFindings
  • [Jovanovic and Tuba, 2013] Raka Jovanovic and Milan Tuba. Ant colony optimization algorithm with pheromone correction strategy for the minimum connected dominating set problem. Comput. Sci. Inf. Syst., 10(1):133–149, 2013.
    Google ScholarLocate open access versionFindings
  • [Kann, 1992] Viggo Kann. On the approximability of NP-complete optimization problems. PhD thesis, Royal Institute of Technology Stockholm, 1992.
    Google ScholarFindings
  • [Khuller and Yang, 2019] Samir Khuller and Sheng Yang. Revisiting connected dominating sets: An almost optimal local information algorithm. Algorithmica, 81(6):2592–2605, 2019.
    Google ScholarLocate open access versionFindings
  • [Li et al., 2017] Ruizhi Li, Shuli Hu, Jian Gao, Yupeng Zhou, Yiyuan Wang, and Minghao Yin. Grasp for connected dominating set problems. Neural Computing and Applications, 28(1):1059–1067, 2017.
    Google ScholarLocate open access versionFindings
  • [Li et al., 2019] Ruizhi Li, Shuli Hu, Huan Liu, Ruiting Li, Dantong Ouyang, and Minghao Yin. Multi-start local search algorithm for the minimum connected dominating set problems. Mathematics, 7(12):1173, 2019.
    Google ScholarLocate open access versionFindings
  • [Lin et al., 2017] Jinkun Lin, Shaowei Cai, Chuan Luo, and Kaile Su. A reduction based method for coloring very large graphs. In IJCAI, pages 517–523, 2017.
    Google ScholarLocate open access versionFindings
  • [Lucena et al., 2010] Abilio Lucena, Nelson Maculan, and Luidi Simonetti. Reformulations and solution algorithms for the maximum leaf spanning tree problem. Computational Management Science, 7(3):289–311, 2010.
    Google ScholarLocate open access versionFindings
  • [Milenkovicet al., 2011] Tijana Milenkovic, Vesna Memisevic, Anthony Bonato, and Natasa Przulj. Dominating biological networks. PloS one, 6(8):e23016, 2011.
    Google ScholarLocate open access versionFindings
  • [Misra and Mandal, 2009] Rajiv Misra and Chittaranjan Mandal. Minimum connected dominating set using a collaborative cover heuristic for ad hoc sensor networks. IEEE Transactions on parallel and distributed systems, 21(3):292–302, 2009.
    Google ScholarLocate open access versionFindings
  • [Morgan and Grout, 2007] Mike Morgan and Vic Grout. Metaheuristics for wireless network optimisation. In AICT, pages 15– 15, 2007.
    Google ScholarLocate open access versionFindings
  • [Rossi and Ahmed, 2015] Ryan A Rossi and Nesreen K Ahmed. The network data repository with interactive graph analytics and visualization. pages 4292–4293, 2015.
    Google ScholarFindings
  • [Ruan et al., 2004] Lu Ruan, Hongwei Du, Xiaohua Jia, Weili Wu, Yingshu Li, and Ker-I Ko. A greedy approximation for minimum connected dominating sets. Theoretical Computer Science, 329(1-3):325–330, 2004.
    Google ScholarLocate open access versionFindings
  • [Simonetti et al., 2011] Luidi Simonetti, Alexandre Salles Da Cunha, and Abilio Lucena. The minimum connected dominating set problem: Formulation, valid inequalities and a branch-and-cut algorithm. In International Conference on Network Optimization, pages 162–169.
    Google ScholarLocate open access versionFindings
  • [Wang et al., 2017] Yiyuan Wang, Shaowei Cai, and Minghao Yin. Local search for minimum weight dominating set with two-level configuration checking and frequency based scoring function. Journal of Artificial Intelligence Research, 58:267–295, 2017.
    Google ScholarLocate open access versionFindings
  • [Wu et al., 2017] Xinyun Wu, Zhipeng Lu, and Philippe Galinier. Restricted swap-based neighborhood search for the minimum connected dominating set problem. Networks, 69(2):222–236, 2017.
    Google ScholarLocate open access versionFindings
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