Skip to main content
SpringerLink
Log in

An improved ant-based heuristic approach for solving the longest cycle problem in large-scale complex networks

  • Published:
The Journal of Supercomputing Aims and scope Submit manuscript

Abstract

The longest cycle problem (LCP) has a crucial significance in graph theory and has a wide range of applications in the real-world. Although some excellent LCP solvers have been proposed in recent years, there is still a need for more efficient algorithms to solve the LCP of large-scale real-world complex networks. This paper proposed a fast algorithm ANTH-PDLS (ant heuristic with path disturbance local search) for the LCP. In ANTH-PDLS, two reduction strategies are proposed to reduce the scale of the networks, and a path disturbance strategy is proposed to expand the search ability. Experiments with randomly generated instances and real-world instances show that these strategies are effective. The average solution time of ANTH-PDLS on 21 real-world instances is only 15.5% of the existing excellent algorithms.

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
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Diestel R (2005) Graph Theory (Graduate Texts in Mathematics). Heidelberg, Springer, Berlin

  2. Garey MR (1979) Computers and intractability: a guide to the theory of np-completeness. Revista Da Escola De Enfermagem Da USP 44(2):340

    Google Scholar 

  3. Mateti P, Deo N (1976) On algorithms for enumerating all circuits of a graph. SIAM J Comput 5(1):90–99

    Article  MathSciNet  Google Scholar 

  4. Tarjan R (1973) Enumeration of the elementary circuits of a directed graph. SIAM J Comput 2(3):211–216

    Article  MathSciNet  Google Scholar 

  5. Liu H, Wang J (2006) A new way to enumerate cycles in graph. Advanced Int’1 Conference on Telecommunications and Int’1 Conference on Internet and Web Applications and Services (AICT-ICIW’06). Guadeloupe, French Caribbean, pp 57–57

  6. Jie W, Watts DJ (2002) Small worlds: the dynamics of networks between order and randomness. Acm Sigmod Record 31(4):74–75

    Article  Google Scholar 

  7. Hawick K, James H, Scogings C (2007) Structural circuits and attractors in kauffman networks. Australian Conference on Artificial Life (ACAL’07). Gold Coast, Australia, pp 189–200

    Google Scholar 

  8. Dixon ET, Goodman Seymour E (1976) An algorithm for the longest cycle problem. Networks 6(2):139–149

    Article  MathSciNet  Google Scholar 

  9. Chalupa D, Balaghan P, Hawick KA, Gordon NA (2017) Computational methods for finding long simple cycles in complex networks. Knowl Based Syst 100(125):96–107

    Article  Google Scholar 

  10. Chalupa D, Balaghan P, Hawick KA (2018) A probabilistic ant-based heuristic for the longest simple cycle problem in complex net- works. arXiv:1801.09227

  11. Kumar P, Gupta N (2014) A heuristic algorithm for longest simple cycle problem. In: Proceedings of the International Conference on Wireless Networks (ICWN’14), Venice , Italy. pp 202-208

  12. Sun Y, Cao Q, Wang B, Li S (2018) Sum rate maximization of d2d communications in cognitive radio network using cheating strategy. Wireless Communications & Mobile Computing, article ID 6065920. https://doi.org/10.1155/2018/6065920

  13. Bodlaender HL (1993) On linear time minor tests with depth-first search. J Algorithms 14(1):1–23

    Article  MathSciNet  Google Scholar 

  14. Karger D, Motwani R, Ramkumar GDS (1997) On approximating the longest path in a graph. Algorithmica 18(1):82–98

    Article  MathSciNet  Google Scholar 

  15. Li MC (1995) Longest cycles in regular 2-connected claw-free graphs. Dis-crete Math 137(1–3):277–295

    Article  MathSciNet  Google Scholar 

  16. Paulusma D, Yoshimoto K (2008) Relative length of longest paths and longest cycles in triangle-free graphs. Discret Math 308(7):1222–1229

    Article  MathSciNet  Google Scholar 

  17. Feder T, Motwani R, Subi C (2002) Approximating the longest cycle problem in sparse graphs. SIAM J Comput 31(5):1596–1607

    Article  MathSciNet  Google Scholar 

  18. Chen G, Gao Z, Xingxing Y, Zang W (2005) Approximating the longest cycle problem on graphs with bounded degree. International Computing and Combinatorics Conference (COCOON’05). Kunming, China, pp 870–884

    Chapter  Google Scholar 

  19. Sardroud AA, Bagheri A (2016) An approximation algorithm for the longest cycle problem in solid grid graphs. Discrete Appl Math 100(204):6–12

    Article  MathSciNet  Google Scholar 

  20. Takahara Y, Teramoto S, Uehara R (2008) Longest path problems on ptolemaic graphs. IEICE Trans Inf Syst 91(2):170–177

    Article  Google Scholar 

  21. Shang J, Li P, Shi Y (2021) The longest cycle problem is polynomial on interval graphs. Theoret Comput Sci 859:37–47

    Article  MathSciNet  Google Scholar 

  22. Liu C, Li H, Leonce A, Burge L, Trimble J, Keiller P, Yakubu AA (2010) A Heuristic Algorithm for Finding the Longest Pathways in a Biochemical Network. The Ninth International Conference on Machine Learning and Applications. DC, USA, Washington, pp 515–522

  23. Adriaens F, Aslay C, De Bie T, Gionis A, Lijffijt J (2019) Discovering interesting cycles in directed graphs. In: Proceedings of the 28th ACM International Conference on Information and Knowledge Management, NewYork, US, pp. 1191–1200

  24. Becker MY, Rojas I (2001) A graph layout algorithm for drawing metabolic pathways. Bioinformatics 17(5):461–467

    Article  Google Scholar 

  25. Ma X, Huang L, Lai YC, Zheng Z (2009) Emergence of loop structure in scale-free networks and dynamical consequences. Phys Rev E 79(5):056106

    Article  Google Scholar 

  26. Tamassia R (2013) Handbook of graph drawing and visualization. CRC Press, Boca Raton, US

    Book  Google Scholar 

  27. Chalupa D, Hawick KA (2019) Graphcombex: a software tool for exploration of combinatorial optimization properties of large graphs. Soft Computi 23(14):5715–5724

    Article  Google Scholar 

  28. Minjing Y, Ye Z, Liu YJ, He Y, Wang CCL (2019) Lineup: computing chain-based physical transformation. ACM Trans Graph (TOG) 38(1):1–16

    Google Scholar 

  29. Zhang WQ, Liu YJ (2011) Approximating the longest paths in grid graphs. Theor Comput Sci 412(39):5340–5350

    Article  MathSciNet  Google Scholar 

  30. Rossi RA, Ahmed NK (2015) The Network Data Repository with Interactive Graph Analytics and Visualization. In: Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence AAAI Press, Texas, USA, pp.4292-4293

  31. Bastian M, Heymann S, Jacomy M (2009) Gephi: an open source software for exploring and manipulating networks. International AAAI Conference on Weblogs and Social Media. California USA, San Jose, pp 361–362

Download references

Author information

Authors and Affiliations

  1. College of Computer Science, Chongqing University, Chongqing, 400044, China

    Ping Guo & Yicheng Jiang

  2. Chongqing Key Laboratory of Software Theory and Technology, Chongqing, 400044, China

    Ping Guo

Authors
  1. Ping Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yicheng Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ping Guo.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Guo, P., Jiang, Y. An improved ant-based heuristic approach for solving the longest cycle problem in large-scale complex networks. J Supercomput 78, 14164–14190 (2022). https://doi.org/10.1007/s11227-022-04409-3

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11227-022-04409-3

Keywords

Search

Navigation