Scalable approximations to k-cycle transversal problems on dynamic networks

  • Alan KuhnleEmail author
  • Victoria G. Crawford
  • My T. Thai
Regular Paper


We study scalable approximation algorithms for the k-cycle transversal problem, which is to find a minimum-size set of edges that intersects all simple cycles of length k in a network. This problem is relevant to network reliability through the important metric of network clustering coefficient of order k. We formulate two algorithms to be both scalable and have good solution quality in practice: CARL and DARC. DARC is able to efficiently update its solution under dynamic node and edge insertion and removal to the network. In our experimental evaluation, we demonstrate that DARC is able to run on networks with billions of 3-cycles within 2 h and is able to dynamically update its solution in microseconds.


Dynamic networks Cycle transversal Triangle interdiction Scalable algorithms 



This work was supported in part by NSFCCF-1422116, DTRAHDTRA1-14-1-0055 and NSF EFRI 1441231.


  1. 1.
    Arulselvan A, Commander CW, Elefteriadou L, Pardalos PM (2009) Detecting critical nodes in sparse graphs. Comput Oper Res 36(7):2193–2200MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Bafna V, Berman P, Fujito T (1999) A 2-approximation algorithm for the undirected feedback vertex set problem. SIAM J Discrete Math 12(3):289–297MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Barclay KJ, Edling C, Rydgren J (2013) Peer clustering of exercise and eating behaviours among young adults in Sweden: a cross-sectional study of egocentric network data. BMC Public Health 13:1–3CrossRefGoogle Scholar
  4. 4.
    Bhattacharya S (2017) Fully dynamic approximate maximum matching and minimum vertex cover in O ( log 3 n ) worst case update time. In: Proceedings of the twenty-eighth annual ACM-SIAM symposium on discrete algorithms (SODA’17), (340506), pp 470–489Google Scholar
  5. 5.
    Bhattacharya S, Henzinger M, Italiano GF (2015) Design of dynamic algorithms via primal–dual method. In: International colloquium on automata, languages, and programming. Lecture notes in computer science, vol 9134, pp 206–218Google Scholar
  6. 6.
    Caldarelli G, Pastor-Satorras R, Vespignani A (2004) Structure of cycles and local ordering in complex networks. Eur Phys J B 38(2):183–186CrossRefGoogle Scholar
  7. 7.
    Centola D (2010) The spread of behavior in an online social network experiment. Science 329(5996):1194–1197CrossRefGoogle Scholar
  8. 8.
    Centola D (2011) An experimental study of homophily in the adoption of health behavior. Science 334(December):1269–1272CrossRefGoogle Scholar
  9. 9.
    Cui Y, Xiao D, Loguinov D (2016) On efficient external-memory triangle listing. In: IEEE 16th international conference on data mining. IEEEjGoogle Scholar
  10. 10.
    Grubesic TH, Matisziw TC, Murray AT, Snediker D (2008) Comparative approaches for assessing network vulnerability. Int Reg Sci Rev 31(1):88–112CrossRefGoogle Scholar
  11. 11.
    Gupta A, Krishnaswamy R, Kumar A, Panigrahi D (2017) Online and dynamic algorithms for set cover. In: Symposium on the theory of computing (STOC), pp 537–550Google Scholar
  12. 12.
    Guruswami V, Lee E (2014) Inapproximability of feedback vertex set for bounded length cycles. In: Electronic colloquium on computation complexity (ECCC), vol 21, p 2Google Scholar
  13. 13.
    Kortsarz G (2010) Approximating maximum subgraphs without short cycles. SIAM J Discrete Math 24(1):255–269MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Krivelevich M (1995) On a conjecture of Tuza about packing and covering of triangles. Discrete Math 142(1–3):281–286MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Kuhnle A, Crawford VG, Thai MT (2017a) Scalable and adaptive algorithms for the triangle interdiction problem on billion-scale networks. In: IEEE international conference on data mining (ICDM)Google Scholar
  16. 16.
    Kuhnle A, Pan T, Crawford VG, Alim MA, Thai MT (2017b) Pseudo-separation for assessment of structural vulnerability of a network. In: Proceedings of the 2017 ACM SIGMETRICS/international conference on measurement and modeling of computer systemsGoogle Scholar
  17. 17.
    Kuhnle A, Nguyen NP, Dinh TN, Thai MT (2017c) Vulnerability of clustering under node failure in complex networks. Soc Netw Anal Min 7:8Google Scholar
  18. 18.
    Kuhnle A, Crawford VG, Thai MT (2018) Network resilience and the length-bounded multicut problem: reaching the dynamic billion-scale with guarantees. Proc ACM Meas Anal Comput Syst 2(1).
  19. 19.
    Leskovec J, Krevl A (2014) SNAP datasets: Stanford large network dataset collection. Accessed Mar 2018
  20. 20.
    Lind PG, Gonzãlez MC, Herrmann HJ (2005) Cycles and clustering in bipartite networks. Phys Rev E Stat Nonlinear Soft Matter Phys 72(5):1–9Google Scholar
  21. 21.
    Myers SA, Leskovec J (2014) The bursty dynamics of the Twitter information network. In: Proceedings of the 23rd international conference on world wide web, pp 913–924Google Scholar
  22. 22.
    Nguyen HT, Nguyen NP, Vu T, Hoang HX, Dinh TN (2017) Transitivity demolition and the fall of social networks. IEEE Access 5:15913–15926CrossRefGoogle Scholar
  23. 23.
    Nguyen NP, Dinh TN, Shen Y, Thai MT (2014) Dynamic social community detection and its applications. PLoS ONE 9(4):e91431CrossRefGoogle Scholar
  24. 24.
    Onnela JP, Saramäki J, Kertész J, Kaski K (2005) Intensity and coherence of motifs in weighted complex networks. Phys Rev E Stat Nonlinear Soft Matter Phys 71(6):1–4CrossRefGoogle Scholar
  25. 25.
    O’Sullivan DJP, O’Keeffe GJ, Fennell PG, Gleeson JP (2015) Mathematical modeling of complex contagion on clustered networks. Front Phys 3:71Google Scholar
  26. 26.
    Ponton J, Wei P, Sun D (2013) Weighted clustering coefficient maximization for air transportation networks. In: IEEE European control conference (ECC)Google Scholar
  27. 27.
    Schank T, Wagner D (2005) Finding, counting and listing all triangles in large graphs, an experimental study. In: International workshop on experimental and efficient algorithms 2. Springer, Berlin, pp 606–609Google Scholar
  28. 28.
    Tsourakakis CE (2008) Fast counting of triangles in large real networks. In: Eighth IEEE international conference on data mining (ICDM). IEEEGoogle Scholar
  29. 29.
    Vazirani VV (2003) Approximation algorithms, 1st edn. Springer, BerlinCrossRefGoogle Scholar
  30. 30.
    Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393(6684):440–442zbMATHCrossRefGoogle Scholar
  31. 31.
    Zaki N, Efimov D, Berengueres J (2013) Protein complex detection using interaction reliability assessment and weighted clustering coefficient. BMC Bioinform 14(1):1–9CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Computer and Information Science and EngineeringUniversity of FloridaGainesvilleUSA

Personalised recommendations