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Erschienen in: Knowledge and Information Systems 1/2019

19.12.2018 | Regular Paper

Scalable approximations to k-cycle transversal problems on dynamic networks

verfasst von: Alan Kuhnle, Victoria G. Crawford, My T. Thai

Erschienen in: Knowledge and Information Systems | Ausgabe 1/2019

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Abstract

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.

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Fußnoten
1
The conference version of this paper studied the 3-cycle (triangle) version of this problem [15].
 
Literatur
1.
Zurück zum Zitat Arulselvan A, Commander CW, Elefteriadou L, Pardalos PM (2009) Detecting critical nodes in sparse graphs. Comput Oper Res 36(7):2193–2200MathSciNetCrossRefMATH Arulselvan A, Commander CW, Elefteriadou L, Pardalos PM (2009) Detecting critical nodes in sparse graphs. Comput Oper Res 36(7):2193–2200MathSciNetCrossRefMATH
2.
Zurück zum Zitat Bafna V, Berman P, Fujito T (1999) A 2-approximation algorithm for the undirected feedback vertex set problem. SIAM J Discrete Math 12(3):289–297MathSciNetCrossRefMATH Bafna V, Berman P, Fujito T (1999) A 2-approximation algorithm for the undirected feedback vertex set problem. SIAM J Discrete Math 12(3):289–297MathSciNetCrossRefMATH
3.
Zurück zum Zitat 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 13:1–3CrossRef 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 13:1–3CrossRef
4.
Zurück zum Zitat 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 470–489 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 470–489
5.
Zurück zum Zitat 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 206–218 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 206–218
6.
Zurück zum Zitat Caldarelli G, Pastor-Satorras R, Vespignani A (2004) Structure of cycles and local ordering in complex networks. Eur Phys J B 38(2):183–186CrossRef Caldarelli G, Pastor-Satorras R, Vespignani A (2004) Structure of cycles and local ordering in complex networks. Eur Phys J B 38(2):183–186CrossRef
7.
Zurück zum Zitat Centola D (2010) The spread of behavior in an online social network experiment. Science 329(5996):1194–1197CrossRef Centola D (2010) The spread of behavior in an online social network experiment. Science 329(5996):1194–1197CrossRef
8.
Zurück zum Zitat Centola D (2011) An experimental study of homophily in the adoption of health behavior. Science 334(December):1269–1272CrossRef Centola D (2011) An experimental study of homophily in the adoption of health behavior. Science 334(December):1269–1272CrossRef
9.
Zurück zum Zitat Cui Y, Xiao D, Loguinov D (2016) On efficient external-memory triangle listing. In: IEEE 16th international conference on data mining. IEEEj Cui Y, Xiao D, Loguinov D (2016) On efficient external-memory triangle listing. In: IEEE 16th international conference on data mining. IEEEj
10.
Zurück zum Zitat Grubesic TH, Matisziw TC, Murray AT, Snediker D (2008) Comparative approaches for assessing network vulnerability. Int Reg Sci Rev 31(1):88–112CrossRef Grubesic TH, Matisziw TC, Murray AT, Snediker D (2008) Comparative approaches for assessing network vulnerability. Int Reg Sci Rev 31(1):88–112CrossRef
11.
Zurück zum Zitat 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 537–550 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 537–550
12.
Zurück zum Zitat Guruswami V, Lee E (2014) Inapproximability of feedback vertex set for bounded length cycles. In: Electronic colloquium on computation complexity (ECCC), vol 21, p 2 Guruswami V, Lee E (2014) Inapproximability of feedback vertex set for bounded length cycles. In: Electronic colloquium on computation complexity (ECCC), vol 21, p 2
14.
15.
Zurück zum Zitat 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) 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)
16.
Zurück zum Zitat 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 systems 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 systems
17.
Zurück zum Zitat Kuhnle A, Nguyen NP, Dinh TN, Thai MT (2017c) Vulnerability of clustering under node failure in complex networks. Soc Netw Anal Min 7:8 Kuhnle A, Nguyen NP, Dinh TN, Thai MT (2017c) Vulnerability of clustering under node failure in complex networks. Soc Netw Anal Min 7:8
18.
20.
Zurück zum Zitat Lind PG, Gonzãlez MC, Herrmann HJ (2005) Cycles and clustering in bipartite networks. Phys Rev E Stat Nonlinear Soft Matter Phys 72(5):1–9 Lind PG, Gonzãlez MC, Herrmann HJ (2005) Cycles and clustering in bipartite networks. Phys Rev E Stat Nonlinear Soft Matter Phys 72(5):1–9
21.
Zurück zum Zitat 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 913–924 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 913–924
22.
Zurück zum Zitat Nguyen HT, Nguyen NP, Vu T, Hoang HX, Dinh TN (2017) Transitivity demolition and the fall of social networks. IEEE Access 5:15913–15926CrossRef Nguyen HT, Nguyen NP, Vu T, Hoang HX, Dinh TN (2017) Transitivity demolition and the fall of social networks. IEEE Access 5:15913–15926CrossRef
23.
Zurück zum Zitat Nguyen NP, Dinh TN, Shen Y, Thai MT (2014) Dynamic social community detection and its applications. PLoS ONE 9(4):e91431CrossRef Nguyen NP, Dinh TN, Shen Y, Thai MT (2014) Dynamic social community detection and its applications. PLoS ONE 9(4):e91431CrossRef
24.
Zurück zum Zitat 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):1–4CrossRef 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):1–4CrossRef
25.
Zurück zum Zitat O’Sullivan DJP, O’Keeffe GJ, Fennell PG, Gleeson JP (2015) Mathematical modeling of complex contagion on clustered networks. Front Phys 3:71 O’Sullivan DJP, O’Keeffe GJ, Fennell PG, Gleeson JP (2015) Mathematical modeling of complex contagion on clustered networks. Front Phys 3:71
26.
Zurück zum Zitat Ponton J, Wei P, Sun D (2013) Weighted clustering coefficient maximization for air transportation networks. In: IEEE European control conference (ECC) Ponton J, Wei P, Sun D (2013) Weighted clustering coefficient maximization for air transportation networks. In: IEEE European control conference (ECC)
27.
Zurück zum Zitat 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 606–609 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 606–609
28.
Zurück zum Zitat Tsourakakis CE (2008) Fast counting of triangles in large real networks. In: Eighth IEEE international conference on data mining (ICDM). IEEE Tsourakakis CE (2008) Fast counting of triangles in large real networks. In: Eighth IEEE international conference on data mining (ICDM). IEEE
29.
Zurück zum Zitat Vazirani VV (2003) Approximation algorithms, 1st edn. Springer, BerlinCrossRef Vazirani VV (2003) Approximation algorithms, 1st edn. Springer, BerlinCrossRef
30.
Zurück zum Zitat Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393(6684):440–442CrossRefMATH Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393(6684):440–442CrossRefMATH
31.
Zurück zum Zitat Zaki N, Efimov D, Berengueres J (2013) Protein complex detection using interaction reliability assessment and weighted clustering coefficient. BMC Bioinform 14(1):1–9CrossRef Zaki N, Efimov D, Berengueres J (2013) Protein complex detection using interaction reliability assessment and weighted clustering coefficient. BMC Bioinform 14(1):1–9CrossRef
Metadaten
Titel
Scalable approximations to k-cycle transversal problems on dynamic networks
verfasst von
Alan Kuhnle
Victoria G. Crawford
My T. Thai
Publikationsdatum
19.12.2018
Verlag
Springer London
Erschienen in
Knowledge and Information Systems / Ausgabe 1/2019
Print ISSN: 0219-1377
Elektronische ISSN: 0219-3116
DOI
https://doi.org/10.1007/s10115-018-1296-5

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