Triangle minimization in large networks

Li, Ronghua; Yu, Jeffrey Xu

doi:10.1007/s10115-014-0800-9

Cited by 18 publications

(16 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [36] and [18], the authors propose approximation algorithms with proven guarantees for the problem of making the number of triangles in a graph minimum and maximum, respectively. In [44], the author studies the problem of minimizing the characteristic path length.…”

Section: Related Workmentioning

confidence: 99%

Improving the Betweenness Centrality of a Node by Adding Links

Bergamini

Crescenzi

D’Angelo

et al. 2018

ACM J. Exp. Algorithmics

View full text Add to dashboard Cite

Betweenness is a well-known centrality measure that ranks the nodes according to their participation in the shortest paths of a network. In several scenarios, having a high betweenness can have a positive impact on the node itself. Hence, in this paper we consider the problem of determining how much a vertex can increase its centrality by creating a limited amount of new edges incident to it. In particular, we study the problem of maximizing the betweenness score of a given node -Maximum Betweenness Improvement (MBI) -and that of maximizing the ranking of a given node -Maximum Ranking Improvement (MRI). We show that MBI cannot be approximated in polynomial-time within a factor (1 − 1 2e ) and that MRI does not admit any polynomial-time constant factor approximation algorithm, both unless P = N P. We then propose a simple greedy approximation algorithm for MBI with an almost tight approximation ratio and we test its performance on several real-world networks. We experimentally show that our algorithm highly increases both the betweenness score and the ranking of a given node and that it outperforms several competitive baselines. To speed up the computation of our greedy algorithm, we also propose a new dynamic algorithm for updating the betweenness of one node after an edge insertion, which might be of independent interest. Using the dynamic algorithm, we are now able to compute an approximation of MBI on networks with up to 10 5 edges in most cases in a matter of seconds or a few minutes.

show abstract

Section: Related Workmentioning

confidence: 99%

Improving the Betweenness Centrality of a Node by Adding Links

Bergamini

Crescenzi

D’Angelo

et al. 2018

ACM J. Exp. Algorithmics

View full text Add to dashboard Cite

show abstract

“…In a recent work, the time complexity for Alg. 1 is brought down to O(km 3/2 ) in [18] using the fast triangle computation method in [34]. For large value of k = θ(n), the time-complexity of the algorithm in [18] could be as high as O(nm 3/2 ) which is very expensive and not scalable for practical large size data.…”

Section: A Naive Greedy Algorithmmentioning

confidence: 99%

“…1 is brought down to O(km 3/2 ) in [18] using the fast triangle computation method in [34]. For large value of k = θ(n), the time-complexity of the algorithm in [18] could be as high as O(nm 3/2 ) which is very expensive and not scalable for practical large size data. To this end, we present in next section our scalable Discounting Algorithms for ktriangle-breaking-node with time complexity O(m 3/2 +km) which is up to m 1/2 times faster than the algorithm in [18].…”

Section: A Naive Greedy Algorithmmentioning

confidence: 99%

“…Implementation and Testing Environment: We implemented our algorithms DAK-n and DAK-e in C++ programming language with GCC 4.8 C++11 compiler. We also implemented the GreedyAll [18] algorithm following closely the provided description and pseudo-code. All the experiments are run on a Linux environment with 2.2Ghz Xeon 8 core processor and 100GB of RAM.…”

Section: A Experimental Settingsmentioning

confidence: 99%

“…[18] also proposed another algorithm, namely Approx which used FMsketch to approximate the triangle-breaking gain; however, this approximation algorithm imposes the same time complexity with GreedyAll.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Transitivity Demolition and the Fall of Social Networks

Nguyen

et al. 2017

IEEE Access

View full text Add to dashboard Cite

In this paper, we study crucial elements of a complex network, namely its nodes and connections, which play a key role in maintaining the network's structure and function under unexpected structural perturbations of nodes and edges removal. Specifically, we want to identify vital nodes and edges whose failure (either random or intentional) will break the most number of connected triples (or triangles) in the network. This problem is extremely important because connected triples form the foundation of strong connections in many real-world systems, such as mutual relationships in social networks, reliable data transmission in communication networks, and stable routing strategies in mobile networks. Disconnected triples, analog to broken mutual connections, can greatly affect the network's structure and disrupt its normal function, which can further lead to the corruption of the entire system. The analysis of such crucial elements will shed light on key factors behind the resilience and robustness of many complex systems in practice.We formulate the analysis under multiple optimization problems and show their intractability. We next propose efficient approximation algorithms, namely DAK-n and DAK-e, which guarantee an (1 − 1/e)-approximate ratio (compared to the overall optimal solutions) while having the same time complexity as the best triangle counting and listing algorithm on power-law networks. This advantage makes our algorithms scale extremely well even for very large networks. In an application perspective, we perform comprehensive experiments on real social traces with millions of nodes and billions of edges. These empirical experiments indicate that our approaches achieve comparably better results while are up to 100x faster than current state-ofthe-art methods.

show abstract