Relevant bibliographies by topics / Triangle counting in graphs

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Triangle counting in graphs'

Author: Grafiati
Published: 24 April 2022

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Journal articles on the topic "Triangle counting in graphs"

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Burkhardt, Paul. "Graphing trillions of triangles." Information Visualization 16, no. 3 (September 12, 2016): 157–66. http://dx.doi.org/10.1177/1473871616666393.

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The increasing size of Big Data is often heralded but how data are transformed and represented is also profoundly important to knowledge discovery, and this is exemplified in Big Graph analytics. Much attention has been placed on the scale of the input graph but the product of a graph algorithm can be many times larger than the input. This is true for many graph problems, such as listing all triangles in a graph. Enabling scalable graph exploration for Big Graphs requires new approaches to algorithms, architectures, and visual analytics. A brief tutorial is given to aid the argument for thoughtful representation of data in the context of graph analysis. Then a new algebraic method to reduce the arithmetic operations in counting and listing triangles in graphs is introduced. Additionally, a scalable triangle listing algorithm in the MapReduce model will be presented followed by a description of the experiments with that algorithm that led to the current largest and fastest triangle listing benchmarks to date. Finally, a method for identifying triangles in new visual graph exploration technologies is proposed.
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Sridevi, P. "A Note on Detection of Communities in Social Networks." International Journal of Engineering and Computer Science 9, no. 03 (March 19, 2020): 24978–83. http://dx.doi.org/10.18535/ijecs/v9i03.4452.

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The modern Science of Social Networks has brought significant advances to our understanding of the Structure, dynamics and evolution of the Network. One of the important features of graphs representing the Social Networks is community structure. The communities can be considered as fairly independent components of the social graph that helps identify groups of users with similar interests, locations, friends, or occupations. The community structure is closely tied to triangles and their count forms the basis of community detection algorithms. The present work takes into consideration, a triangle instead of the edge as the basic indicator of a strong relation in the social graph. A simple triangle counting algorithm is then used to evaluate different metrics that are employed to detect strong communities. The methodology is applied to Zachary Social network and discussed. The results bring out the usefulness of counting triangles in a network to detect strong communities in a Social Network.
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Cooper, Jeff, and Dhruv Mubayi. "Counting independent sets in triangle-free graphs." Proceedings of the American Mathematical Society 142, no. 10 (June 6, 2014): 3325–34. http://dx.doi.org/10.1090/s0002-9939-2014-12068-5.

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Shin, Kijung, Euiwoong Lee, Jinoh Oh, Mohammad Hammoud, and Christos Faloutsos. "CoCoS: Fast and Accurate Distributed Triangle Counting in Graph Streams." ACM Transactions on Knowledge Discovery from Data 15, no. 3 (April 12, 2021): 1–30. http://dx.doi.org/10.1145/3441487.

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Given a graph stream, how can we estimate the number of triangles in it using multiple machines with limited storage? Specifically, how should edges be processed and sampled across the machines for rapid and accurate estimation? The count of triangles (i.e., cliques of size three) has proven useful in numerous applications, including anomaly detection, community detection, and link recommendation. For triangle counting in large and dynamic graphs, recent work has focused largely on streaming algorithms and distributed algorithms but little on their combinations for “the best of both worlds.” In this work, we propose CoCoS , a fast and accurate distributed streaming algorithm for estimating the counts of global triangles (i.e., all triangles) and local triangles incident to each node. Making one pass over the input stream, CoCoS carefully processes and stores the edges across multiple machines so that the redundant use of computational and storage resources is minimized. Compared to baselines, CoCoS is: (a) accurate: giving up to smaller estimation error; (b) fast : up to faster, scaling linearly with the size of the input stream; and (c) theoretically sound : yielding unbiased estimates.
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Xuan, Wei, Huawei Cao, Mingyu Yan, Zhimin Tang, Xiaochun Ye, and Dongrui Fan. "BSR-TC: Adaptively Sampling for Accurate Triangle Counting over Evolving Graph Streams." International Journal of Software Engineering and Knowledge Engineering 31, no. 11n12 (December 2021): 1561–81. http://dx.doi.org/10.1142/s021819402140012x.

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Triangle counting is a fundamental graph mining problem, widely employed in various real-world application scenarios. Given the large scale of graph streams and limited memory space, it is feasible to achieve the estimation of global and local triangles by sampling. Existing streaming algorithms for triangle counting can be generalized into two categories: Reservoir-based methods and Bernoulli-based methods. The former use a fixed memory budget, whose size is difficult to set for accurate estimation without any prior knowledge about graph streams. The latter sample edges by a specified probability, but memory budget is uncontrollable for following a binomial distribution. In this work, we propose a novel and bounded-sampling-ratio algorithm for both global and local triangle counting, called BSR-TC, by adaptively resizing memory budget upwards over evolving graph streams. Specifically, our proposed single-pass BSR-TC can gain more advantage than the state-of-the-art algorithms over the continuous growth of graph streams. Experimental results show that BSR-TC achieves accuracy of at least 99.8% for global triangles, when the ratio of initial memory budget against whole graph streams [Formula: see text] and given [Formula: see text], respectively.
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Che, Yulin, Zhuohang Lai, Shixuan Sun, Yue Wang, and Qiong Luo. "Accelerating truss decomposition on heterogeneous processors." Proceedings of the VLDB Endowment 13, no. 10 (June 2020): 1751–64. http://dx.doi.org/10.14778/3401960.3401971.

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Truss decomposition is to divide a graph into a hierarchy of subgraphs, or trusses. A subgraph is a k -truss ( k ≥ 2) if each edge is in at least k --- 2 triangles in the subgraph. Existing algorithms work by first counting the number of triangles each edge is in and then iteratively incrementing k to peel off the edges that will not appear in ( k + 1)-truss. Due to the data and computation intensity, truss decomposition on billion-edge graphs takes hours to complete on a commodity computer. We propose to accelerate in-memory truss decomposition by (1) compacting intermediate results to optimize memory access, (2) dynamically adjusting the computation based on data characteristics, and (3) parallelizing the algorithm on both the multicore CPU and the GPU. In particular, we optimize the triangle enumeration with data skew handling, and determine at runtime whether to pursue peeling or direct triangle counting to obtain a certain k -truss. We further develop a CPU-GPU co-processing strategy in which the CPU first computes intermediate results and sends the compacted results to the GPU for further computation. Our experiments on real-world datasets show that our implementations outperform the state of the art by up to an order of magnitude. Our source code is publicly available at https://github.com/RapidsAtHKUST/AccTrussDecomposition.
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Yang, Xu, Chao Song, Mengdi Yu, Jiqing Gu, and Ming Liu. "Distributed Triangle Approximately Counting Algorithms in Simple Graph Stream." ACM Transactions on Knowledge Discovery from Data 16, no. 4 (August 31, 2022): 1–43. http://dx.doi.org/10.1145/3494562.

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Recently, the counting algorithm of local topology structures, such as triangles, has been widely used in social network analysis, recommendation systems, user portraits and other fields. At present, the problem of counting global and local triangles in a graph stream has been widely studied, and numerous triangle counting steaming algorithms have emerged. To improve the throughput and scalability of streaming algorithms, many researches of distributed streaming algorithms on multiple machines are studied. In this article, we first propose a framework of distributed streaming algorithm based on the Master-Worker-Aggregator architecture. The two core parts of this framework are an edge distribution strategy, which plays a key role to affect the performance, including the communication overhead and workload balance, and aggregation method, which is critical to obtain the unbiased estimations of the global and local triangle counts in a graph stream. Then, we extend the state-of-the-art centralized algorithm TRIÈST into four distributed algorithms under our framework. Compared to their competitors, experimental results show that DVHT-i is excellent in accuracy and speed, performing better than the best existing distributed streaming algorithm. DEHT-b is the fastest algorithm and has the least communication overhead. What’s more, it almost achieves absolute workload balance.
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Bulteau, Laurent, Vincent Froese, Konstantin Kutzkov, and Rasmus Pagh. "Triangle Counting in Dynamic Graph Streams." Algorithmica 76, no. 1 (July 23, 2015): 259–78. http://dx.doi.org/10.1007/s00453-015-0036-4.

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Kolountzakis, Mihail N., Gary L. Miller, Richard Peng, and Charalampos E. Tsourakakis. "Efficient Triangle Counting in Large Graphs via Degree-Based Vertex Partitioning." Internet Mathematics 8, no. 1-2 (March 2012): 161–85. http://dx.doi.org/10.1080/15427951.2012.625260.

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Sheshbolouki, Aida, and M. Tamer Özsu. "sGrapp: Butterfly Approximation in Streaming Graphs." ACM Transactions on Knowledge Discovery from Data 16, no. 4 (August 31, 2022): 1–43. http://dx.doi.org/10.1145/3495011.

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We study the fundamental problem of butterfly (i.e., (2,2)-bicliques) counting in bipartite streaming graphs. Similar to triangles in unipartite graphs, enumerating butterflies is crucial in understanding the structure of bipartite graphs. This benefits many applications where studying the cohesion in a graph shaped data is of particular interest. Examples include investigating the structure of computational graphs or input graphs to the algorithms, as well as dynamic phenomena and analytic tasks over complex real graphs. Butterfly counting is computationally expensive, and known techniques do not scale to large graphs; the problem is even harder in streaming graphs. In this article, following a data-driven methodology, we first conduct an empirical analysis to uncover temporal organizing principles of butterflies in real streaming graphs and then we introduce an approximate adaptive window-based algorithm, sGrapp, for counting butterflies as well as its optimized version sGrapp-x. sGrapp is designed to operate efficiently and effectively over any graph stream with any temporal behavior. Experimental studies of sGrapp and sGrapp-x show superior performance in terms of both accuracy and efficiency.
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Dissertations / Theses on the topic "Triangle counting in graphs"

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Hoens, T. Ryan. "Counting and sampling paths in graphs /." Online version of thesis, 2008. http://hdl.handle.net/1850/7545.

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Leung, Yiu-cho. "Counting combinatorial structures in recursively constructible graphs /." View abstract or full-text, 2007. http://library.ust.hk/cgi/db/thesis.pl?CSED%202007%20LEUNG.

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Creed, Patrick John. "Counting and sampling problems on Eulerian graphs." Thesis, University of Edinburgh, 2010. http://hdl.handle.net/1842/4759.

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In this thesis we consider two sets of combinatorial structures defined on an Eulerian graph: the Eulerian orientations and Euler tours. We are interested in the computational problems of counting (computing the number of elements in the set) and sampling (generating a random element of the set). Specifically, we are interested in the question of when there exists an efficient algorithm for counting or sampling the elements of either set. The Eulerian orientations of a number of classes of planar lattices are of practical significance as they correspond to configurations of certain models studied in statistical physics. In 1992 Mihail and Winkler showed that counting Eulerian orientations of a general Eulerian graph is #P-complete and demonstrated that the problem of sampling an Eulerian orientation can be reduced to the tractable problem of sampling a perfect matching of a bipartite graph. We present a proof that this problem remains #Pcomplete when the input is restricted to being a planar graph, and analyse a natural algorithm for generating random Eulerian orientations of one of the afore-mentioned planar lattices. Moreover, we make some progress towards classifying the range of planar graphs on which this algorithm is rapidly mixing by exhibiting an infinite class of planar graphs for which the algorithm will always take an exponential amount of time to converge. The problem of counting the Euler tours of undirected graphs has proven to be less amenable to analysis than that of Eulerian orientations. Although it has been known for many years that the number of Euler tours of any directed graph can be computed in polynomial time, until recently very little was known about the complexity of counting Euler tours of an undirected graph. Brightwell and Winkler showed that this problem is #P-complete in 2005 and, apart from a few very simple examples, e.g., series-parellel graphs, there are no known tractable cases, nor are there any good reasons to believe the problem to be intractable. Moreover, despite several unsuccessful attempts, there has been no progress made on the question of approximability. Indeed, this problem was considered to be one of the more difficult open problems in approximate counting since long before the complexity of exact counting was resolved. By considering a randomised input model, we are able to show that a very simple algorithm can sample or approximately count the Euler tours of almost every d-in/d-out directed graph in expected polynomial time. Then, we present some partial results towards showing that this algorithm can be used to sample or approximately count the Euler tours of almost every 2d-regular graph in expected polynomial time. We also provide some empirical evidence to support the unproven conjecture required to obtain this result. As a sideresult of this work, we obtain an asymptotic characterisation of the distribution of the number of Eulerian orientations of a random 2d-regular graph.
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Mohr, Elena [Verfasser]. "Some counting problems in graphs / Elena Mohr." Ulm : Universität Ulm, 2021. http://d-nb.info/1232323918/34.

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Guzman, Christopher Abraham. "Counting Threshold Graphs and Finding Inertia Sets." BYU ScholarsArchive, 2013. https://scholarsarchive.byu.edu/etd/3847.

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This thesis is separated into two parts: threshold graphs and inertia sets. First we present an algorithmic approach to finding the minimum rank of threshold graphs and then progress to counting the number of threshold graphs with a specific minimum rank. Second, we find an algorithmic and more automated way of determining the inertia set of graphs with seven or fewer vertices using theorems and lemmata found in previous papers. Inertia sets are a relaxation of the inverse eigenvalue problem. Instead of determining all the possible eigenvalues that can be obtained by matrices with a specific zero/nonzero pattern we restrict to counting the number of positive and negative eigenvalues.
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Zhang, Yuanping. "Counting the number of spanning trees in some special graphs /." View Abstract or Full-Text, 2002. http://library.ust.hk/cgi/db/thesis.pl?COMP%202002%20ZHANG.

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Flores, Nicandro. "Counting directed acyclic graphs and its application to Monte Carlo learning of Bayesian networks." Connect to online resource, 2007. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:1447692.

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Roth, Marc [Verfasser], and Holger [Akademischer Betreuer] Dell. "Counting Problems on Quantum Graphs : Parameterized and Exact Complexity Classifications / Marc Roth ; Betreuer: Holger Dell." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2019. http://d-nb.info/1191755622/34.

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Roth, Marc Verfasser], and Holger [Akademischer Betreuer] [Dell. "Counting Problems on Quantum Graphs : Parameterized and Exact Complexity Classifications / Marc Roth ; Betreuer: Holger Dell." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2019. http://nbn-resolving.de/urn:nbn:de:bsz:291--ds-283486.

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Arifuzzaman, S. M. "Parallel Mining and Analysis of Triangles and Communities in Big Networks." Diss., Virginia Tech, 2016. http://hdl.handle.net/10919/72281.

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A network (graph) is a powerful abstraction for interactions among entities in a system. Examples include various social, biological, collaboration, citation, and co-purchase networks. Real-world networks are often characterized by an abundance of triangles and the existence of well-structured communities. Thus, counting triangles and detecting communities in networks have become important algorithmic problems in network mining and analysis. In the era of big data, the network data emerged from numerous scientific disciplines are very large. Online social networks such as Twitter and Facebook have millions to billions of users. Such massive networks often do not fit in the main memory of a single machine, and the existing sequential methods might take a prohibitively large runtime. This motivates the need for scalable parallel algorithms for mining and analysis. We design MPI-based distributed-memory parallel algorithms for counting triangles and detecting communities in big networks and present related analysis. The dissertation consists of four parts. In Part I, we devise parallel algorithms for counting and enumerating triangles. The first algorithm employs an overlapping partitioning scheme and novel load-balancing schemes leading to a fast algorithm. We also design a space-efficient algorithm using non-overlapping partitioning and an efficient communication scheme. This space efficiency allows the algorithm to work on even larger networks. We then present our third parallel algorithm based on dynamic load balancing. All these algorithms work on big networks, scale to a large number of processors, and demonstrate very good speedups. An important property, very related to triangles, of many real-world networks is high transitivity, which states that two nodes having common neighbors tend to become neighbors themselves. In Part II, we characterize networks by quantifying the number of common neighbors and demonstrate its relationship to community structure of networks. In Part III, we design parallel algorithms for detecting communities in big networks. We propose efficient load balancing and communication approaches, which lead to fast and scalable algorithms. Finally, in Part IV, we present scalable parallel algorithms for a useful graph preprocessing problem-- converting edge list to adjacency list. We present non-trivial parallelization with efficient HPC-based techniques leading to fast and space-efficient algorithms.
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Books on the topic "Triangle counting in graphs"

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Dyer, Martin. Approximately counting Hamilton cycles in dense graphs. Edinburgh: LFCS, Dept. of Computer Science, University of Edinburgh, 1993.

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Cai, Jiazhen. Counting embeddings of planar graphs using DFS trees. New York: Courant Institute of Mathematical Sciences, New York University, 1992.

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Miss B's class makes tables and graphs. Place of publication not identified]: Harcourt School Publishers, 2006.

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1949-, Rödl Vojtěch, Ruciński Andrzej, and Tetali Prasad, eds. A Sharp threshold for random graphs with a monochromatic triangle in every edge coloring. Providence, R.I: American Mathematical Society, 2006.

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Master math: Trigonometry : including everything from trigonometric functions, equations, triangle, and graphs to identities, coordinate systems, and complex numbers. Clifton Park, NY: Thomson/Delmar Learning, 2002.

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Smoothey, Marion. Let's investigate. North Bellmore, N. Y: Marshall Cavendish, 1993.

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Jones, Charles Harold. Triangle intersection graphs and visibility graphs. 1993.

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Marvin, Bittinger, Judith A. Penna, and David Ellenbogen. Precalculus: Graphs and Models, A Right Triangle Approach. Pearson, 2016.

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Marvin, Bittinger, Judith A. Penna, and David Ellenbogen. Precalculus: Graphs and Models - A Right Triangle Approach. Pearson Education, Limited, 2012.

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Bondarenko, Boris A. Generalized Pascal Triangles and Pyramids, Their Fractals, Graphs, and Applications. Fibonacci Assn, 1992.

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Book chapters on the topic "Triangle counting in graphs"

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Wang, Wenan, Yu Gu, Zhigang Wang, and Ge Yu. "Parallel Triangle Counting over Large Graphs." In Database Systems for Advanced Applications, 301–8. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-37450-0_23.

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Kutzkov, Konstantin, and Rasmus Pagh. "Triangle Counting in Dynamic Graph Streams." In Algorithm Theory – SWAT 2014, 306–18. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-08404-6_27.

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Kolountzakis, Mihail N., Gary L. Miller, Richard Peng, and Charalampos E. Tsourakakis. "Efficient Triangle Counting in Large Graphs via Degree-Based Vertex Partitioning." In Algorithms and Models for the Web-Graph, 15–24. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-18009-5_3.

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Jowhari, Hossein, and Mohammad Ghodsi. "New Streaming Algorithms for Counting Triangles in Graphs." In Lecture Notes in Computer Science, 710–16. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11533719_72.

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Han, Guyue, and Harish Sethu. "On Counting Triangles Through Edge Sampling in Large Dynamic Graphs." In Lecture Notes in Social Networks, 133–57. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11286-8_6.

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Singh, Paramvir, Venkatesh Srinivasan, and Alex Thomo. "Fast and Scalable Triangle Counting in Graph Streams: The Hybrid Approach." In Advanced Information Networking and Applications, 107–19. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-75075-6_9.

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Shin, Kijung, Jisu Kim, Bryan Hooi, and Christos Faloutsos. "Think Before You Discard: Accurate Triangle Counting in Graph Streams with Deletions." In Machine Learning and Knowledge Discovery in Databases, 141–57. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-10928-8_9.

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Schank, Thomas, and Dorothea Wagner. "Finding, Counting and Listing All Triangles in Large Graphs, an Experimental Study." In Experimental and Efficient Algorithms, 606–9. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11427186_54.

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Jha, Madhav. "Counting Triangles in Graph Streams." In Encyclopedia of Algorithms, 458–64. New York, NY: Springer New York, 2016. http://dx.doi.org/10.1007/978-1-4939-2864-4_705.

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Jha, Madhav. "Counting Triangles in Graph Streams." In Encyclopedia of Algorithms, 1–7. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-642-27848-8_705-1.

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Conference papers on the topic "Triangle counting in graphs"

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Do, Hoang Giang, and Wee Keong Ng. "Privacy-Preserving Triangle Counting in Distributed Graphs." In 2016 IEEE 30th International Conference on Advanced Information Networking and Applications (AINA). IEEE, 2016. http://dx.doi.org/10.1109/aina.2016.28.

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Tangwongsan, Kanat, A. Pavan, and Srikanta Tirthapura. "Parallel triangle counting in massive streaming graphs." In the 22nd ACM international conference. New York, New York, USA: ACM Press, 2013. http://dx.doi.org/10.1145/2505515.2505741.

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Ding, Xiaofeng, Xiaodong Zhang, Zhifeng Bao, and Hai Jin. "Privacy-Preserving Triangle Counting in Large Graphs." In CIKM '18: The 27th ACM International Conference on Information and Knowledge Management. New York, NY, USA: ACM, 2018. http://dx.doi.org/10.1145/3269206.3271736.

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Makkar, Devavret, David A. Bader, and Oded Green. "Exact and Parallel Triangle Counting in Dynamic Graphs." In 2017 IEEE 24th International Conference on High Performance Computing (HiPC). IEEE, 2017. http://dx.doi.org/10.1109/hipc.2017.00011.

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García-Soriano, David, and Konstantin Kutzkov. "Triangle counting in streamed graphs via small vertex covers." In Proceedings of the 2014 SIAM International Conference on Data Mining. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2014. http://dx.doi.org/10.1137/1.9781611973440.40.

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Becchetti, Luca, Paolo Boldi, Carlos Castillo, and Aristides Gionis. "Efficient semi-streaming algorithms for local triangle counting in massive graphs." In the 14th ACM SIGKDD international conference. New York, New York, USA: ACM Press, 2008. http://dx.doi.org/10.1145/1401890.1401898.

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Pearce, Roger. "Triangle counting for scale-free graphs at scale in distributed memory." In 2017 IEEE High Performance Extreme Computing Conference (HPEC). IEEE, 2017. http://dx.doi.org/10.1109/hpec.2017.8091051.

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Ouyang, Zhiyou, Shanni Wu, Tongtong Zhao, Dong Yue, and Tengfei Zhang. "Memory-Efficient GPU-Based Exact and Parallel Triangle Counting in Large Graphs." In 2019 IEEE 21st International Conference on High Performance Computing and Communications; IEEE 17th International Conference on Smart City; IEEE 5th International Conference on Data Science and Systems (HPCC/SmartCity/DSS). IEEE, 2019. http://dx.doi.org/10.1109/hpcc/smartcity/dss.2019.00304.

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Gou, Xiangyang, and Lei Zou. "Sliding Window-based Approximate Triangle Counting over Streaming Graphs with Duplicate Edges." In SIGMOD/PODS '21: International Conference on Management of Data. New York, NY, USA: ACM, 2021. http://dx.doi.org/10.1145/3448016.3452800.

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Yu, Mengdi, Chao Song, Jiqing Gu, and Ming Liu. "Distributed Triangle Counting Algorithms in Simple Graph Stream." In 2019 IEEE 25th International Conference on Parallel and Distributed Systems (ICPADS). IEEE, 2019. http://dx.doi.org/10.1109/icpads47876.2019.00049.

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Reports on the topic "Triangle counting in graphs"

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Yasar, Abdurrahman, Sivasankaran Rajamanickam, Jonathan Berry, and Umit Catalyurek. A Block-Based Triangle Counting Algorithm on Heterogeneous Environments. Office of Scientific and Technical Information (OSTI), September 2020. http://dx.doi.org/10.2172/1669197.

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