Zhuoxu Zhang, Zezhong Ding · 2022 IEEE 5th International Conference on Automation, Electronics and Electrical Engineering (AUTEEE) · 2022
Graph partition, as a mandatory step in the process of large scale graph and distributed graph analysis system, has been heavily examined in the past decade. Generally, they have been categorized into two types, offline and online. As the massive growth of the modern graph, tradition offline methods fail in achieving both effectiveness and efficiency. Hence, there is an urgent need for fast and scalable online graph partition approaches. Most state-of-art online algorithms focus on the design of streaming methods to reach the merit. In such a context, a series of novel approaches emerge recently, most of which concentrate on partitioning the original graph based on the streaming clustering results. These innovative manners have been experimentally proved to have a better performance compared with the mainstream methods. Hence, it is essential to design a high-quality streaming graph clustering algorithm in order to refine these cluster-based partitioners. In this article, we purpose a fine-grained streaming clustering algorithms specifically designed for cluster-based partitioner. Our experimental results demonstrated that the purposed clustering approach can achieve a better replication factor w.r.t the constrained balanced factor compared to the baseline methods.
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Satyabrata Jana, Supantha Pandit, Sasanka Roy · Lecture notes in computer science · 2021
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Zsófia Kallus (741703), Norbert Barankai (741704), János Szüle (657305) et al. · Figshare · 2015
<p>Modularities of the found and of the competing partition of the same regional subgraph and their two measures of difference: normalized mutual information and adjusted Rand index. (<i>combined</i> refers to result mixed with partial second-level clustering. <i>adm0</i> denotes the country-level, while <i>adm1</i> and <i>adm2</i> the corresponding first- and the second-level subnational administrative divisions, respectively.)</p><p>Regional graph partition comparisons.</p>
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Zsófia Kallus (741703), Norbert Barankai (741704), János Szüle (657305) et al. · Figshare · 2015
<p>Each point represents a comparison of two partitions of the same regional graph, i.e., one line from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0126713#pone.0126713.t003" target="_blank">Table 3</a>. The modularity of the partition found by our method is shown on the vertical axis while the modularity of the competing partition is given on the horizontal axis. Color shows the difference between the two partitions measured by the <i>adjusted Rand index</i> and the area of the disk is proportional to the <i>number of pixels</i> in the graph.</p>
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Nguyen, Thinh D. · Figshare · 2019
In this paper, we consider the task of partitioning a given graph intwo two non-empty subgraphs such that one of them has no vertex of degree less than 2, the other has no vertex of degree less than 3. We show that this problem is a difficult one.
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Sebastian M. Cioabă, Peter J. Cameron · American Mathematical Monthly · 2015
Given a graph G on n vertices, for which m is it possible to partition the edge set of the m-fold complete graph mKn into copies of G? We show that there is an integer m0, which we call the partition modulus of G, such that the set M(G) of values of m for which such a partition exists consists of all but finitely many multiples of m0. Trivial divisibility conditions derived from G give an integer m1 that divides m0; we call the quotient m0/m1 the partition index of G. It seems that most graphs G have partition index equal to 1, but we give two infinite families of graphs for which this is not true. We also compute M(G) for various graphs and outline some connections between our problem and the existence of designs of various types.
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Peter J. Cameron, Sebastian M. Cioabă · arXiv (Cornell University) · 2014
Given a graph $G$ on $n$ vertices, for which $m$ is it possible to partition the edge set of the $m$-fold complete graph $mK_n$ into copies of $G$? We show that there is an integer $m_0$, which we call the \emph{partition modulus of $G$}, such that the set $M(G)$ of values of $m$ for which such a partition exists consists of all but finitely many multiples of $m_0$. Trivial divisibility conditions derived from $G$ give an integer $m_1$ which divides $m_0$; we call the quotient $m_0/m_1$ the \emph{partition index of $G$}. It seems that most graphs $G$ have partition index equal to $1$, but we give two infinite families of graphs for which this is not true. We also compute $M(G)$ for various graphs, and outline some connections between our problem and the existence of designs of various types.
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Tomas Feder , Pavol Hell , Sulamita Klein , Rajeev Motwani · 2008
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Julien Darlay, Nadia Brauner, Julien Moncel · HAL (Le Centre pour la Communication Scientifique Directe) · 2012
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Alexander Barvinok · Algorithms and combinatorics · 2016
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Montresor, Alberto, Centellegher, Simone · Institutional Research Information System (Università degli Studi di Trento) · 2016
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Hadil H. Sami, Mohammed Kassim Ahmed, Ammar S. Mahmood · Iraqi Journal of Science · 2023
The Syriac language is one of the ancient Semitic languages that appeared in the first century AD. It is currently used in a number of cities in Iraq, Turkey, and others. In this research paper, we tried to apply the work of Ali and Mahmood 2020 on the letters and words in the Syriac language to find a new encoding for them and increase the possibility of reading the message by other people.
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Wenfei Fan, Muyang Liu, Ping Lü et al. · IEEE Transactions on Knowledge and Data Engineering · 2021
Graph computations often have to be conducted in parallel on partitioned graphs. The choice of graph partitioning strategies, however, has strong impact on the design of graph computation algorithms. A graph algorithm developed under edge-cut partitions may not work correctly under vertex-cut, and vice versa. We often have to rewrite our algorithms when we switch from, e.g., edge-cut to vertex-cut. To cope with this, we propose a notion of partition transparency, such that graph algorithms are able to work correctly under different partitions without changes and moreover, benefit from recent hybrid partitions to speed up computations. Furthermore, we identify conditions under which graph algorithms are guaranteed to be partition-transparent, in graph-centric and vertex-centric models. We show that a variety of graph algorithms can be made partition-transparent. Using real-life and synthetic graphs, we experimentally verify that partition-transparent algorithms compute correct answers under different partitions; better still, under hybrid partitions these algorithms perform better than algorithms tailored for edge-cut and vertex-cut partitions in efficiency.
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Dorit S. Hochbaum, Anu Pathria · Networks · 1996
The bottleneck graph partition problem is to partition the nodes of a graph into two equally sized sets, so that the maximum edge weight in the cut separating the two sets is minimum. Whereas the graph partition problem, where the sum of the edge weights in the cut is to be minimized, is NP-hard, the bottleneck version is polynomial. This paper describes an O(n2 log n) algorithm for the bottleneck graph partition problem, where n is the number of nodes in the graph. We point out two interesting issues related to dynamic algorithms. We also generalize our polynomiality result (for fixed k) to the bottleneck k-cut problem with specified vertices and bounded components. © 1996 John Wiley & Sons, Inc.
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Yan Jin, Yunshu Gao, Beibei Zhang · Discrete Applied Mathematics · 2013
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Alessio Guerrieri, Alberto Montresor, Simone Centellegher · 2016
This paper presents ETSCH, a novel paradigm for processing large graphs. ETSCH departs from the vertex-based approach of BSP frameworks like PREGEL in two ways: first, the units of computation are not the vertices, but rather a collection of subgraphs, obtained by partitioning the input graph, second, the subgraphs are obtained through an edge-partitioning algorithm, in which edges, rather than vertices, are subdivided into disjoint subsets Global computations over the graph are then easily expressed using classical centralized algorithms executed on each of the partitions, with the only additional burden of specifying simple reconciliation procedures when vertices are replicated in multiple computing nodes. The ETSCH paradigm has been implemented both on top of existing frameworks like HADOOP, SPARK, as a stand-alone service based on AKKA, a toolkit for building distributed message-driven applications. When considering problems like single-source shortest path, PageRank, our experiments show that solutions based on ETSCH/HADOOP, ETSCH/SPARK already outperform the standard solutions to the same problems in HADOOP, SPARK, respectively. But it is our AKKA implementation that really shines: the execution time on graphs with millions of edges falls down from from thousands of seconds (ETSCH/HADOOP) to tens of seconds (ETSCH/SPARK) to seconds (ETSCH/AKKA), while easily scaling to graphs with billions of edges. ETSCH/AKKA is also faster than other partition-centric frameworks like BLOGEL, GPS.
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Julien Darlay, Nadia Brauner, Julien Moncel · Discrete Applied Mathematics · 2012
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Annie Sabitha Paul, K. K. Gireesan · Advances and Applications in Discrete Mathematics · 2023
For two vertices $u$ and $v$ in a connected graph $G$, the cyclic distance between them is defined as the minimum number of cycles to be traversed from a cycle containing $u$ to a cycle containing $v$. This paper deals with a partition of the edges of a graph using cyclic distance, and discusses how to reduce a graph using this notion of distance and some properties of reduced graph of a graph. Received: March 17, 2023Revised: June 16, 2023Accepted: July 1, 2023
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Yves Métivier, J. M. Robson, Nasser Saheb-Djahromi et al. · Information and Computation · 2010
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Joaquim Pinto da Costa, P. R. Rao · SHILAP Revista de lepidopterología · 2022
When several clustering algorithms are applied to a dataset E or the same algorithm with different parameters, we get several different partitions of the dataset. In this paper we consider the problem of finding a consensus partition between the set of these partitions. This consensus partition, called central partition, minimises the average number of disagreements between all of the partitions and has been considered for instance in [14, 5] in a different context from ours. We consider it in the context of partition-distance defined in [7]. We focus our attention in two particular distance functions between partitions and then do an experimental comparison between the two corresponding central partitions. In addition, by using the concept of strong patterns (maximal subset of elements that are always clustered together in all partitions), we define a new graph where the nodes are the strong patterns. This graph contains essentially the same information as the partition graph corresponding to the set E defined in [7], but is much simpler as the number of strong patterns is expected to be much smaller than the cardinal of E. Then, some properties of this new graph are proved.
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