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Partitioning into graphs with only small components

Noga Alon, Guoli Ding, Bogdan Oporowski, Dirk Vertigan
2003 Journal of combinatorial theory. Series B (Print)  
The paper presents several results on edge partitions and vertex partitions of graphs into graphs with bounded size components.  ...  We also show that an arbitrary graph of maximum degree four has a vertex partition into two graphs, each of which has components on at most 57 vertices.  ...  In this paper, we investigate the existence of vertex and edge partitions into graphs with only components of bounded size.  ... 
doi:10.1016/s0095-8956(02)00006-0 fatcat:no23xsfilzaiddeq3hibj2nn6i

Geographically Organized Small Communities and the Hardness of Clustering Social Networks [chapter]

Miklós Kurucz, András A. Benczúr
2010 Annals of Information Systems  
that handle tentacles and small dense communities.  ...  Spectral clustering, while perhaps the most efficient heuristics for graph partitioning, has recently gathered bad reputation for failure over large-scale power law graphs.  ...  Thanks to Zoltán Gyöngyi for providing us with the host graph with labels from the Open Directory top hierarchy for the UK2007-WEBSPAM crawl of the UbiCrawler [6] .  ... 
doi:10.1007/978-1-4419-6287-4_10 fatcat:gmfz6mezdva4rh2d2aespmm6kq

Bipartitioning of directed and mixed random graphs

Adam Lipowski, António Luis Ferreira, Dorota Lipowska, Manuel A Barroso
2019 Journal of Statistical Mechanics: Theory and Experiment  
In particular, the satisfability threshold coincides with the relative size of the giant OUT component reaching 1/2.  ...  Moreover, when counting undirected links as two directed ones, the partition cost, and cluster properties, as well as location of the replica symmetry breaking transition for these random graphs depend  ...  As expected, in the regime g O < 1/2 partitions with b = 0 (or with very small b) are easily found.  ... 
doi:10.1088/1742-5468/ab3280 fatcat:usw3pxniw5dinasfh5r2esarly

Multiscale visualization of small world networks

D. Auber, Y. Chiricota, F. Jourdan, G. Melancon
2003 IEEE Symposium on Information Visualization 2003 (IEEE Cat. No.03TH8714)  
We describe a metric that has been designed in order to identify the weakest edges in a small world network leading to an easy and low cost filtering procedure that breaks up a graph into smaller and highly  ...  connected components.  ...  Most networks not only are small world, but their highly connected components themselves are small world.  ... 
doi:10.1109/infvis.2003.1249011 dblp:conf/infovis/AuberCJM03 fatcat:oaoolslmd5b5rgajv7kgsakjfa

A Hybrid Genetic Algorithm for the Traveling Salesman Problem Using Generalized Partition Crossover [chapter]

Darrell Whitley, Doug Hains, Adele Howe
2010 Parallel Problem Solving from Nature, PPSN XI  
We present a hybrid Genetic Algorithm that incorporates the Generalized Partition Crossover (GPX) operator to produce an algorithm that is competitive with the state of the art for the Traveling Salesman  ...  Additional analysis shows that all the edges found in the globally optimal solution are present in a population after only a few generations in almost every run.  ...  If there are multiple ways to partition graph G into subgraphs, where each partition has cost 2, PX uses only one of these partitions.  ... 
doi:10.1007/978-3-642-15844-5_57 dblp:conf/ppsn/WhitleyHH10 fatcat:scvhvxnsrjfotcal56do3gl7dm

Efficiently Processing Workflow Provenance Queries on SPARK [article]

Rajmohan C, Pranay Lohia, Himanshu Gupta, Siddhartha Brahma, Mauricio Hernandez, Sameep Mehta
2018 arXiv   pre-print
The framework exploits the workflow dependency graph to effectively partition the large components into a collection of weakly connected sets.  ...  The proposed framework computes weakly connected components on the workflow provenance graph and further partitions the large components as a collection of weakly connected sets.  ...  With hash-partitioning enabled, a lookup needs to scan only one partition.  ... 
arXiv:1808.08424v2 fatcat:lamtyq2x2ras5oi2jspysgt4fi

Bipartitioning of directed and mixed random graphs [article]

Adam Lipowski, Antonio Luis Ferreira, Dorota Lipowska, Manuel A. Barroso
2019 arXiv   pre-print
In particular, the satisfability threshold coincides with the relative size of the giant OUT component reaching 1/2.  ...  Moreover, when counting undirected links as two directed ones, the partition cost, and cluster properties, as well as location of the replica symmetry breaking transition for these random graphs depend  ...  As expected, in the regime g O < 1/2 partitions with b = 0 (or with very small b) are easily found.  ... 
arXiv:1901.09298v1 fatcat:lsc7cv2ibfg6hlmu7gvv44zlxy

An Adaptive Parallel Algorithm for Computing Connected Components [article]

Chirag Jain, Patrick Flick, Tony Pan, Oded Green, Srinivas Aluru
2017 arXiv   pre-print
However, running parallel BFS is not efficient for computing large diameter components or large number of small components.  ...  Our approach achieves a runtime of 215 seconds using 32K cores of Cray XC30 for a metagenomic graph with over 50 billion edges.  ...  with large diameter, as well as for graphs with a large number of small sized components.  ... 
arXiv:1607.06156v3 fatcat:nclknvs2vbgejggkeqmzjpqd4i

What Does the Local Structure of a Planar Graph Tell Us About Its Global Structure? [chapter]

Christian Sohler
2014 Lecture Notes in Computer Science  
The local k-neighborhood of a vertex v in an unweighted graph G = (V, E) with vertex set V and edge set E is the subgraph induced by all vertices of distance at most k from v.  ...  If we only know this vector, what does it tell us about the structure of G?  ...  They showed that if the frequency vector of a graph is close to that of a planar graph, then this graph can be partitioned into small components by removing, say, ǫdn/2 edges.  ... 
doi:10.1007/978-3-662-44522-8_4 fatcat:qetybess6vaw3ow2ahgxy7upqe

Graph partitioning and a componentwise PageRank algorithm [article]

Christopher Engström, Sergei Silvestrov
2016 arXiv   pre-print
In this article we will present a graph partitioning algorithm which partitions a graph into two different types of components: the well-known 'strongly connected components' as well as another type of  ...  We will also show that the partitioning given by the algorithm is unique and that the underlying graph can be represented as a directed acyclic graph (similar to a pure strongly connected component partitioning  ...  Consider a directed graph G with a partition into SCCs. Let the underlying graph be the DAG constructed by replacing every component with a single vertex.  ... 
arXiv:1609.09068v1 fatcat:im4sjmz2ejbcnideaijwdgwnhu

Decomposing a graph into subgraphs with small components [article]

Rain Jiang, Kai Jiang, Minghui Jiang
2021 arXiv   pre-print
Given a graph G and two integers k and c, (k,c)-Decomposition is the problem of deciding whether G admits an edge partition into k subgraphs with component size at most c.  ...  The component size of a graph is the maximum number of edges in any connected component of the graph.  ...  and only if G 2 admits an edge partition into two subgraphs with component size at most c, if and only if G 2 admits an edge partition into two forests with component size at most c, if and only if G 2  ... 
arXiv:2110.00692v1 fatcat:iwriqxv3bffkzbpkjigezorhly

Bounded size components—partitions and transversals

Penny Haxell, Tibor Szabó, Gábor Tardos
2003 Journal of combinatorial theory. Series B (Print)  
A related theorem is also proved about transversals inducing only small components in graphs of a given maximum degree. r  ...  ., we show that there exists an absolute constant C such that every graph G with maximum degree 5 has a vertex partition into 2 parts, such that the subgraph induced by each part has no component of size  ...  T with the property that G½T has only small components.  ... 
doi:10.1016/s0095-8956(03)00031-5 fatcat:hsnat4j2f5gzhnyipbgcs4ztjy

Scaling metagenome sequence assembly with probabilistic de Bruijn graphs

J. Pell, A. Hintze, R. Canino-Koning, A. Howe, J. M. Tiedje, C. T. Brown
2012 Proceedings of the National Academy of Sciences of the United States of America  
We apply this data structure to the problem of partitioning assembly graphs into components as a prelude to assembly, and show that this reduces the overall memory requirements for de novo assembly of  ...  Here we introduce a memory-efficient graph representation with which we can analyze the k-mer connectivity of metagenomic samples.  ...  Partitioning separates a de Bruijn graph into disconnected graph components; these components can be used to subdivide sequencing reads into disconnected subsets that can be assembled separately.  ... 
doi:10.1073/pnas.1121464109 pmid:22847406 pmcid:PMC3421212 fatcat:c3pcp6fgfvc2rkkkdpqlehma6m

Fully Decomposable Split Graphs [chapter]

Hajo Broersma, Dieter Kratsch, Gerhard J. Woeginger
2009 Lecture Notes in Computer Science  
We discuss various questions around partitioning a split graph into connected parts.  ...  In contrast, we show that the decision problem whether a given split graph can be partitioned into connected parts of orders α 1 , α 2 , . . . , α k for a given partition α 1 , α 2 , . . . , α k of the  ...  Primitive partitions The special structure of split graphs enables us to focus on very specific partitions into small parts in order to prove Theorem 2.  ... 
doi:10.1007/978-3-642-10217-2_13 fatcat:vyex3y3mrnfhfac6njjldiqdcm

Balanced Graph Partitioning

Konstantin Andreev, Harald Racke
2006 Theory of Computing Systems  
In this paper we consider the problem of (k, ν)-balanced graph partitioning -dividing the vertices of a graph into k almost equal size components (each of size less than ν · n k ) so that the capacity  ...  Previous work has only considered the (k, ν)-balanced partitioning problem for ν ≥ 2.  ...  Therefore it is necessary to combine the graph partitioning algorithm with an algorithm for scheduling the resulting pieces into partitions of small size.  ... 
doi:10.1007/s00224-006-1350-7 fatcat:j62uqospbvg5pgm5373e6xheea
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