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Partitioning into graphs with only small components

2003
*
Journal of combinatorial theory. Series B (Print)
*

The paper presents several results on edge

doi:10.1016/s0095-8956(02)00006-0
fatcat:no23xsfilzaiddeq3hibj2nn6i
*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. ...##
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Geographically Organized Small Communities and the Hardness of Clustering Social Networks
[chapter]

2010
*
Annals of Information Systems
*

that handle tentacles and

doi:10.1007/978-1-4419-6287-4_10
fatcat:gmfz6mezdva4rh2d2aespmm6kq
*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] . ...##
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Bipartitioning of directed and mixed random graphs

2019
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Journal of Statistical Mechanics: Theory and Experiment
*

In particular, the satisfability threshold coincides

doi:10.1088/1742-5468/ab3280
fatcat:usw3pxniw5dinasfh5r2esarly
*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. ...##
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Multiscale visualization of small world networks

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

doi:10.1109/infvis.2003.1249011
dblp:conf/infovis/AuberCJM03
fatcat:oaoolslmd5b5rgajv7kgsakjfa
*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. ...##
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A Hybrid Genetic Algorithm for the Traveling Salesman Problem Using Generalized Partition Crossover
[chapter]

2010
*
Parallel Problem Solving from Nature, PPSN XI
*

We present a hybrid Genetic Algorithm that incorporates the Generalized

doi:10.1007/978-3-642-15844-5_57
dblp:conf/ppsn/WhitleyHH10
fatcat:scvhvxnsrjfotcal56do3gl7dm
*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*. ...##
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Efficiently Processing Workflow Provenance Queries on SPARK
[article]

2018
*
arXiv
*
pre-print

The framework exploits the workflow dependency

arXiv:1808.08424v2
fatcat:lamtyq2x2ras5oi2jspysgt4fi
*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*. ...##
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Bipartitioning of directed and mixed random graphs
[article]

2019
*
arXiv
*
pre-print

In particular, the satisfability threshold coincides

arXiv:1901.09298v1
fatcat:lsc7cv2ibfg6hlmu7gvv44zlxy
*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. ...##
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An Adaptive Parallel Algorithm for Computing Connected Components
[article]

2017
*
arXiv
*
pre-print

However, running parallel BFS is not efficient for computing large diameter

arXiv:1607.06156v3
fatcat:nclknvs2vbgejggkeqmzjpqd4i
*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*. ...##
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What Does the Local Structure of a Planar Graph Tell Us About Its Global Structure?
[chapter]

2014
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Lecture Notes in Computer Science
*

The local k-neighborhood of a vertex v in an unweighted

doi:10.1007/978-3-662-44522-8_4
fatcat:qetybess6vaw3ow2ahgxy7upqe
*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. ...##
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Graph partitioning and a componentwise PageRank algorithm
[article]

2016
*
arXiv
*
pre-print

In this article we will present a

arXiv:1609.09068v1
fatcat:im4sjmz2ejbcnideaijwdgwnhu
*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. ...##
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Decomposing a graph into subgraphs with small components
[article]

2021
*
arXiv
*
pre-print

Given a

arXiv:2110.00692v1
fatcat:iwriqxv3bffkzbpkjigezorhly
*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 ...##
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Bounded size components—partitions and transversals

2003
*
Journal of combinatorial theory. Series B (Print)
*

A related theorem is also proved about transversals inducing

doi:10.1016/s0095-8956(03)00031-5
fatcat:hsnat4j2f5gzhnyipbgcs4ztjy
*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*. ...##
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Scaling metagenome sequence assembly with probabilistic de Bruijn graphs

2012
*
Proceedings of the National Academy of Sciences of the United States of America
*

We apply this data structure to the problem of

doi:10.1073/pnas.1121464109
pmid:22847406
pmcid:PMC3421212
fatcat:c3pcp6fgfvc2rkkkdpqlehma6m
*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. ...##
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Fully Decomposable Split Graphs
[chapter]

2009
*
Lecture Notes in Computer Science
*

We discuss various questions around

doi:10.1007/978-3-642-10217-2_13
fatcat:vyex3y3mrnfhfac6njjldiqdcm
*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. ...##
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Balanced Graph Partitioning

2006
*
Theory of Computing Systems
*

In this paper we consider the problem of (k, ν)-balanced

doi:10.1007/s00224-006-1350-7
fatcat:j62uqospbvg5pgm5373e6xheea
*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. ...
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