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Complexity and Approximation of Satisfactory Partition Problems
[chapter]

2005
*
Lecture Notes in Computer Science
*

*The*Satisfactory

*Partition*

*problem*consists of deciding if a given

*graph*has a

*partition*of its vertex set into two nonempty parts such that each vertex has at least as many neighbors

*in*its part as

*in*... Similar results hold for

*balanced*

*partitions*where each vertex is required to have at most as many neighbors

*in*its part as

*in*

*the*other part. ... This

*problem*called Co-Satisfactory

*Partition*corresponds to finding

*in*

*the*

*graph*a

*maximal*cut with respect to moving a vertex from its part to

*the*other. ...

##
###
Page 488 of Mathematical Reviews Vol. , Issue 98A
[page]

1998
*
Mathematical Reviews
*

*maximally*

*balanced*

*connected*

*partition*

*problem*

*in*

*graphs*. ... Summary: “

*The*

*approximability*of

*the*following optimization

*problem*is investigated: Given a

*connected*

*graph*G = (V, E), find a

*maximally*

*balanced*

*connected*

*partition*for G, i.e. a

*partition*(V\,¥2) of ...

##
###
Balance Maximization in Signed Networks via Edge Deletions
[article]

2020
*
arXiv
*
pre-print

*In*a

*balanced*(sub)

*graph*,

*the*vertices can be

*partitioned*into two subsets with negative edges present only across

*the*

*partitions*. ... While existing works have focused primarily on finding

*the*largest

*balanced*subgraph inside a

*graph*, we study

*the*network design

*problem*of

*maximizing*

*balance*of a target community (subgraph). ... Fig. 5 CONCLUSIONS

*In*this paper, we studied

*the*

*problem*of

*maximizing*

*the*

*balance*

*in*signed networks via edge deletion. ...

##
###
FENNEL

2014
*
Proceedings of the 7th ACM international conference on Web search and data mining - WSDM '14
*

For instance, for

doi:10.1145/2556195.2556213
dblp:conf/wsdm/TsourakakisGRV14
fatcat:wh5soym5xbfspaobgolmvkktsa
*the*Twitter*graph*with more than 1.4 billion of edges, our method*partitions**the**graph**in*about 40 minutes achieving a*balanced**partition*that cuts as few as 6.8% of edges, whereas it ... Finally, we evaluate*the*performance gains by using our*graph**partitioner*while solving standard PageRank computation*in*a*graph*processing platform, and observe significant gains*in*terms of*the*communication ... Acknowledgements We would like to thank to those who kindly helped us*in*getting access to some of*the**graph*data that we used for our evaluation, including Nick Craswell, Bodo Billerbeck, Gabriel Kliot ...##
###
The Product Cut

2016
*
Neural Information Processing Systems
*

We introduce a theoretical and algorithmic framework for multi-way

dblp:conf/nips/0001BBS16
fatcat:m4hiw3jhmjda7iz6yyve2qnb4i
*graph**partitioning*that relies on a multiplicative cut-based objective. We refer to this objective as*the*Product Cut. ...*The*proposed model has strong mathematical underpinnings, and*the*corresponding algorithm achieves state-of-*the*-art performance on benchmark data sets. ... On*the*other hand Pcut(P) = e −H(P) , which shows that,*in**the*absence of "cut information,"*the*Product Cut will choose*the**partition*that*maximizes**the*entropic*balance*. ...##
###
Approximation and parameterized algorithms to find balanced connected partitions of graphs
[article]

2021
*
arXiv
*
pre-print

*The*

*balanced*

*connected*k-

*partition*

*problem*consists

*in*finding a

*connected*k-

*partition*

*in*which every class has roughly

*the*same weight. ... To model this concept of

*balance*, one may seek

*connected*k-

*partitions*that either

*maximize*

*the*weight of a lightest class (max-min BCP_k) or minimize

*the*weight of a heaviest class (min-max BCP_k). ...

*The*concept of

*balance*of

*the*classes of a

*connected*

*partition*of a

*graph*can be expressed

*in*different ways. ...

##
###
Fast approximation algorithms on maxcut, k-coloring, and k-color ordering for VLSI applications

1998
*
IEEE transactions on computers
*

For a

doi:10.1109/12.736440
fatcat:pjvya66jfndujfreml72kkvkiy
*graph*G with e edges and n vertices, our maxcut*approximation*algorithm runs*in*O(e + n) sequential time yielding a node-*balanced*maxcut with size at least (w(E) + w(E)=n)=2, improving*the*time complexity ... Along*the*line, we rst propose a linear-time*approximation*algorithm on maxcut and two closely related*problems*: kcoloring and*maximal*k-color ordering*problem*. ...*Maximal*k-Color Ordering*Problem**In*this section, we show*the*NP-completeness of nding*the**maximal*k-color ordering (MCO), and then present an e cient*approximation*algorithm running*in*O(e2 k=2 ) time ...##
###
Inapproximability of NP-complete Problems, Discrete Fourier Analysis, and Geometry

2011
*
Proceedings of the International Congress of Mathematicians 2010 (ICM 2010)
*

This article gives a survey of recent results that

doi:10.1142/9789814324359_0163
fatcat:64vr5c2f6fbfnosflfpff2t5mu
*connect*three areas*in*computer science and mathematics: (1) (Hardness of) computing*approximate*solutions to NP-complete*problems*. (2) Fourier analysis ... of boolean functions on boolean hypercube. (3) Certain*problems**in*geometry, especially related to isoperimetry and embeddings between metric spaces. ...*The*optimization*problem*concerns*balanced*cuts*in**graphs*. ...##
###
On a method of applied symbolic dynamics for investigation of dynamical systems

2019
*
Vibroengineering PROCEDIA
*

*The*main idea of

*the*method is to describe

*the*system behaviour

*approximately*by means of an oriented

*graph*(called symbolic image). ...

*The*method has received wide acceptance

*in*studying complex dynamical systems. ... coding smooth dynamical systems

*in*such a way to describe

*the*dynamics of a system by an oriented

*graph*constructed

*in*accordance with a given

*partition*. ...

##
###
Balanced Bipartite Graph Based Register Allocation for Network Processors in Mobile and Wireless Networks

2010
*
Mobile Information Systems
*

*The*paper presents a

*graph*uniform 2-way

*partition*algorithm (FPT), which provides an optimal solution to

*the*

*graph*

*partition*, and a heuristic algorithm for generating

*balanced*bipartite

*graph*. ...

*In*this paper, we investigate an approach for efficiently generating

*balanced*bipartite

*graph*and register allocation algorithms for

*the*dual-bank register allocation

*in*IXPs. ... Acknowledgement Feilong Tang would like to thank

*The*Japan Society for

*the*Promotion of Science (JSPS) and

*The*Un- ...

##
###
Traffic-based Load Balance for Scalable Network Emulation

2003
*
Proceedings of the 2003 ACM/IEEE conference on Supercomputing - SC '03
*

We formulate load

doi:10.1145/1048935.1050190
dblp:conf/sc/LiuC03
fatcat:dpeiexrh55g5vbg6vfpoufaerm
*balance*as a*graph**partitioning**problem*and apply classical*graph**partitioning*algorithms to it. ...*in**the*original emulation*problem*. ...*The*authors also acknowledge*the*contributions of Alex Olugbile and Huaxia Xia to*the*system infrastructure which made this work possible. ...##
###
Page 3778 of Mathematical Reviews Vol. , Issue 2000e
[page]

2000
*
Mathematical Reviews
*

A p-separator is a subset of edges whose removal

*partitions**the*vertex set into*connected*components such that*the*sum of*the*vertex weights*in*each com- ponent is at most p times*the*weight of*the**graph*...*The**problems*of b-*balanced*cuts and k-*balanced**partitions*are unified into a new*problem*called minimum capacity p-separators. ...##
###
Satisfactory graph partition, variants, and generalizations

2010
*
European Journal of Operational Research
*

*The*Satisfactory

*Partition*

*problem*asks for deciding if a given

*graph*has a

*partition*of its vertex set into two nonempty parts such that each vertex has at least as many neighbors

*in*its part as

*in*

*the*... This

*problem*was introduced by Gerber and Kobler [EJOR, 125 (2000), 283-291] and studied further by other authors.

*In*this paper we first review some applications and related

*problems*. ... We are grateful to Csilla Bujtás for calling our attention to

*the*literature on

*the*Matching Cut

*problem*. ...

##
###
Approximation and inapproximability results on balanced connected partitions of graphs

2007
*
Discrete Mathematics & Theoretical Computer Science
*

This

doi:10.46298/dmtcs.384
fatcat:vojgr3mexbha5fq22vkaojdgxe
*problem*is called \textitMax*Balanced**Connected*q-*Partition*and is denoted by BCP_q. ... When q is not fixed (it is part of*the*instance),*the*corresponding*problem*is called \textitMax*Balanced**Connected**Partition*, and denoted as BCP. ...*The*Max*Balanced**Connected*q-*Partition**Problem*(BCP q ) consists*in*finding for a given w-weighted*connected**graph*G = (V, E), a*connected*q-*partition*(V 1 , V 2 , . . . , V q ) that*maximizes**the*function ...##
###
Parallel Cut Pursuit For Minimization of the Graph Total Variation
[article]

2019
*
arXiv
*
pre-print

We demonstrate experimentally

arXiv:1905.02316v1
fatcat:adik542ckjakvfbrz6tuszpczu
*the*efficiency of our method*in*a wide variety of settings, from simple denoising on huge*graphs*to more complex inverse*problems*with nondifferentiable penalties. ... We show that*the*decomposition of*the*iterate into constant*connected*components, which is at*the*center of this method, allows for*the*seamless parallelization of*the*otherwise costly*graph*-cut based ...*The*search for a steepest descent direction restricted to a finite set D defines a new*partition*by computing*the*cross*partition*between*the*current*partition*and*the**maximal*constant*connected*components ...
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