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Complexity and Approximation of Satisfactory Partition Problems [chapter]

Cristina Bazgan, Zsolt Tuza, Daniel Vanderpooten
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.  ... 
doi:10.1007/11533719_84 fatcat:uurz22a5lfdk3nt4tgk3ahkznm

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]

Kartik Sharma, Iqra Altaf Gillani, Sourav Medya, Sayan Ranu, Amitabha Bagchi
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.  ... 
arXiv:2010.10991v1 fatcat:hvw53xqkxnasjjacuu5yu2eox4

FENNEL

Charalampos Tsourakakis, Christos Gkantsidis, Bozidar Radunovic, Milan Vojnovic
2014 Proceedings of the 7th ACM international conference on Web search and data mining - WSDM '14  
For instance, for 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  ... 
doi:10.1145/2556195.2556213 dblp:conf/wsdm/TsourakakisGRV14 fatcat:wh5soym5xbfspaobgolmvkktsa

The Product Cut

Thomas Laurent, James H. von Brecht, Xavier Bresson, Arthur Szlam
2016 Neural Information Processing Systems  
We introduce a theoretical and algorithmic framework for multi-way 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.  ... 
dblp:conf/nips/0001BBS16 fatcat:m4hiw3jhmjda7iz6yyve2qnb4i

Approximation and parameterized algorithms to find balanced connected partitions of graphs [article]

Phablo F. S. Moura, Matheus J. Ota, Yoshiko Wakabayashi
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.  ... 
arXiv:2108.10398v1 fatcat:h2nuyeil2zbt7pwovhlm7gpupm

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

Jun-Dong Cho, S. Raje, M. Sarrafzadeh
1998 IEEE transactions on computers  
For a 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  ... 
doi:10.1109/12.736440 fatcat:pjvya66jfndujfreml72kkvkiy

Inapproximability of NP-complete Problems, Discrete Fourier Analysis, and Geometry

Subhash Khot
2011 Proceedings of the International Congress of Mathematicians 2010 (ICM 2010)  
This article gives a survey of recent results that 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.  ... 
doi:10.1142/9789814324359_0163 fatcat:64vr5c2f6fbfnosflfpff2t5mu

On a method of applied symbolic dynamics for investigation of dynamical systems

Igor Soloviev, Natalia Ampilova
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.  ... 
doi:10.21595/vp.2019.20698 fatcat:dfv6civpyrh5jkmysvb2btcmj4

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

Feilong Tang, Ilsun You, Minyi Guo, Song Guo, Long Zheng
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-  ... 
doi:10.1155/2010/986192 fatcat:llofit5ce5hq5bg5lqu53v6rmu

Traffic-based Load Balance for Scalable Network Emulation

Xin Liu, Andrew A. Chien
2003 Proceedings of the 2003 ACM/IEEE conference on Supercomputing - SC '03  
We formulate load 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.  ... 
doi:10.1145/1048935.1050190 dblp:conf/sc/LiuC03 fatcat:dpeiexrh55g5vbg6vfpoufaerm

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

Cristina Bazgan, Zsolt Tuza, Daniel Vanderpooten
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.  ... 
doi:10.1016/j.ejor.2009.10.019 fatcat:3ov3h5dvgjea7dt3lhvnygps2q

Approximation and inapproximability results on balanced connected partitions of graphs

Frédéric Chataigner, Liliane R. B. Salgado, Yoshiko Wakabayashi
2007 Discrete Mathematics & Theoretical Computer Science  
This 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  ... 
doi:10.46298/dmtcs.384 fatcat:vojgr3mexbha5fq22vkaojdgxe

Parallel Cut Pursuit For Minimization of the Graph Total Variation [article]

Hugo Raguet, Loic Landrieu
2019 arXiv   pre-print
We demonstrate experimentally 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  ... 
arXiv:1905.02316v1 fatcat:adik542ckjakvfbrz6tuszpczu
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