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The Asymmetric Matrix Partition Problem [chapter]

Noga Alon, Michal Feldman, Iftah Gamzu, Moshe Tennenholtz
2013 Lecture Notes in Computer Science  
An instance of the asymmetric matrix partition problem consists of a matrix A ∈ R n×m + and a probability distribution p over its columns.  ...  The goal is to find a partition scheme that maximizes the resulting partition value. A partition scheme S = {S1, . . . , Sn} consists of a partition Si of [m] for each row i of the matrix.  ...  In the competition-aware model, the optimal asymmetric signaling scheme obtains the same expected revenue as a signaling scheme that is symmetric and partitions the items into singleton subsets.  ... 
doi:10.1007/978-3-642-45046-4_1 fatcat:c4wx4rirajfrhblaxd435jdj4m

Near-Optimal Asymmetric Binary Matrix Partitions [chapter]

Fidaa Abed, Ioannis Caragiannis, Alexandros A. Voudouris
2015 Lecture Notes in Computer Science  
Alon et al. [2] were the first to consider the asymmetric matrix partition problem.  ...  We study the asymmetric binary matrix partition problem that was recently introduced by Alon et al.  ...  Introduction We study the asymmetric binary matrix partition problem, recently proposed by Alon et al. [2] .  ... 
doi:10.1007/978-3-662-48054-0_1 fatcat:pwrjxinozffvjf7sjsrbf7hdj4

Near-Optimal Asymmetric Binary Matrix Partitions

Fidaa Abed, Ioannis Caragiannis, Alexandros A. Voudouris
2016 Algorithmica  
Alon et al. [2] were the first to consider the asymmetric matrix partition problem.  ...  We study the asymmetric binary matrix partition problem that was recently introduced by Alon et al.  ...  Introduction We study the asymmetric binary matrix partition problem, recently proposed by Alon et al. [2] .  ... 
doi:10.1007/s00453-016-0238-4 fatcat:6axdy5i7vrdzpf6pw45gwoe3vm

Provisioning a Virtual Private Network Under the Presence of Non-communicating Groups [chapter]

Friedrich Eisenbrand, Edda Happ
2006 Lecture Notes in Computer Science  
In this paper we consider a variant of the virtual private network design problem which generalizes the previously studied symmetric and asymmetric case.  ...  In our model the terminal set is partitioned into a number of groups, where terminals of each group do not communicate with each other.  ...  Then there exists a valid traffic matrix corresponding to a k-partite matching M that cannot be routed on the tree solution to the asymmetric virtual private network design problem.  ... 
doi:10.1007/11758471_13 fatcat:yw33j2awh5gajfkpsllqbbmam4

Near-optimal asymmetric binary matrix partitions [article]

Fidaa Abed, Ioannis Caragiannis, Alexandros A. Voudouris
2015 arXiv   pre-print
We study the asymmetric binary matrix partition problem that was recently introduced by Alon et al.  ...  Instances of the problem consist of an n × m binary matrix A and a probability distribution over its columns. A partition scheme B=(B_1,...,B_n) consists of a partition B_i for each row i of A.  ...  Introduction We study the asymmetric binary matrix partition problem, recently proposed by Alon et al. [2] .  ... 
arXiv:1407.8170v3 fatcat:tr5jcdbmwvdcvhn7wyvxgxn7ri

A cone-copositive approach for the stability of piecewise linear differential inclusions

Raffaele Iervolino, Francesco Vasca, Luigi Iannelli
2011 IEEE Conference on Decision and Control and European Control Conference  
The absolute stability problem for Lur'e systems with unknown feedback characteristic belonging to an asymmetric domain, is shown to be tractable as a particular case.  ...  By using piecewise quadratic Lyapunov function the stability problem is formulated as a set of linear matrix inequalities each constrained into a specific cone, i.e. a set of cone-copositive programming  ...  because consists in finding, for each cone of the state partition, an unknown matrix that results cone-copositive.  ... 
doi:10.1109/cdc.2011.6160752 dblp:conf/cdc/IervolinoVI11 fatcat:wciityrukfd7blusniokihybyu

Biclustering methods for one-mode asymmetric matrices

Michael J. Brusco, Patrick Doreian, Douglas Steinley
2015 Behavior Research Methods  
An asymmetric one-mode data matrix has rows and columns that correspond to the same set of objects. However, the roles of the objects frequently differ for the rows and the columns.  ...  When seeking to establish a partition of the objects in such applications, it is overly restrictive to require the partitions of the row and column objects to be identical, or even the numbers of clusters  ...  However, unlike the sequential approach, the entire asymmetric proximity matrix is used when establishing the row-object and column-object partitions.  ... 
doi:10.3758/s13428-015-0587-y pmid:25899042 fatcat:ol6tlkkhtnfq5hwvubwmhqnaem

A Partition Method for Graph Isomorphism

Lijun Tian, Chaoqun Liu, Jianquan Xie
2012 Physics Procedia  
For almost all asymmetric graphs, the path length is a small value, e.g., for 6-regular graphs with 100~1000 vertices the average path length is 4 to get all cells to trivial ones.  ...  Complexity of the graph isomorphism algorithms mainly depends on matching time which is directly related to efficiency of their partition methods.  ...  As in (5) , we can detect that partition graph G of Fig.1 into a discrete partition only used length-2, let F be the matrix of G.  ... 
doi:10.1016/j.phpro.2012.03.308 fatcat:oqsdmavxebbhbnu37spagdlkfe

DESICOM : DECOMPOSITION OF ASYMMETRIC RELATIONSHIPS DATA INTO SIMPLE COMPONENTS

Henk A.L. Kiers
1997 Behaviormetrika  
DEDICOM is a method for decomposing an asymmetric data matrix with relation ships among a set of objects into a loading matrix and a matrix of relationships between "underlying" aspects .  ...  The present paper offers a procedure for finding a partitioning on the basis of the data.  ...  DESICOM avoids this problem, because it searches the partitioning itself.  ... 
doi:10.2333/bhmk.24.203 fatcat:nbgx4drdkbd23mb6jik4waljoy

Digraph Spectral Clustering with Applications in Distributed Sensor Validation

Yue-Jin Du, Hui Lu, Li-Dong Zhai
2014 International Journal of Distributed Sensor Networks  
Instead of simply symmetrizing the adjacency matrix, our method takes into consideration the network circulation while clustering the sensors.  ...  Hence, monitoring the status is essential in sensor network maintenance. Spectral clustering has been employed as an enabling technique to solve this problem.  ...  Conflict of Interests The authors declare that there is no conflict of interests regarding the publication of this paper.  ... 
doi:10.1155/2014/536901 fatcat:ze7l3fblkje3tmvalr4xwf3oaq

Classification of Asymmetric Proximity Data

Donatella Vicari
2014 Journal of Classification  
The clustering model proposed here relies on the decomposition of the asymmetric dissimilarity matrix into symmetric and skew-symmetric effects both decomposed in within and between cluster effects.  ...  When clustering asymmetric proximity data, only the average amounts are often considered by assuming that the asymmetry is due to noise.  ...  Generally, the model proposed detects optimal partitions of the objects with respect to both rows and columns of the asymmetric dissimilarity matrix, respectively, i.e. the oriented dissimilarities between  ... 
doi:10.1007/s00357-014-9159-6 fatcat:3rtowwyyrzcjrowdaiux2tzdmq

A New Anticorrelation-Based Spectral Clustering Formulation [chapter]

Julia Dietlmeier, Ovidiu Ghita, Paul F. Whelan
2011 Lecture Notes in Computer Science  
The column-wise processing allows the applicability of SCE to Very Large Scale problems and asymmetric datasets.  ...  Instead of solving for the spectral decomposition of a similarity matrix as in SC, SCE converts the similarity matrix to a columncentered dissimilarity matrix and searches for a pair of the most anticorrelated  ...  Acknowledgments This research was supported by the National Biophotonics and Imaging Platform Ireland funded under the HEA PRTLI Cycle 4, co-funded by the Irish Government and the European Union -Investing  ... 
doi:10.1007/978-3-642-23687-7_13 fatcat:4ucqdyakbnandi67yjjwu4hedi

Page 8697 of Mathematical Reviews Vol. , Issue 2002K [page]

2002 Mathematical Reviews  
The authors investigate the problem of finding a partitioning minimizing the cost of the submatrix having largest cost.  ...  Extending his own work on the asymmetric traveling salesman problem with pyramidal weights [Part I, Discrete Appl.  ... 

Minimal digraph obstructions for small matrices [article]

Pavol Hell, César Hernández-Cruz
2016 arXiv   pre-print
Given a { 0, 1, ∗}-matrix M, a minimal M-obstruction is a digraph D such that D is not M-partitionable, but every proper induced subdigraph of D is.  ...  In this note we present a list of all the M-obstructions for every 2 × 2 matrix M. Notice that this note will be part of a larger paper, but we are archiving it now so we can cite the results.  ...  Given a pattern M , the M -partition problem is the decision problem of determining whether a digraph admits an M -partition.  ... 
arXiv:1605.09587v1 fatcat:4qykvkvisrdc3ev4dvi3yakoha

Contiguous Graph Partitioning For Optimal Total Or Bottleneck Communication [article]

Peter Ahrens
2021 arXiv   pre-print
We propose the first near-linear time algorithms for several graph partitioning problems in the contiguous regime.  ...  We consider contiguous partitions, where the m rows (or columns) of a sparse matrix with N nonzeros are split into K parts without reordering.  ...  The KaHyPar hypergraph partitioner produced the best quality solutions, but took far too long to partition. Asymmetric problems were less amenable to reorderingbased approaches.  ... 
arXiv:2007.16192v4 fatcat:lrjtllq7e5emfclfu3wfcejhne
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