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Matrix decomposition on the star graph

1997
*
IEEE Transactions on Parallel and Distributed Systems
*

computation complexity and uses O(Nn) communication time to decompose

doi:10.1109/71.605767
fatcat:poyomvnha5dt3kz4tatolf7qm4
*a**matrix*of order N*on**a**star**graph*of dimension n, where N ≥ (n -1)!. ... We present and evaluate, for the first time,*a*parallel algorithm for solving the LU decomposition problem*on*the*star**graph*. The proposed parallel algorithm is of O(N 3 /n!) ... Unfortunately, natural mappings of*matrix*elements to*star**graph*nodes does not seem to be simple, which has crippled the efforts of designing efficient*matrix*-*based*parallel algorithms*on*the*star**graph*...##
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Block-cyclic matrix triangulation on the Cartesian product of star graphs

1998
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Computers and Mathematics with Applications
*

We propose to consider the Cartesian product of

doi:10.1016/s0898-1221(98)00154-0
fatcat:zka3mjl3gzeqddi2wbdekudpre
*star**graphs*as*interconnection**networks*and we design and evaluate blockcyclic*matrix*triangulation*on*these*networks*. ... By its own nature, the*star**graph*seems to be inadequate for eertaln types of algorithms especially those*based**on**matrix*computations. ... This study justifies why we are proposing this*new*topology*based**on*the*star**graph*while the*star**graph*itself presents difficulties in terms of supporting real applications. ...##
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An Algorithm for One-to-One Mapping Matrix-star Graph into Transposition Graph

행렬-스타 그래프를 전위 그래프에 일-대-일 사상하는 알고리즘

2014
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The Journal of the Korean Institute of Information and Communication Engineering
*

행렬-스타 그래프를 전위 그래프에 일-대-일 사상하는 알고리즘

This paper describes an

doi:10.6109/jkiice.2014.18.5.1110
fatcat:ittudainhfdbxnrlubqt26ad6i
*one*-to-*one*mapping algorithm from*a**matrix*-*star**graph*to*a*transposition*graph*using adjacent properties in*graph*theory. ... The result show that*a**matrix*-*star**graph*MS 2,n can be embedded in*a*transposition*graph*T 2n with dilation n or less and average dilation 2 or less. ... Oh, "*Matrix*-*Star**Graphs*:*A**New**Interconnection**Network**Based**on**Matrix**Operations*," in Proceedings of the International Conference*on*Asia-Pacific Computer Systems Architecture, pp. 478-487, 2005. [ 6 ...##
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Nonnegative matrix tri-factorization based clustering in a heterogeneous information network with star network schema

2022
*
Tsinghua Science and Technology
*

In our study, we applied

doi:10.26599/tst.2020.9010049
fatcat:vo3f3b4oczhmrcm5cxu6ojpw4u
*a*Nonnegative*Matrix*Tri-Factorization (NMTF) in*a*cluster analysis of multiple metapaths in HIN. ... Cluster analysis using an HIN has obvious advantages over*a*transformation into*a*homogenous information*network*, which can promote the clustering results of different types of nodes. ... The M*a*c*matrix*is obtained*based**on*the metapath APC, the M t c*matrix*is obtained*based**on*the metapath TPC, and the M*a*t*matrix*is obtained*based**on*the metapath APT. ...##
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Graph-Informed Neural Networks for Regressions on Graph-Structured Data

2022
*
Mathematics
*

In this work, we extend the formulation of the spatial-

doi:10.3390/math10050786
fatcat:s62o23rqzrhizdwzazidwaibvi
*based**graph*convolutional*networks*with*a**new*architecture, called the*graph*-informed neural*network*(GINN). ... In particular, we formulate*a**new**graph*-informed (GI) layer that exploits the adjacent*matrix*of*a*given*graph*to define the unit connections in the neural*network*architecture, describing*a**new*convolution ... Mathematical Formulation of the*Graph*-Informed Layers In this section, we describe the mathematical formulation of the*new*GI layers,*based**on*the adjacency*matrix*of*a**graph*. ...##
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Efficient quantum circuits for continuous-time quantum walks on composite graphs

2017
*
Journal of Physics A: Mathematical and Theoretical
*

This allows us to identify

doi:10.1088/1751-8121/aa53a9
fatcat:zqjor4cugngftbgoerdx6yyb5e
*new*families of*graphs*that we can efficiently simulate in*a*quantum circuit framework, providing practical and explicit means to explore quantum-walk*based*algorithms in laboratories ... In this paper, we investigate the simulation of continuous-time quantum walks*on*specific classes of*graphs*, for which it is possible to fast-forward the time-evolution*operator*to achieve constant-time ... Some examples of quantum walk-*based*algorithms are searching for*a*marked element*on**a**graph*[9] [10] [11] , determining the relative importance of nodes in*a**graph*[12, 13] , and testing*graph*isomorphism ...##
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Graph Signal Processing – Part III: Machine Learning on Graphs, from Graph Topology to Applications
[article]

2020
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arXiv
*
pre-print

Many modern data analytics applications

arXiv:2001.00426v1
fatcat:t7323epqsve2na7q7imuyhlkeq
*on**graphs**operate**on*domains where*graph*topology is not known*a*priori, and hence its determination becomes part of the problem definition, rather than serving ...*A*particular emphasis is*on**graph*topology definition*based**on*the correlation and precision matrices of the observed data, combined with additional prior knowledge and structural conditions, such as the ... (c)*A**graph*tree*based**on*the 1 K+1 scheme. ...##
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On Summarizing Large-Scale Dynamic Graphs

2017
*
IEEE Data Engineering Bulletin
*

How can we describe

dblp:journals/debu/ShahKJZGF17
fatcat:2hlkrczafbhmtm2ndichnk4qte
*a*large, dynamic*graph*over time? Is it random? ... If not, what are the most apparent deviations from randomness -*a*dense block of actors that persists over time, or perhaps*a**star*with many satellite nodes that appears with some fixed periodicity? ... More recent works*on*time-evolving*networks*include*graph*stream summarization [34] for query efficiency, and influence-*based**graph*summarization [35, 33] , which aim to summarize*network*propagation ...##
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Spectral recognition of graphs

2012
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Yugoslav Journal of Operations Research
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Spectral

doi:10.2298/yjor120925025c
fatcat:grql72fepvearizxhgm4slhlwa
*graph*parameters contain*a*lot of information*on*the*graph*structure (both global and local) including some information*on**graph*parameters that, in general, are computed by exponential algorithms ... Some other spectral distances (also*based**on*various*graph*matrices) have been considered as well. Two*graphs*are considered as similar if their spectral distance is small. ... We could use the Manhattan distance*based**on*the adjacency*matrix*or*on*the signless Laplacian. ...##
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Visualizing large graphs

2015
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Wiley Interdisciplinary Reviews: Computational Statistics
*

Throughout the paper we use the terms

doi:10.1002/wics.1343
fatcat:j4mg4hizwfbs3ky67j6d67uiqq
*network*and*graph*interchangably.*A**graph*is traditionally visualized as*a*node-link diagram like Fig. 1 . ... The most widely used techniques turn the problem of*graph*layout into*one*of finding*a*minimal energy configuration of*a*physical system. ... GrouseFlock [3] provides high-level hierarchy modification*operators**based**on*the low-level delete and merge*operations*. ...##
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Graph Summarization Methods and Applications: A Survey
[article]

2018
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arXiv
*
pre-print

Finally, we discuss applications of summarization

arXiv:1612.04883v3
fatcat:fhg2g5eldfdgfkzoqdmbfl5er4
*on*real-world*graphs*and conclude by describing some open problems in the field. ... This survey is*a*structured, comprehensive overview of the state-of-the-art methods for summarizing*graph*data. We first broach the motivation behind, and the challenges of,*graph*summarization. ... This survey focuses*on*the summarization of*interconnected*data, otherwise known as*graphs*or*networks*,*a*problem in*graph*mining with connections to relational data management and visualization. ...##
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Graph Summarization
[article]

2020
*
arXiv
*
pre-print

As this problem is common to several areas studying

arXiv:2004.14794v3
fatcat:4g4l3exin5dxpoe6pdggbtcory
*graph*topologies, different approaches, such as clustering, compression, sampling, or influence detection, have been proposed, primarily*based**on*statistical ...*One*method for condensing and simplifying such datasets is*graph*summarization. ... The underlying method in [9] is*based**on**a**star*-schema*graph*representation, in which attributes are modeled as different node types. ...##
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Graph OLAP: Towards Online Analytical Processing on Graphs

2008
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2008 Eighth IEEE International Conference on Data Mining
*

OLAP (

doi:10.1109/icdm.2008.30
dblp:conf/icdm/ChenYZHY08
fatcat:oiaypfst5faobpau47fsnkbhse
*On*-Line Analytical Processing) is an important notion in data analysis. Recently, more and more*graph*or*networked*data sources come into being. ... ., what are dimensions and measures in the*graph*OLAP scenario, we develop*a*conceptual framework for data cubes*on**graphs*. ... • Drill-down:*A*reverse*operation*of roll-up. • Slice/dice: Select*a*subgraph of the*network**based**on*Topo-Dims. [6] . ...##
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The Laplacian on planar graphs and graphs on surfaces

2011
*
Current Developments in Mathematics
*

We discuss the Laplacian

doi:10.4310/cdm.2011.v2011.n1.a1
fatcat:zs4aibc2n5fwvnquu3ehmxmt6a
*operator**on**graphs*embedded*on**a*surface, concentrating*on*simple surfaces (disk, annulus, torus). ... In particular we review and extend results*on*the reconstruction of the*network*from boundary measurements, connections with the spanning tree and grove model, and the characteristic polynomial of the ... The Laplacian*on**a**network*G is the*operator*Δ : (1) . ...##
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Generalized graph products for network design and analysis

2011
*
2011 19th IEEE International Conference on Network Protocols
*

designers no longer work

doi:10.1109/icnp.2011.6089084
dblp:conf/icnp/ParsonageNBKFR11
fatcat:dz43wrsawzazplw7kcqs723phi
*on*that*network*. ... In this paper we develop generalized*graph*products that allow the mathematical design of*a**network*in terms of small subgraphs that directly express business policy. ... G H D m,1 ÂH*Star*product G H*A*H*A*H TABLE I FUNCTIONAL BASIS FOR*GRAPH*PRODUCTS. ...
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