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Matrix decomposition on the star graph

A.-E. Al-Ayyoub, K. Day
1997 IEEE Transactions on Parallel and Distributed Systems  
computation complexity and uses O(Nn) communication time to decompose 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  ... 
doi:10.1109/71.605767 fatcat:poyomvnha5dt3kz4tatolf7qm4

Block-cyclic matrix triangulation on the Cartesian product of star graphs

A.-E. Al-Ayyoub, K. Day
1998 Computers and Mathematics with Applications  
We propose to consider the Cartesian product of 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.  ... 
doi:10.1016/s0898-1221(98)00154-0 fatcat:zka3mjl3gzeqddi2wbdekudpre

An Algorithm for One-to-One Mapping Matrix-star Graph into Transposition Graph
행렬-스타 그래프를 전위 그래프에 일-대-일 사상하는 알고리즘

Jong-Seok Kim, Hyeong-Ok Lee
2014 The Journal of the Korean Institute of Information and Communication Engineering  
This paper describes an 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  ... 
doi:10.6109/jkiice.2014.18.5.1110 fatcat:ittudainhfdbxnrlubqt26ad6i

Nonnegative matrix tri-factorization based clustering in a heterogeneous information network with star network schema

Juncheng Hu, Yongheng Xing, Mo Han, Feng Wang, Kuo Zhao, Xilong Che
2022 Tsinghua Science and Technology  
In our study, we applied 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.  ... 
doi:10.26599/tst.2020.9010049 fatcat:vo3f3b4oczhmrcm5cxu6ojpw4u

Graph-Informed Neural Networks for Regressions on Graph-Structured Data

Stefano Berrone, Francesco Della Santa, Antonio Mastropietro, Sandra Pieraccini, Francesco Vaccarino
2022 Mathematics  
In this work, we extend the formulation of the spatial-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.  ... 
doi:10.3390/math10050786 fatcat:s62o23rqzrhizdwzazidwaibvi

Efficient quantum circuits for continuous-time quantum walks on composite graphs

T Loke, J B Wang
2017 Journal of Physics A: Mathematical and Theoretical  
This allows us to identify 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  ... 
doi:10.1088/1751-8121/aa53a9 fatcat:zqjor4cugngftbgoerdx6yyb5e

Graph Signal Processing – Part III: Machine Learning on Graphs, from Graph Topology to Applications [article]

Ljubisa Stankovic, Danilo Mandic, Milos Dakovic, Milos Brajovic, Bruno Scalzo, Shengxi Li, Anthony G. Constantinides
2020 arXiv   pre-print
Many modern data analytics applications 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.  ... 
arXiv:2001.00426v1 fatcat:t7323epqsve2na7q7imuyhlkeq

On Summarizing Large-Scale Dynamic Graphs

Neil Shah, Danai Koutra, Lisa Jin, Tianmin Zou, Brian Gallagher, Christos Faloutsos
2017 IEEE Data Engineering Bulletin  
How can we describe 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  ... 
dblp:journals/debu/ShahKJZGF17 fatcat:2hlkrczafbhmtm2ndichnk4qte

Spectral recognition of graphs

Dragos Cvetkovic
2012 Yugoslav Journal of Operations Research  
Spectral 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.  ... 
doi:10.2298/yjor120925025c fatcat:grql72fepvearizxhgm4slhlwa

Visualizing large graphs

Yifan Hu, Lei Shi
2015 Wiley Interdisciplinary Reviews: Computational Statistics  
Throughout the paper we use the terms 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.  ... 
doi:10.1002/wics.1343 fatcat:j4mg4hizwfbs3ky67j6d67uiqq

Graph Summarization Methods and Applications: A Survey [article]

Yike Liu, Tara Safavi, Abhilash Dighe, Danai Koutra
2018 arXiv   pre-print
Finally, we discuss applications of summarization 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.  ... 
arXiv:1612.04883v3 fatcat:fhg2g5eldfdgfkzoqdmbfl5er4

Graph Summarization [article]

Angela Bonifati, Stefania Dumbrava, Haridimos Kondylakis
2020 arXiv   pre-print
As this problem is common to several areas studying 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.  ... 
arXiv:2004.14794v3 fatcat:4g4l3exin5dxpoe6pdggbtcory

Graph OLAP: Towards Online Analytical Processing on Graphs

Chen Chen, Xifeng Yan, Feida Zhu, Jiawei Han, Philip S. Yu
2008 2008 Eighth IEEE International Conference on Data Mining  
OLAP (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] .  ... 
doi:10.1109/icdm.2008.30 dblp:conf/icdm/ChenYZHY08 fatcat:oiaypfst5faobpau47fsnkbhse

The Laplacian on planar graphs and graphs on surfaces

Richard Kenyon
2011 Current Developments in Mathematics  
We discuss the Laplacian 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) .  ... 
doi:10.4310/cdm.2011.v2011.n1.a1 fatcat:zs4aibc2n5fwvnquu3ehmxmt6a

Generalized graph products for network design and analysis

Eric Parsonage, Hung X. Nguyen, Rhys Bowden, Simon Knight, Nickolas Falkner, Matthew Roughan
2011 2011 19th IEEE International Conference on Network Protocols  
designers no longer work 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.  ... 
doi:10.1109/icnp.2011.6089084 dblp:conf/icnp/ParsonageNBKFR11 fatcat:dz43wrsawzazplw7kcqs723phi
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