606 results on '"graph embedding problem"'
Search Results
2. Edge frames of graphs: A graph embedding problem.
- Author
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Hiren Maharaj
- Published
- 1997
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3. Spectral Solution of Large-Scale Extrinsic Camera Calibration as a Graph Embedding Problem
- Author
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Brand, Matthew, primary, Antone, Matthew, additional, and Teller, Seth, additional
- Published
- 2004
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4. The Complexity of the Graph Embedding Problem
- Author
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Archdeacon, D., primary
- Published
- 1990
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- View/download PDF
5. A result on k-valent graphs and its application to a graph embedding problem
- Author
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Dunne, Paul E.
- Published
- 1987
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6. A Result on k -Valent Graphs and Its Application to a Graph Embedding Problem.
- Author
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Paul E. S. Dunne
- Published
- 1987
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7. Edge frames of graphs: A graph embedding problem
- Author
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Maharaj, Hiren, primary
- Published
- 1997
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- View/download PDF
8. The Complexity of the Graph Embedding Problem
- Author
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Dan Archdeacon
- Subjects
Combinatorics ,Discrete mathematics ,Book embedding ,Graph bandwidth ,Planar straight-line graph ,Computational complexity theory ,Graph embedding ,Computer science ,Search algorithm ,Embedding ,Topological graph theory ,MathematicsofComputing_DISCRETEMATHEMATICS - Abstract
We investigate the computational complexity of determining if a graph G on v vertices embeds in a surface S. Robertson and Seymour have given an O(v 3) decision algorithm for this embedding problem. We show here how the use the yes/no output from their algorithm to construct the embedding, that is, we self-reduce the search algorithm to the decision algorithm. We conclude that for each fixed surface S there exists an O(v 10) algorithm for constructing an embedding or answering that no embedding exists.
- Published
- 1990
9. On the general graph embedding problem with applications to circuit layout.
- Author
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Jonathan S. Turner
- Published
- 1984
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10. Solution to König's Graph Embedding Problem
- Author
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R. Bodendiek and K. Wagner
- Subjects
Combinatorics ,Book embedding ,Linkless embedding ,Planar straight-line graph ,Graph embedding ,General Mathematics ,Voltage graph ,Topological graph theory ,Cubic graph ,Null graph ,Mathematics - Published
- 1989
11. Executing Distributed Applications on Virtualized Infrastructures Specified with the VXDL Language and Managed by the HIPerNET Framework
- Author
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Koslovski, Guilherme, Huu, Tram Truong, Montagnat, Johan, Primet, Pascale Vicat-Blanc, Akan, Ozgur, editor, Bellavista, Paolo, editor, Cao, Jiannong, editor, Dressler, Falko, editor, Ferrari, Domenico, editor, Gerla, Mario, editor, Kobayashi, Hisashi, editor, Palazzo, Sergio, editor, Sahni, Sartaj, editor, Shen, Xuemin, editor, Stan, Mircea, editor, Xiaohua, Jia, editor, Zomaya, Albert, editor, Coulson, Geoffrey, editor, Avresky, Dimiter R., editor, Diaz, Michel, editor, Bode, Arndt, editor, Ciciani, Bruno, editor, and Dekel, Eliezer, editor
- Published
- 2010
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- View/download PDF
12. Solution to König's Graph Embedding Problem
- Author
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Bodendiek, R., primary and Wagner, K., additional
- Published
- 1989
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- View/download PDF
13. On the general graph embedding problem with applications to circuit layout
- Author
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Turner, Jonathan S., primary
- Published
- 1984
- Full Text
- View/download PDF
14. Strong 2-degenerate graph embeddings.
- Author
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Ying, Peng and Zhang, Xia
- Subjects
SUBGRAPHS ,TREES ,SPANNING trees - Abstract
A result of Friedman and Pippenger gives a sufficient condition on the expansion properties of a graph to contain all small trees with bounded maximum degree. In this paper, we extend the tree embedding problem of expanding graphs to the degenerate graph embedding problem, and give a sufficient condition for a graph to contain strong 2 -degenerate subgraphs with bounded maximum codegree. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
15. Embedding Wheel-like Networks.
- Author
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Rajan, R. Sundara, Rajalaxmi, T. M., Stephen, Sudeep, Shantrinal, A. Arul, and Kumar, K. Jagadeesh
- Subjects
PETERSEN graphs ,VIRTUAL networks ,HAMILTONIAN graph theory ,CUBES ,PARALLEL algorithms - Abstract
One of the important features of an interconnection network is its ability to efficiently simulate programs or parallel algorithms written for other architectures. Such a simulation problem can be mathematically formulated as a graph embedding problem. In this paper we compute the lower bound for dilation and congestion of embedding onto wheel-like networks. Further, we compute the exact dilation of embedding wheellike networks into hypertrees, proving that the lower bound obtained is sharp. Again, we compute the exact congestion of embedding windmill graphs into circulant graphs, proving that the lower bound obtained is sharp. Further, we compute the exact wirelength of embedding wheels and fans into 1,2-fault hamiltonian graphs. Using this we estimate the exact wirelength of embedding wheels and fans into circulant graphs, generalized Petersen graphs, augmented cubes, crossed cubes, Mobius cubes, twisted cubes, twisted n-cubes, locally twisted cubes, generalized twisted cubes, odd-dimensional cube connected cycle, hierarchical cubic networks, alternating group graphs, arrangement graphs, 3-regular planer hamiltonian graphs, star graphs, generalised matching networks, fully connected cubic networks, tori and 1-fault traceable graphs. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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16. On Optimal Embeddings in 3-Ary n -Cubes.
- Author
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Rajeshwari, S. and Rajesh, M.
- Subjects
ISOPERIMETRICAL problems ,CUBES - Abstract
The efficiency of a graph embedding problem when simulating one interconnection network in another interconnection network is characterized by the influential parameter of wirelength. Obtaining the minimum wirelength in an embedding problem determines the quality of that embedding. In this paper, we obtained the convex edge partition of 3-Ary n-Cubes and the minimized wirelength of the embeddings of both 3-Ary n-Cubes and circulant networks. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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17. A survey on bipartite graphs embedding.
- Author
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Giamphy, Edward, Guillaume, Jean-Loup, Doucet, Antoine, and Sanchis, Kevin
- Abstract
Research on graph representation learning (a.k.a. embedding) has received great attention in recent years and shows effective results for various types of networks. Nevertheless, few initiatives have been focused on the particular case of embeddings for bipartite graphs. In this paper, we first define the graph embedding problem in the case of bipartite graphs. Next, we propose a taxonomy of approaches used to tackle this problem and draw a description of state-of-the-art methods. Then, we establish their pros and cons with respect to conventional network embeddings. Finally, we provide a description of available resources to lead experiments on the subject. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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18. A combinatorial approach to phase transitions in random graph isomorphism problems
- Author
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Diamantidis, Dimitris, Konstantopoulos, Takis, and Yuan, Linglong
- Subjects
Mathematics - Combinatorics ,Mathematics - Probability ,60C05, 05C60, 60F99, 05A19 - Abstract
We consider two independent Erd\H{o}s-R\'enyi random graphs, with possibly different parameters, and study two isomorphism problems, a graph embedding problem and a common subgraph problem. Under certain conditions on the graph parameters we show a sharp asymptotic phase transition as the graph sizes tend to infinity. This extends known results for the case of uniform Erd\H{o}s-R\'enyi random graphs. Our approach is primarily combinatorial, naturally leading to several related problems for further exploration., Comment: 38 pages
- Published
- 2024
19. Executing distributed applications on virtualized infrastructures specified with the VXDL language and managed by the HIPerNET framework
- Author
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Pascale Vicat-Blanc Primet, Johan Montagnat, Tram Truong Huu, Guilherme Piêgas Koslovski, Protocols and softwares for very high-performance network (RESO), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de l'Informatique du Parallélisme (LIP), Centre National de la Recherche Scientifique (CNRS)-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-École normale supérieure - Lyon (ENS Lyon), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe MODALIS, Scalable and Pervasive softwARe and Knowledge Systems (Laboratoire I3S - SPARKS), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Laboratoire de l'Informatique du Parallélisme (LIP), This work has been funded by the ANR CIS HIPCAL grant (contract ANR06- CIS-005), the French ministry of Education and Research, INRIA, and CNRS, via ACI GRID's Grid'5000 project and Aladdin ADT., Dimiter R. Avresky, Michel Diaz, Arndt Bode, Bruno Ciciani, Eliezer Dekel, Grid'5000, ANR-06-CIS6-0005,HIPCAL,Performances previsibles et sécurité des communications dans un contexte de clusters virtuels dynamiques. Application aux domaines biomédical et bio-informatique.(2006), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), Protocols and softwares for very high-performance network ( RESO ), Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Laboratoire de l'Informatique du Parallélisme ( LIP ), École normale supérieure - Lyon ( ENS Lyon ) -Université Claude Bernard Lyon 1 ( UCBL ), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique ( Inria ) -Centre National de la Recherche Scientifique ( CNRS ) -École normale supérieure - Lyon ( ENS Lyon ) -Université Claude Bernard Lyon 1 ( UCBL ), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique ( CNRS ), Scalable and Pervasive softwARe and Knowledge Systems ( SPARKS ), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis ( I3S ), Université Nice Sophia Antipolis ( UNS ), Université Côte d'Azur ( UCA ) -Université Côte d'Azur ( UCA ) -Centre National de la Recherche Scientifique ( CNRS ) -Université Nice Sophia Antipolis ( UNS ), Université Côte d'Azur ( UCA ) -Université Côte d'Azur ( UCA ) -Centre National de la Recherche Scientifique ( CNRS ) -Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis ( I3S ), Université Côte d'Azur ( UCA ) -Université Côte d'Azur ( UCA ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de l'Informatique du Parallélisme ( LIP ), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique ( Inria ) -Centre National de la Recherche Scientifique ( CNRS ), and ANR : 1604,1604
- Subjects
Virtual Infrastructure as a service ,Computer science ,business.industry ,Distributed computing ,Testbed ,020206 networking & telecommunications ,Cloud computing ,02 engineering and technology ,Workflow engine ,workflow language ,[ INFO.INFO-DC ] Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC] ,Software deployment ,application mapping ,0202 electrical engineering, electronic engineering, information engineering ,topology language ,020201 artificial intelligence & image processing ,[INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC] ,business ,resource virtualization ,graph embedding problem - Abstract
International audience; With the convergence of computing and communication, and the expansion of cloud computing, new models and tools are needed to allow users to define, create, and exploit on-demand virtual infras- tructures within wide area distributed environments. Optimally design- ing customized virtual execution-infrastructure and executing them on a physical substrate remains a complex problem. This paper presents the VXDL language, a language for specifying and describing virtual infras- tructures and the HIPerNET framework to manage them. Based on the example of a specific biomedical application and workflow engine, this paper illustrates how VXDL enables to specify different customized vir- tual infrastructures and the HIPerNET framework to execute them on a distributed substrate. The paper presents experiments of the deploy- ment and execution of this application on different virtual infrastructures managed by our HIPerNet system. All the experiments are performed on the Grid'5000 testbed substrate.
- Published
- 2009
20. Block Coordinate Descent Methods for Optimization under J-Orthogonality Constraints with Applications
- Author
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He, Di, Yuan, Ganzhao, Wang, Xiao, and Xu, Pengxiang
- Subjects
Computer Science - Data Structures and Algorithms - Abstract
The J-orthogonal matrix, also referred to as the hyperbolic orthogonal matrix, is a class of special orthogonal matrix in hyperbolic space, notable for its advantageous properties. These matrices are integral to optimization under J-orthogonal constraints, which have widespread applications in statistical learning and data science. However, addressing these problems is generally challenging due to their non-convex nature and the computational intensity of the constraints. Currently, algorithms for tackling these challenges are limited. This paper introduces JOBCD, a novel Block Coordinate Descent method designed to address optimizations with J-orthogonality constraints. We explore two specific variants of JOBCD: one based on a Gauss-Seidel strategy (GS-JOBCD), the other on a variance-reduced and Jacobi strategy (VR-J-JOBCD). Notably, leveraging the parallel framework of a Jacobi strategy, VR-J-JOBCD integrates variance reduction techniques to decrease oracle complexity in the minimization of finite-sum functions. For both GS-JOBCD and VR-J-JOBCD, we establish the oracle complexity under mild conditions and strong limit-point convergence results under the Kurdyka-Lojasiewicz inequality. To demonstrate the effectiveness of our method, we conduct experiments on hyperbolic eigenvalue problems, hyperbolic structural probe problems, and the ultrahyperbolic knowledge graph embedding problem. Extensive experiments using both real-world and synthetic data demonstrate that JOBCD consistently outperforms state-of-the-art solutions, by large margins.
- Published
- 2024
21. HUGE: Huge Unsupervised Graph Embeddings with TPUs
- Author
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Mayer, Brandon, Tsitsulin, Anton, Fichtenberger, Hendrik, Halcrow, Jonathan, Perozzi, Bryan, Mayer, Brandon, Tsitsulin, Anton, Fichtenberger, Hendrik, Halcrow, Jonathan, and Perozzi, Bryan
- Abstract
Graphs are a representation of structured data that captures the relationships between sets of objects. With the ubiquity of available network data, there is increasing industrial and academic need to quickly analyze graphs with billions of nodes and trillions of edges. A common first step for network understanding is Graph Embedding, the process of creating a continuous representation of nodes in a graph. A continuous representation is often more amenable, especially at scale, for solving downstream machine learning tasks such as classification, link prediction, and clustering. A high-performance graph embedding architecture leveraging Tensor Processing Units (TPUs) with configurable amounts of high-bandwidth memory is presented that simplifies the graph embedding problem and can scale to graphs with billions of nodes and trillions of edges. We verify the embedding space quality on real and synthetic large-scale datasets., Comment: As appeared at KDD 2023
- Published
- 2023
- Full Text
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22. Consistency and Complementarity Jointly Regularized Subspace Support Vector Data Description for Multimodal Data.
- Author
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Wang, Chuang, Hu, Wenjun, Wang, Juan, Qian, Pengjiang, Wang, Shitong, and Ortale, Riccardo
- Abstract
The one‐class classification (OCC) problem has always been a popular topic because it is difficult or expensive to obtain abnormal data in many practical applications. Most of OCC methods focused on monomodal data, such as support vector data description (SVDD) and its variants, while we often face multimodal data in reality. The data come from the same task in multimodal learning, and thus, the inherent structures among all modalities should be hold, which is called the consistency principle. However, each modality contains unique information that can be used to repair the incompleteness of other modalities. It is called the complementarity principle. To follow the above two principles, we designed a multimodal graph–regularized term and a sparse projection matrix–regularized term. The former aims to preserve the within‐modal structural and between‐modal relationships, while the latter aims to richly use the complementarity information hidden in multimodal data. Further, we follow the multimodal subspace (MS) SVDD architecture and use two regularized terms to regularize SVDD. Consequently, a novel OCC method for multimodal data is proposed, called the consistency and complementarity jointly regularized subspace SVDD (CCS‐SVDD). Extensive experimental results demonstrate that our approach is more effective and competitive than other algorithms. The source codes are available at https://github.com/wongchuang/CCS_SVDD. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
23. Decomposing User-APP Graph into Subgraphs for Effective APP and User Embedding Learning
- Author
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Yu, Tan, Zhi, Jun, Zhang, Yufei, Li, Jian, Fei, Hongliang, Li, Ping, Yu, Tan, Zhi, Jun, Zhang, Yufei, Li, Jian, Fei, Hongliang, and Li, Ping
- Abstract
APP-installation information is helpful to describe the user's characteristics. The users with similar APPs installed might share several common interests and behave similarly in some scenarios. In this work, we learn a user embedding vector based on each user's APP-installation information. Since the user APP-installation embedding is learnable without dependency on the historical intra-APP behavioral data of the user, it complements the intra-APP embedding learned within each specific APP. Thus, they considerably help improve the effectiveness of the personalized advertising in each APP, and they are particularly beneficial for the cold start of the new users in the APP. In this paper, we formulate the APP-installation user embedding learning into a bipartite graph embedding problem. The main challenge in learning an effective APP-installation user embedding is the imbalanced data distribution. In this case, graph learning tends to be dominated by the popular APPs, which billions of users have installed. In other words, some niche/specialized APPs might have a marginal influence on graph learning. To effectively exploit the valuable information from the niche APPs, we decompose the APP-installation graph into a set of subgraphs. Each subgraph contains only one APP node and the users who install the APP. For each mini-batch, we only sample the users from the same subgraph in the training process. Thus, each APP can be involved in the training process in a more balanced manner. After integrating the learned APP-installation user embedding into our online personal advertising platform, we obtained a considerable boost in CTR, CVR, and revenue.
- Published
- 2022
24. Learning Adaptive Node Embeddings Across Graphs
- Author
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Guo, Gaoyang, Wang, Chaokun, Yan, Bencheng, Lou, Yunkai, Feng, Hao, Zhu, Junchao, Chen, Jun, He, Fei, and Yu, Philip S.
- Abstract
Recently, learning embeddings of nodes in graphs has attracted increasing research attention. There are two main kinds of graph embedding methods, i.e., transductive embedding methods and inductive embedding methods. The former focuses on directly optimizing the embedding vectors, and the latter tries to learn a mapping function for the given nodes and features. However, little work has focused on applying the learned model from one graph to another, which is a pervasive idea in Computer Vision or Natural Language Processing. Although some of the graph neural networks (GNNs) present a similar motivation, none of them considers both the structure bias and the feature bias between graphs. In this paper, we present a novel graph embedding problem called Adaptive Task (AT), and propose a unified framework for the adaptive task, which introduces two types of alignment to learn adaptive node embeddings across graphs. Then, based on the proposed framework, a novel Graph Adaptive Embedding network (GraphAE) is designed to address the adaptive task. Furthermore, we extend GraphAE to a multi-graph version to consider a more complex adaptive situation. The extensive experimental results demonstrate that our model significantly outperforms the state-of-the-art methods, and also show that our framework can make a great improvement over a number of existing GNNs.
- Published
- 2023
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25. A Comprehensive Survey of Graph Embedding: Problems, Techniques, and Applications.
- Author
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Cai, Hongyun, Zheng, Vincent W., and Chang, Kevin Chen-Chuan
- Subjects
EMBEDDING theorems ,REPRESENTATIONS of graphs ,NODAL analysis ,TAXONOMY ,COMPUTATIONAL mechanics - Abstract
Graph is an important data representation which appears in a wide diversity of real-world scenarios. Effective graph analytics provides users a deeper understanding of what is behind the data, and thus can benefit a lot of useful applications such as node classification, node recommendation, link prediction, etc. However, most graph analytics methods suffer the high computation and space cost. Graph embedding is an effective yet efficient way to solve the graph analytics problem. It converts the graph data into a low dimensional space in which the graph structural information and graph properties are maximumly preserved. In this survey, we conduct a comprehensive review of the literature in graph embedding. We first introduce the formal definition of graph embedding as well as the related concepts. After that, we propose two taxonomies of graph embedding which correspond to what challenges exist in different graph embedding problem settings and how the existing work addresses these challenges in their solutions. Finally, we summarize the applications that graph embedding enables and suggest four promising future research directions in terms of computation efficiency, problem settings, techniques, and application scenarios. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
26. SLIGHTLY SUPEREXPONENTIAL PARAMETERIZED PROBLEMS.
- Author
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LOKSHTANOV, DANIEL, MARX, DÁNIEL, and SAURABH, SAKET
- Subjects
PARAMETERIZATION ,ALGORITHMS ,PROBLEM solving ,COMPUTATIONAL complexity ,MATHEMATICAL bounds - Abstract
A central problem in parameterized algorithms is to obtain algorithms with running time f(k) · n
O (1) such that f is as slow growing a function of the parameter k as possible. In particular, a large number of basic parameterized problems admit parameterized algorithms where f(k) is single-exponential, that is, ck for some constant c, which makes aiming for such a running time a natural goal for other problems as well. However, there are still plenty of problems where the f(k) appearing in the best-known running time is worse than single-exponential and it remained "slightly superexponential" even after serious attempts to bring it down. A natural question to ask is whether the f(k) appearing in the running time of the best-known algorithms is optimal for any of these problems. In this paper, we examine parameterized problems where f(k) is kO(k) = 2O(k log k) in the best-known running time, and for a number of such problems we show that the dependence on k in the running time cannot be improved to single-exponential. More precisely we prove the following tight lower bounds, for four natural problems, arising from three different domains: (1) In the Closest String problem, given strings s1 , ..., st over an alphabet Σ of length L each, and an integer d, the question is whether there exists a string s over Σ of length L, such that its hamming distance from each of the strings si, 1 ≤ i ≤ t, is at most d. The pattern matching problem Closest String is known to be solvable in times 2O(d log d) · nO(1) and 2O(d log |Σ|) · nO(1) . We show that there are no 2o(d log d) · nO(1) or 2o(d log |Σ|) · nO(1) time algorithms, unless the Exponential Time Hypothesis (ETH) fails. (2) The graph embedding problem Distortion, that is, deciding whether a graph G has a metric embedding into the integers with distortion at most d can be solved in time 2O(d log d) · nO(1) . We show that there is no 2o(d log d) · nO(1) time algorithm, unless the ETH fails. (3) The Disjoint Paths problem can be solved in time 2O(w log w) · nO(1) on graphs of treewidth at most w. We show that there is no 2o(w log w) · nO(1) time algorithm, unless the ETH fails. (4) The Chromatic Number problem can be solved in time 2O(w log w) ·nO(1) on graphs of treewidth at most w. We show that there is no 2o(w log w) · nO(1) time algorithm, unless the ETH fails. To obtain our results, we first prove the lower bound for variants of basic problems: finding cliques, independent sets, and hitting sets. These artificially constrained variants form a good starting point for proving lower bounds on natural problems without any technical restrictions and could be of independent interest. Several follow-up works have already obtained tight lower bounds by using our framework, and we believe it will prove useful in obtaining even more lower bounds in the future. [ABSTRACT FROM AUTHOR]- Published
- 2018
- Full Text
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27. General Knowledge Embedded Image Representation Learning.
- Author
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Cui, Peng, Liu, Shaowei, and Zhu, Wenwu
- Abstract
Image representation learning is a fundamental problem in understanding semantics of images. However, traditional classification-based representation learning methods face the noisy and incomplete problem of the supervisory labels. In this paper, we propose a general knowledge base embedded image representation learning approach, which uses general knowledge graph, which is a multitype relational knowledge graph consisting of human commonsense beyond image space, as external semantic resource to capture the relations of concepts in image representation learning. A relational regularized regression CNN (R$^3$CNN) model is designed to jointly optimize the image representation learning problem and knowledge graph embedding problem. In this manner, the learnt representation can capture not only labeled tags but also related concepts of images, which involves more precise and complete semantics. Comprehensive experiments are conducted to investigate the effectiveness and transferability of our approach in tag prediction task, zero-shot tag inference task, and content-based image retrieval task. The experimental results demonstrate that the proposed approach performs significantly better than the existing representation learning methods. Finally, observation of the learnt relations show that our approach can somehow refine the knowledge base to describe images and label the images with structured tags. [ABSTRACT FROM PUBLISHER]
- Published
- 2018
- Full Text
- View/download PDF
28. Continual Learning of Knowledge Graph Embeddings
- Author
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Daruna, Angel, Gupta, Mehul, Sridharan, Mohan, Chernova, Sonia, Daruna, Angel, Gupta, Mehul, Sridharan, Mohan, and Chernova, Sonia
- Abstract
In recent years, there has been a resurgence in methods that use distributed (neural) representations to represent and reason about semantic knowledge for robotics applications. However, while robots often observe previously unknown concepts, these representations typically assume that all concepts are known a priori, and incorporating new information requires all concepts to be learned afresh. Our work relaxes this limiting assumption of existing representations and tackles the incremental knowledge graph embedding problem by leveraging the principles of a range of continual learning methods. Through an experimental evaluation with several knowledge graphs and embedding representations, we provide insights about trade-offs for practitioners to match a semantics-driven robotics applications to a suitable continual knowledge graph embedding method., Comment: 8 pages, 4 figures. Accepted for publication in IEEE Robotics and Automation Letters (RA-L)
- Published
- 2021
29. Dynamic community detection algorithm based on hyperbolic graph convolution.
- Author
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Wu, Weijiang, Tan, Heping, and Zheng, Yifeng
- Abstract
Purpose: Community detection is a key factor in analyzing the structural features of complex networks. However, traditional dynamic community detection methods often fail to effectively solve the problems of deep network information loss and computational complexity in hyperbolic space. To address this challenge, a hyperbolic space-based dynamic graph neural network community detection model (HSDCDM) is proposed. Design/methodology/approach: HSDCDM first projects the node features into the hyperbolic space and then utilizes the hyperbolic graph convolution module on the Poincaré and Lorentz models to realize feature fusion and information transfer. In addition, the parallel optimized temporal memory module ensures fast and accurate capture of time domain information over extended periods. Finally, the community clustering module divides the community structure by combining the node characteristics of the space domain and the time domain. To evaluate the performance of HSDCDM, experiments are conducted on both artificial and real datasets. Findings: Experimental results on complex networks demonstrate that HSDCDM significantly enhances the quality of community detection in hierarchical networks. It shows an average improvement of 7.29% in NMI and a 9.07% increase in ARI across datasets compared to traditional methods. For complex networks with non-Euclidean geometric structures, the HSDCDM model incorporating hyperbolic geometry can better handle the discontinuity of the metric space, provides a more compact embedding that preserves the data structure, and offers advantages over methods based on Euclidean geometry methods. Originality/value: This model aggregates the potential information of nodes in space through manifold-preserving distribution mapping and hyperbolic graph topology modules. Moreover, it optimizes the Simple Recurrent Unit (SRU) on the hyperbolic space Lorentz model to effectively extract time series data in hyperbolic space, thereby enhancing computing efficiency by eliminating the reliance on tangent space. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
30. Maximizing the algebraic connectivity in multilayer networks with arbitrary interconnections
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Tavasoli, Ali, Ardjmand, Ehsan, Shakeri, Heman, Tavasoli, Ali, Ardjmand, Ehsan, and Shakeri, Heman
- Abstract
The second smallest eigenvalue of the Laplacian matrix is determinative in characterizing many network properties and is known as algebraic connectivity. In this paper, we investigate the problem of maximizing algebraic connectivity in multilayer networks by allocating interlink weights subject to a budget while allowing arbitrary interconnections. For budgets below a threshold, we identify an upper-bound for maximum algebraic connectivity which is independent of interconnections pattern and is reachable with satisfying a certain regularity condition. For efficient numerical approaches in regions of no analytical solution, we cast the problem into a convex framework that explores the problem from several perspectives and, particularly, transforms into a graph embedding problem that is easier to interpret and related to the optimum diffusion phase. Allowing arbitrary interconnections entails regions of multiple transitions, giving more diverse diffusion phases with respect to one-to-one interconnection case. When there is no limitation on the interconnections pattern, we derive several analytical results characterizing the optimal weights by individual Fiedler vectors. We use the ratio of algebraic connectivity and the layer sizes to explain the results. Finally, we study the placement of a limited number of interlinks by greedy heuristics, using the Fiedler vector components of each layer., Comment: 46 pages, 25 figures
- Published
- 2020
31. RiQ-KGC: Relation Instantiation Enhanced Quaternionic Attention for Complex-Relation Knowledge Graph Completion.
- Author
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Wang, Yunpeng, Ning, Bo, Jiang, Shuo, Zhou, Xin, Li, Guanyu, and Ma, Qian
- Subjects
KNOWLEDGE graphs ,RECOMMENDER systems ,COMPLETE graphs ,QUATERNIONS ,QUATERNION functions - Abstract
A knowledge graph is a structured semantic network designed to describe physical entities and relations in the world. A comprehensive and accurate knowledge graph is essential for tasks such as knowledge inference and recommendation systems, making link prediction a popular problem for knowledge graph completion. However, existing approaches struggle to model complex relations among entities, which severely hampers their ability to complete knowledge graphs effectively. To address this challenge, we propose a novel hierarchical multi-head attention network embedding framework, called RiQ-KGC, which integrates different-grained contextual information of knowledge graph triples and models quaternion rotation relations between entities. Furthermore, we propose a relation instantiation method for alleviating the difficulty of expressing complex relations between entities. To enhance the expressiveness of relation representation, the relation is integrated by Transformer to obtain multi-hop neighbor information, so that one relation can be embedded into different embeddings according to different entities. Experimental results on four datasets demonstrate that RiQ-KGC exhibits strong competitiveness compared to state-of-the-art models in link prediction, while the ablation experiments reveal that the proposed relation instantiation method achieves great performance. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
32. Digital Three-dimensional Smocking Design.
- Author
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JING REN, SEGALL, AVIV, and SORKINE-HORNUNG, OLGA
- Published
- 2024
- Full Text
- View/download PDF
33. Embeddability and Universal Theory of Partially Commutative Groups.
- Author
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Casals-Ruiz, Montserrat
- Subjects
EMBEDDINGS (Mathematics) ,ABELIAN groups ,SUBGRAPHS ,GEOMETRIC rigidity ,ARBITRARY constants - Abstract
The first part of the paper centers in the study of embeddability between partially commutative groups. In [10], for a finite simplicial graph Γ, the authors introduce an infinite, locally infinite graph Γ
e , called the extension graph of Γ . They show that each finite-induced subgraph Δ of Γe gives rise to an embedding between the partially commutative groups G(Δ) and G(Γ ). Furthermore, it is proved that, in many instances, the converse also holds. Our first result is the decidability of the Extension Graph Embedding Problem: there is an algorithm that given two finite simplicial graphs Δ and Γ decides whether or not Δ is an induced subgraph of Γe . As a corollary, we obtain the decidability of the Embedding Problem for 2D partially commutative groups. In the second part of the paper, we relate the Embedding Problem between partially commutative groups to the model-theoretic question of classification up to universal equivalence. We use our characterization to transfer algebraic and algorithmic results on embeddability to model-theoretic ones and obtain some rigidity results on the elementary theory of atomic pc groups as well as to deduce the existence of an algorithm to decide if an arbitrary pc group is universally equivalent to a 2D one. [ABSTRACT FROM AUTHOR]- Published
- 2015
- Full Text
- View/download PDF
34. Heuristics for the data arrangement problem on regular trees.
- Author
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Çela, Eranda and Staněk, Rostislav
- Abstract
The data arrangement problem on regular trees (DAPT) consists in assigning the vertices of a given graph G to the leaves of a d-regular tree T such that the sum of the pairwise distances of all pairs of leaves in T which correspond to edges of G is minimised. This problem is a special case of the generic graph embedding problem and is NP-hard for every fixed $$d\ge 2$$ . In this paper we propose construction and local search heuristics for the DAPT and introduce a lower bound for this problem. The analysis of the performance of the heuristics is based on two considerations: (a) the quality of the solutions produced by the heuristics as compared to the respective lower bound (b) for a special class of instances with known optimal solution we evaluate the gap between the optimal value of the objective function and the objective function value attained by the heuristic solution, respectively. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
35. Embedding of Complete graphs and Cycles into Grids with holes.
- Author
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Mary, R. Stalin and Rajasingh, Indra
- Subjects
COMPLETE graphs ,DEFINITIONS - Abstract
An important feature of an interconnection network is its ability to efficiently simulate one architecture by another. Such a simulation problem can be mathematically formulated as a graph embedding problem. Although the definition of an embedding is an into mapping from Guest Graph to Host Graph, so far in the literature, the embedding has been considered as a mapping from G onto H. In other words, the number of processors in G and H are considered to be the same. In this paper, we increase the number of processors in H by 1. The question is to find the processor in H which does not have the pre-image under the embedding mapping, so that the wirelength of the embedding is minimum. We relate this problem to finding transmission of vertices in the host graph. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
36. All Graphs Lead to Rome: Learning Geometric and Cycle-Consistent Representations with Graph Convolutional Networks
- Author
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Phillips, Stephen, Daniilidis, Kostas, Phillips, Stephen, and Daniilidis, Kostas
- Abstract
Image feature matching is a fundamental part of many geometric computer vision applications, and using multiple images can improve performance. In this work, we formulate multi-image matching as a graph embedding problem then use a Graph Convolutional Network to learn an appropriate embedding function for aligning image features. We use cycle consistency to train our network in an unsupervised fashion, since ground truth correspondence is difficult or expensive to aquire. In addition, geometric consistency losses can be added at training time, even if the information is not available in the test set, unlike previous approaches that optimize cycle consistency directly. To the best of our knowledge, no other works have used learning for multi-image feature matching. Our experiments show that our method is competitive with other optimization based approaches., Comment: 9 pages, 7 figures, 2 tables, 2 supplemental figures
- Published
- 2019
37. FLPI: An Optimal Algorithm for Document Indexing.
- Author
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Tao, Jian-Wen, Yao, Qi-Fu, and Zhao, Jie-Yu
- Abstract
LPI is not efficient in time and memory which makes it difficult to be applied to very large data set. In this paper, we propose a optimal algorithm called FLPI which decomposes the LPI problem as a graph embedding problem plus a regularized least squares problem. Such modification avoids eigen decomposition of dense matrices and can significantly reduce both time and memory cost in computation. Moreover, with a specifically designed graph in supervised situation, LPI only needs to solve the regularized least squares problem which is a further saving of time and memory. Real and synthetic data experimental results show that FLPI obtains similar or better results comparing to LPI and it is significantly faster. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
38. Simultaneous Geometric Graph Embeddings.
- Author
-
Hutchison, David, Kanade, Takeo, Kittler, Josef, Kleinberg, Jon M., Mattern, Friedemann, Mitchell, John C., Naor, Moni, Nierstrasz, Oscar, Pandu Rangan, C., Steffen, Bernhard, Sudan, Madhu, Terzopoulos, Demetri, Tygar, Doug, Vardi, Moshe Y., Weikum, Gerhard, Hong, Seok-Hee, Nishizeki, Takao, Quan, Wu, Estrella-Balderrama, Alejandro, and Gassner, Elisabeth
- Abstract
We consider the following problem known as simultaneous geometric graph embedding (SGE). Given a set of planar graphs on a shared vertex set, decide whether the vertices can be placed in the plane in such a way that for each graph the straight-line drawing is planar. We partially settle an open problem of Erten and Kobourov [5] by showing that even for two graphs the problem is NP-hard. We also show that the problem of computing the rectilinear crossing number of a graph can be reduced to a simultaneous geometric graph embedding problem; this implies that placing SGE in NP will be hard, since the corresponding question for rectilinear crossing number is a long-standing open problem. However, rather like rectilinear crossing number, SGE can be decided in PSPACE. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
39. Finetuning Discrete Architectural Surfaces by use of Circle Packing.
- Author
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Kaji, Shizuo and Zhang, Jingyao
- Published
- 2024
- Full Text
- View/download PDF
40. BITS Darshini.
- Author
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Talasila, Prasad, Kakrambe, Mihir, Rai, Anurag, Santy, Sebastin, Goveas, Neena, and Deshpande, Bharat M.
- Published
- 2018
- Full Text
- View/download PDF
41. Symmetrization for Embedding Directed Graphs
- Author
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Sun, Jiankai, Parthasarathy, Srinivasan, Sun, Jiankai, and Parthasarathy, Srinivasan
- Abstract
Recently, one has seen a surge of interest in developing such methods including ones for learning such representations for (undirected) graphs (while preserving important properties). However, most of the work to date on embedding graphs has targeted undirected networks and very little has focused on the thorny issue of embedding directed networks. In this paper, we instead propose to solve the directed graph embedding problem via a two-stage approach: in the first stage, the graph is symmetrized in one of several possible ways, and in the second stage, the so-obtained symmetrized graph is embedded using any state-of-the-art (undirected) graph embedding algorithm. Note that it is not the objective of this paper to propose a new (undirected) graph embedding algorithm or discuss the strengths and weaknesses of existing ones; all we are saying is that whichever be the suitable graph embedding algorithm, it will fit in the above proposed symmetrization framework., Comment: has been accepted to The Thirty-Third AAAI Conference on Artificial Intelligence (AAAI 2019) Student Abstract and Poster Program
- Published
- 2018
42. FPGA Placement Using Space-Filling Curves: Theory Meets Practice.
- Author
-
BANERJEE, PRITHA, SUR-KOLAY, SUSMITA, BISHNU, ARIJIT, DAS, SANDIP, NANDY, SUBHAS C., and BHATTACHARJEE, SUBHASIS
- Subjects
FIELD programmable gate arrays ,VERY large scale circuit integration ,APPROXIMATION theory ,COMPUTER algorithms ,PROGRAMMABLE logic devices - Abstract
Research in VLSI placement, an NP-hard problem, has branched in two different directions. The first one employs iterative heuristics with many tunable parameters to produce a near-optimal solution but without theoretical guarantee on its quality. The other one considers placement as a graph-embedding problem and designs approximation algorithms with provable bounds on the quality of the solution. In this article, we aim at unifying the above two directions. First, we extend the existing approximation algorithms for graph embedding in 1D and 2D grid to those for hypergraphs, which typically model circuits to be placed on a FPGA. We prove an approximation bound of O(d√log nlog log n) for 1D, that is, linear arrangement and O(d log nlog log n) for the 2D grid, where d is the maximum degree of hyperedges and n, the number of vertices in the hypergraph. Next, we propose an efficient method based on linear arrangement of the CLBs and the notion of space-filling curves for placing the configurable logic blocks (CLBs) of a netlist on island-style FPGAs with an approximation guarantee of O( ∜log n√kd log log n), where k is the number of nets. For the set of FPGA placement benchmarks, the running time is near linear in the number of CLBs thus allowing for scalability towards large circuits. We obtained a 33x speed-up, on average, with only 1.31x degradation in the quality of the solution compared to that produced by the popular FPGA tool VPR, thereby demonstrating the suitability of this very fast method for FPGA placement, with a provable performance guarantee. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
43. THE SOLUTION OF THE DISTANCE GEOMETRY PROBLEM IN PROTEIN MODELING VIA GEOMETRIC BUILDUP.
- Author
-
WU, DI, WU, ZHIJUN, and YUAN, YAXIANG
- Subjects
PROTEIN research ,DISTANCE geometry ,MULTIDIMENSIONAL scaling ,BIOMOLECULES ,GEOMETRY ,ATOMS - Abstract
A well-known problem in protein modeling is the determination of the structure of a protein with a given set of inter-atomic or inter-residue distances obtained from either physical experiments or theoretical estimates. A general form of the problem is known as the distance geometry problem in mathematics, the graph embedding problem in computer science, and the multidimensional scaling problem in statistics. The problem has applications in many other scientific and engineering fields as well such as sensor network localization, image recognition, and protein classification. We describe the formulations and complexities of the problem in its various forms, and introduce a geometric buildup approach to the problem. Central to this approach is the idea that the coordinates of the atoms in a protein can be determined one atom at a time, with the distances from the determined atoms to the undetermined ones. It can determine a structure more efficiently than other conventional approaches, yet without requiring more distance constraints than necessary. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
44. Intelligent and Resource-Conserving Service Function Chain (SFC) Embedding.
- Author
-
Rodis, Panteleimon and Papadimitriou, Panagiotis
- Abstract
Network Function Virtualization (NFV) opens us great opportunities for network processing with higher resource efficiency and flexibility. In this respect, there is an increasing need for intelligent orchestration mechanisms, such that NFV can exploit its potential and live up to its promise. Genetic algorithms have emerged as a promising alternative to the proliferation of heuristic and exact methods for the Service Function Chain (SFC) embedding problem. To this end, we design and evaluate a genetic algorithm (GA), which computes efficient embeddings with runtimes on par with approximate methods. We present a GA model as state-space search in order to clarify the design choices of a GA. Our proposed GA utilizes a heuristic for the generation of the initial population, with the aim of directing the search towards the solution. Given the sensitivity of GAs on their various parameters, we introduce a parameter adjustment framework for GA fine-tuning. A comparative evaluation among a range of GA variants with diverse features sheds light on the impact of these features on SFC embedding efficiency. The GA variant that stands out is further benchmarked against a baseline greedy algorithm and a state-of-the-art heuristic. Our evaluation results indicate that the GA yields notable gains in terms of request acceptance and resource efficiency. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
45. A Comprehensive Survey of Graph Embedding: Problems, Techniques and Applications
- Author
-
Cai, Hongyun, Zheng, Vincent W., Chang, Kevin Chen-Chuan, Cai, Hongyun, Zheng, Vincent W., and Chang, Kevin Chen-Chuan
- Abstract
Graph is an important data representation which appears in a wide diversity of real-world scenarios. Effective graph analytics provides users a deeper understanding of what is behind the data, and thus can benefit a lot of useful applications such as node classification, node recommendation, link prediction, etc. However, most graph analytics methods suffer the high computation and space cost. Graph embedding is an effective yet efficient way to solve the graph analytics problem. It converts the graph data into a low dimensional space in which the graph structural information and graph properties are maximally preserved. In this survey, we conduct a comprehensive review of the literature in graph embedding. We first introduce the formal definition of graph embedding as well as the related concepts. After that, we propose two taxonomies of graph embedding which correspond to what challenges exist in different graph embedding problem settings and how the existing work address these challenges in their solutions. Finally, we summarize the applications that graph embedding enables and suggest four promising future research directions in terms of computation efficiency, problem settings, techniques and application scenarios., Comment: A 20-page comprehensive survey of graph/network embedding for over 150+ papers till year 2018. It provides systematic categorization of problems, techniques and applications. Accepted by IEEE Transactions on Knowledge and Data Engineering (TKDE). Comments and suggestions are welcomed for continuously improving this survey
- Published
- 2017
46. Minced trees, with applications to fault-tolerant VLSI processor arrays.
- Author
-
Chung, Fan and Rosenberg, Arnold
- Abstract
We derive here a lower bound on the number of edges f(c, d) that one must remove from a depth- d complete binary tree in order to partition the tree into c equal size pieces (to within rounding). We show that for the sequence of integers c=3× 2. We then apply this bound to a graph-embedding problem related to the design of fault-tolerant VLSI processor arrays. An earlier study has exhibited a fault-tolerant implementation of arbitrary binary trees, using a particular design strategy. We show here that that implementation is optimal in area consumption (to within constant factors) among designs using that strategy, even when the array to be simulated must have the structure of a complete binary tree. [ABSTRACT FROM AUTHOR]
- Published
- 1986
- Full Text
- View/download PDF
47. Embedding Complete Multipartite Graphs into Certain Trees
- Author
-
Shantrinal, A. Arul, Rajan, R. Sundara, Babu, A. Ramesh, Anil, S., and Ahmed, Mohammed Ali
- Subjects
Mathematics - Combinatorics - Abstract
One of the important features of an interconnection network is its ability to efficiently simulate programs or parallel algorithms written for other architectures. Such a simulation problem can be mathematically formulated as a graph embedding problem. In this paper, we embed complete multipartite graphs into certain trees, such as $k$-rooted complete binary trees and $k$-rooted sibling trees., Comment: Page=14, Figures=4, Journal=Accepted in the special issue of JCMCC. arXiv admin note: text overlap with arXiv:1901.07717
- Published
- 2019
48. Embedding onto Wheel-like Networks
- Author
-
Rajan, R. Sundara, Rajalaxmi, T. M., Stephen, Sudeep, Shantrinal, A. Arul, and Kumar, K. Jagadeesh
- Subjects
Mathematics - Combinatorics - Abstract
One of the important features of an interconnection network is its ability to efficiently simulate programs or parallel algorithms written for other architectures. Such a simulation problem can be mathematically formulated as a graph embedding problem. In this paper we compute the lower bound for dilation and congestion of embedding onto wheel-like networks. Further, we compute the exact dilation of embedding wheel-like networks into hypertrees, proving that the lower bound obtained is sharp. Again, we compute the exact congestion of embedding windmill graphs into circulant graphs, proving that the lower bound obtained is sharp. Further, we compute the exact wirelength of embedding wheels and fans into 1,2-fault hamiltonian graphs. Using this we estimate the exact wirelength of embedding wheels and fans into circulant graphs, generalized Petersen graphs, augmented cubes, crossed cubes, M\"{o}bius cubes, twisted cubes, twisted $n$-cubes, locally twisted cubes, generalized twisted cubes, odd-dimensional cube connected cycle, hierarchical cubic networks, alternating group graphs, arrangement graphs, 3-regular planer hamiltonian graphs, star graphs, generalised matching networks, fully connected cubic networks, tori and 1-fault traceable graphs., Comment: 12 Pages, 5 Figures
- Published
- 2019
49. MinLA of (K9-C9)n and its optimal layout into certain trees.
- Author
-
Afiya, Syeda and Rajesh, M
- Subjects
COMPLETE graphs ,TREES ,ISOPERIMETRICAL problems ,BANANAS - Abstract
Embedding deals with simulating one architecture called guest into another called host, as it helps in modifying algorithms designed for the guest graph to be implemented in the host graph. In this paper, we have obtained the optimal wirelength of embedding (K 9 - C 9) n into P 9 n and certain trees, where (K 9 - C 9) n is the Cartesian product of complete graph on 9 vertices with a deletion of a cycle on 9 vertices and P 9 n is a path on 9 n vertices. Furthermore, we have also obtained the wirelength of embedding the Cartesian product graph (K 9 - C 9) n into Banana trees and Firecracker trees. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
50. Ontological Approach to a Knowledge Graph Construction in a Semantic Library.
- Author
-
Ataeva, O. M., Serebryakov, V. A., and Tuchkova, N. P.
- Abstract
The paper considers an approach to a knowledge graph construction based on the ontological representation of scientific subject areas. The presentation is based on concepts related to information and data mining, such as knowledge, knowledge extraction, domain ontology, scientific domain, thesaurus, semantic digital library, user information need, ontological design method and, in fact, the knowledge graph. The digital semantic library LibMeta is presented as a repository of various structured data with the possibility of their integration with other data sources. Assumes the possibility of specifying personal content by describing a local subject area within LibMeta. The ontology of the content of the semantic library acts as a means of formalization. This paper addresses the experience of building semantic libraries based on thesauri and ontological design. Building ontologies based on the thesaurus of the subject area LibMeta allows us to say that the presence of internal semantic links ensures the consistency and reliability of search results, which is a necessary condition for extracting scientific knowledge. The digital library ontology defines the data structure of the library content. Each data element loaded into the library can be associated with an ontology vertex (top) that determines the position of the data element in the ontology. Based on the ontology links and the links defined at the design stage, you can build a data graph. On the example of the ontology of the LibMeta semantic library, the technology of forming the knowledge graph of modern applications in mathematics is discussed. The problems of filling a graph, embedding in a graph, extracting links and nodes of a graph are discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
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