Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 76 for “"hypergraph"”.
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An effective algorithm for multiway hypergraph partitioning
The problem of hypergraph partitioning has been around for more than a quarter of a century. Its early applications were centered on VLSI circuit design. In recent years, the application of hypergraph partitioning has been extended into the areas including data classifications, efficient storage of …
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Temporal hypergraph modeling via inter-geometrical learning
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-09-16 without embargo terms
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Hypergraph-Based Combinatorial Optimization of Matrix -Vector Multiplication
The second problem we address is parallel matrix-vector multiplication for large sparse matrices. Parallel sparse matrix-vector multiplication is a particularly important numerical kernel in computational science. We have focused on optimizing the parallel performance of this operation by reducing …
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Hypergraph-Based Combinatorial Optimization of Matrix-Vector Multiplication
… multiplication, and both are solved using hypergraph models. For both of these problems, the cost of the combinatorial optimization process can be effectively amortized over many matrix-vector products. The first problem we address is optimization of serial matrix-vector multiplication for …
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On the Expressiveness and Generalization of Hypergraph Neural Networks
… the graph neural networks to be extended to hypergraphs to deal with higher-order relations. It is critical to understand what type of problems these hypergraph neural networks can solve and effectively learn from data. In this thesis, we describe how we use Neural Logical Machines as a …
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The Phase Transition for Recovering a Random Hypergraph from its Edge Data
The weighted projection of a hypergraph is the weighted undirected graph with the same vertex set and edge weight equal to the number of hyperedges that contain the edge; the projection is the unweighted graph with the same vertex set and edge set consisting of edges with weight at least one. For d …
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Hypergraph Distributed Optimization & Decentralized Control with Applications in Economic Networks and Graphical Games
… applied mathematics results focus on the use of hypergraphs instead of their graph analogue, the clique expansion graphs in the settings of distributed optimization and decentralized control. In both settings we present results where the use of hypergraphs provides a scalable and a decentralized …
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Using hypergraph theory to model coexistence management and coordinated spectrum allocation for heterogeneous wireless networks operating in shared spectrum
… only connect two entities. On the other hand, a hypergraph is a generalisation of an undirected graph in which a hyperedge can connect more than two entities. Therefore, this thesis investigates the use of hypergraph theory to model the RF environment and the spectrum allocation scheme.The …
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Universal Hypergraphs.
<p>In this thesis, we study universal hypergraphs. What are these? Let us start with defining a universal graph as a graph on <em>n</em> vertices that contains each of the many possible graphs of a smaller size <em>k</em> < <em>n</em> as an induced subgraph. A <em>hypergraph</em> is a discrete …
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Analyzing Networks with Hypergraphs: Detection, Classification, and Prediction
… This thesis focuses on analyzing networks using hypergraphs for detection, classification, and prediction methods in social media-related problems. In particular, we study four specific applications with four proposed novel methods: detecting topic-specific influential users and tweets via …
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Embedding Problems for Graphs and Hypergraphs
… some substructure within a large graph or hypergraph. In the case of graphs, we consider the substructures consisting of fixed subgraphs or families of subgraphs, perfect graph packings and spanning subgraphs. In the case of hypergraphs we consider the substructure consisting of a …
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Eulerian Properties of Design Hypergraphs and Hypergraphs with Small Edge Cuts
An Euler tour of a hypergraph is a closed walk that traverses every edge exactly once; if a hypergraph admits such a walk, then it is called eulerian. Although this notion is one of the progenitors of graph theory --- dating back to the eighteenth century --- treatment of this subject has only …
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Learning on Inhomogeneous Hypergraphs
… relations. Such relations can be modeled by hypergraphs, where the notion of an edge is generalized to a hyperedge that can connect more than two vertices. Traditional hypergraph models treat all the vertices in a hyperedge equally while in practice these vertices might contribute differently …
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Cuts and connectivity in graphs and hypergraphs
… and connectivity problems on graphs, digraphs, hypergraphs and hedgegraphs. The main results are the following: - We introduce a faster algorithm for finding the reduced graph in element-connectivity computations. We also show its application to node separation. - We present several results on …
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Graph-based Time-series Forecasting in Deep Learning
… K-Means and LSH; The third method, Probabilistic Hypergraph Recurrent Neural Network (PHRNN), targets datasets under the assumption that nodes interact in a simultaneous broadcasting manner. Previous hypergraph approaches leverage a static weight hypergraph, which fails to capture the interaction …
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On Induced Subgraphs, Degree Sequences, and Graph Structure
… A4-structure H of a graph G to be the 4-uniform hypergraph on the vertex set of G where four vertices comprise an edge in H if and only if they form the vertex set of an alternating 4-cycle in G. Our definition is a variation of the notion of the P4-structure, a hypergraph which has been shown to …
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An Overview of the Constructive Local Lemma
… provide an implementation of the algorithm to a hypergraph coloring problem.</p>
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Fractional Chromatic Numbers and Spectra of Graphs
… random graphs, Laplacian spectra of hypergraphs, and loose Laplacian spectra of random hypergraphs.</p> <p>For a graph $G$, let $\chi_f(G)$ be the fractional chromatic number of $G$. Based on the study of independence numbers of triangle-free graphs with maximum degree at most three, …
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