Topic
Adjacency list
About: Adjacency list is a research topic. Over the lifetime, 4419 publications have been published within this topic receiving 78449 citations.
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07 Sep 2015
TL;DR: In this article, the intersection graph is shown to be the 2-section of the incidence dual and the line graph is defined as the vertex-edge intersection graph of an infinite family of oriented hypergraphs.
Abstract: For a given hypergraph, an orientation can be assigned to the vertex-edge incidences. This orientation is used to define the adjacency and Laplacian matrices. Continuing the study of these matrices associated to an oriented hypergraph, several related structures are investigated including: the incidence dual, the intersection graph (line graph), and the 2-section. The intersection graph is shown to be the 2-section of the incidence dual. Also, any simple oriented signed graph is the intersection graph of an infinite family of oriented hypergraphs. Matrix relationships between these new constructions are also established, which lead to new questions regarding associated eigenvalue bounds. Vertex and edge-switchings on these various structures are also studied. A connection is then made between oriented hypergraphs and balanced incomplete block designs.
20 citations
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17 Jun 2007TL;DR: This work learns a small number of aspects, or prototypical views, from video data using K-medoid to find cluster centers and shows that line aspect matching performs significantly better than an alternative approach using Hausdorff distance.
Abstract: Traditional aspect graphs are topology-based and are impractical for articulated objects. In this work we learn a small number of aspects, or prototypical views, from video data. Groundtruth segmentations in video sequences are utilized for both training and testing aspect models that operate on static images. We represent aspects of an articulated object as collections of line segments. In learning aspects, where object centers are known, a linear matching based on line location and orientation is used to measure similarity between views. We use K-medoid to find cluster centers. When using line aspects in recognition, matching is based on pairwise cues of relative location, relative orientation as well adjacency and parallelism. Matching with pairwise cues leads to a quadratic optimization that we solve with a spectral approximation. We show that our line aspect matching is capable of locating people in a variety of poses. Line aspect matching performs significantly better than an alternative approach using Hausdorff distance, showing merits of the line representation.
20 citations
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TL;DR: In this paper, the authors describe the distance spectrum of some self-complementary graphs in terms of their adjacency spectrum, and show that there exist D-equienergetic, D-energy ED(G) of the graph G is the sum of the absolute values of its D-eigenvalues.
Abstract: The D-eigenvalues {μ1,μ2 …, μn}of a graph G are the eigenvalues of its distance matrix D and form the D-spectrum of G denoted by specD(G). The D-energy ED(G) of the graph G is the sum of the absolute values of its D-eigenvalues. We describe here the distance spectrum of some self-complementary graphs in the terms of their adjacency spectrum. These results are used to show that there exists D-equienergetic self-complementary graphs of order n = 48t and 24(2t + 1) for t ≥ 4. .
20 citations
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TL;DR: The results show the advantages of the proposed algorithm for the targeted problem of highly-dense adjacency constrained floor plan generation, which is more time-efficient, more lightweight to implement, and having a larger capacity than other approaches such as Evolution strategy and traditional on-policy search.
20 citations
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TL;DR: This work proposes an implementation scheme that triangulates the constraint graphs of the input networks and uses a hash table based adjacency list to efficiently represent and reason with them and generates random scale-free-like qualitative spatial networks using the Barabasi-Albert model with a preferential attachment mechanism.
Abstract: We improve the state-of-the-art method for checking the consistency of large qualitative spatial networks that appear in the Web of Data by exploiting the scale-free-like structure observed in their constraint graphs. We propose an implementation scheme that triangulates the constraint graphs of the input networks and uses a hash table based adjacency list to efficiently represent and reason with them. We generate random scale-free-like qualitative spatial networks using the Barabasi-Albert (BA) model with a preferential attachment mechanism. We test our approach on the already existing random datasets that have been extensively used in the literature for evaluating the performance of qualitative spatial reasoners, our own generated random scale-free-like spatial networks, and real spatial datasets that have been made available as Linked Data. The analysis and experimental evaluation of our method presents significant improvements over the state-of-the-art approach, and establishes our implementation as t...
20 citations