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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TL;DR: In this paper, the continuous Laplacian on an infinite locally finite network with equal edge lengths under natural transition conditions as continuity at the ramification nodes and classical Kirchhoff conditions at all vertices is considered.
Abstract: We consider the continuous Laplacian on an infinite locally finite network with equal edge lengths under natural transition conditions as continuity at the ramification nodes and classical Kirchhoff conditions at all vertices. It is shown that eigenvalues of the Laplacian in a L∞-setting are closely related to those of the adjacency and transition operator of the network. In this way the point spectrum is determined completely in terms of combinatorial quantities and properties of the underlying graph as in the finite case [2]. Moreover, the occurrence of infinite geometric multiplicity on trees and some periodic graphs is investigated.
34 citations
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TL;DR: This paper formally defines two basic comparison problems for nD open combinatorial maps, and gives polynomial time algorithms for solving them, and illustrates their interest and feasibility for searching patterns in 2D and 3D images, as any child would aim to do when he searches Wally in Martin Handford's books.
34 citations
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TL;DR: This work reports on algorithms and CUDA data-parallel programming techniques for implementing Metropolis Monte Carlo updates for the Ising model using bit-packing storage, and adjacency neighbour lists for various graph structures in addition to regular hypercubic lattices.
Abstract: Data-parallel accelerator devices such as Graphical Processing Units (GPUs) are providing dramatic performance improvements over even multi-core CPUs for lattice-oriented applications in computational physics. Models such as the Ising and Potts models continue to play a role in investigating phase transitions on small-world and scale-free graph structures. These models are particularly well-suited to the performance gains possible using GPUs and relatively high-level device programming languages such as NVIDIA’s Compute Unified Device Architecture (CUDA). We report on algorithms and CUDA data-parallel programming techniques for implementing Metropolis Monte Carlo updates for the Ising model using bit-packing storage, and adjacency neighbour lists for various graph structures in addition to regular hypercubic lattices. We report on parallel performance gains and also memory and performance tradeoffs using GPU/CPU and algorithmic combinations.
34 citations
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TL;DR: A new structure, star-vertex, is proposed to represent general planar meshes, allowing constant adjacency query time, and scalability, and under specific situations requiring less storage space than others.
Abstract: In this paper we propose a new structure star-vertex, to represent general planar meshes. The basic concept is simple, allowing constant adjacency query time, and scalability (able to trade size for speed), and under specific situations requiring less storage space than others. For simplicity, we use a generic traverse element, which resembles the behavior of oriented edges. We present implementation examples of the proposed structure and comparisons with other mesh representation schemes.
34 citations
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TL;DR: It is demonstrated that the sparse representation theory not only serves for automatic graph construction as shown in recent works, but also represents an accurate alternative for out-of-sample embedding.
34 citations