Adjacency list

About: Adjacency list is a research topic. Over the lifetime, 4419 publications have been published within this topic receiving 78449 citations.

Methods for the computer-implemented solution of a class of 'floor plan' design problems

Abstract: : The work presented is intended as a case study in computer-implemented design. Its purpose is to illustrate the relationship between the representation chosen for a design problem and the methods developed for solving that problem. A formal class of 'floor plan'-type design problems is defined. In these problems a set of rectangular rooms is specified, and an allowable list of dimensions is given for each room. In addition, a set of required adjacencies between rooms, or between a room and an outside wall of the building, is given. The problem is to produce a rectangular floor plan of a building that contains all of the specified rooms, and that satisfied all of the adjacency and dimension requirements. A linear graph representation for floor plans is developed. This graph is the dual graph of the floor plan, itself treated as a linear graph. Thus, the nodes of the dual graph correspond to rooms, and the edges correspond to adjacencies between rooms. The design methods are implemented in a computer program, GRAMPA, written in IPL-V. Several illustrative problems solved by GRAMPA are discussed. (Author)

Unitary symmetry and combinatorics

Abstract: Quantum Angular Momentum Composite Systems Graphs and Adjacency Diagrams Generating Functions The D-Polynomials: Form Operator Actions in Hilbert Space The D-Polynomials: Structure The General Linear and Unitary Groups Tensor Operator Theory Compendium A: Basic Algebraic Objects Compendium B: Combinatorial Objects.

Testing Acyclicity of Directed Graphs in Sublinear Time

Abstract: This paper initiates the study of testing properties of directed graphs. In particular, the paper considers the most basic property of directed graphs - acyclicity. Because the choice of representation affects the choice of algorithm, the two main representations of graphs are studied. For the adjacency matrix representation, most appropriate for dense graphs, a testing algorithm is developed that requires query and time complexity of O(1/Ɛ2), where Ɛ is a distance parameter independent of the size of the graph. The algorithm, which can probe the adjacency matrix of the graph, accepts every graph that is acyclic, and rejects, with probability at least 2/3, every graph whose adjacency matrix should be modified in at least Ɛ fraction of its entries so that it become acyclic. For the incidence list representation, most appropriate for sparse graphs, an Ω(|V|1/3) lower bound is proved on the number of queries and the time required for testing, where V is the set of vertices in the graph. These results stand in contrast to what is known about testing acyclicity in undirected graphs.

Efficient computation and simplification of discrete morse decompositions on triangulated terrains

Abstract: We consider the problem of efficient computing and simplifying Morse complexes on a Triangulated Irregular Network (TIN) based on discrete Morse theory. We develop a compact encoding for the discrete Morse gradient field, defined by the terrain elevation, by attaching it to the triangles of the TIN. This encoding is suitable to be combined with any TIN data structure storing just its vertices and triangles. We show how to compute such gradient field from the elevation values given at the TIN vertices, and how to simplify it effectively in order to reduce the number of critical elements. We demonstrate the effectiveness and scalability of our approach over large terrains by developing algorithms for extracting the cells of the Morse complexes as well as the graph joining the critical elements from the discrete gradient field. We compare implementations of our approach on a widely-used and compact adjacency-based topological data structure for a TIN and on a compact spatio-topological data structure that we have recently developed, the PR-star quadtree.

UV-Net: Learning from Boundary Representations

Abstract: We introduce UV-Net, a novel neural network architecture and representation designed to operate directly on Boundary representation (B-rep) data from 3D CAD models. The B-rep format is widely used in the design, simulation and manufacturing industries to enable sophisticated and precise CAD modeling operations. However, B-rep data presents some unique challenges when used with modern machine learning due to the complexity of the data structure and its support for both continuous non-Euclidean geometric entities and discrete topological entities. In this paper, we propose a unified representation for B-rep data that exploits the U and V parameter domain of curves and surfaces to model geometry, and an adjacency graph to explicitly model topology. This leads to a unique and efficient network architecture, UV-Net, that couples image and graph convolutional neural networks in a compute and memory-efficient manner To aid in future research we present a synthetic labelled B-rep dataset, SolidLetters, derived from human designed fonts with variations in both geometry and topology. Finally we demonstrate that UV-Net can generalize to supervised and unsupervised tasks on five datasets, while outperforming alternate 3D shape representations such as point clouds, voxels, and meshes.