Adjacency list

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

Spectra of Uniform Hypergraphs

Abstract: We present a spectral theory of hypergraphs that closely parallels Spectral Graph Theory. A number of recent developments building upon classical work has led to a rich understanding of "hyperdeterminants" of hypermatrices, a.k.a. multidimensional arrays. Hyperdeterminants share many properties with determinants, but the context of multilinear algebra is substantially more complicated than the linear algebra required to address Spectral Graph Theory (i.e., ordinary matrices). Nonetheless, it is possible to define eigenvalues of a hypermatrix via its characteristic polynomial as well as variationally. We apply this notion to the "adjacency hypermatrix" of a uniform hypergraph, and prove a number of natural analogues of basic results in Spectral Graph Theory. Open problems abound, and we present a number of directions for further study.

Geometric reasoning for extraction of manufacturing features in iso-oriented polyhedrons

Abstract: This paper investigates the extraction of machining features from boundary descriptions of iso-oriented (having no inclined faces) polyhedrons. We prove that manufacturing the features proposed by our feature extractor results exactly in the desired part-in this respect, the approach is both sound and complete. Our method uses the adjacency information between faces to derive the features. This keeps the determination of isolated features in a part straightforward. However, interaction of features creates difficulties since the adjacency information between some faces is lost. We derive this lost information by considering faces that when extended intersect other faces to form concave edges. The derived face adjacencies are termed virtual links. Augmenting the virtual links to the cavity graph of the object leads to its feature graph, and subgraph matching of primitive graphs in this graph results in feature hypotheses. A feature hypothesis is considered valid if the volume corresponding to it is not shared with the part in question; therefore, we verify the feature hypotheses by checking the regularized intersection of the feature volume and the part. Thus, feature verification employs a constructive solid geometry approach. We have implemented a prototype of the system in the Smalltalk-80 environment. >

The Topological Structures of Membrane Computing

Abstract: In its initial presentation, the P system formalism describes the topology of the membranes as a set of nested regions. In this paper, we present an algebraic structure developped in combinatorial topology that can be used to describe finer adjacency relationships between membranes. Using an appropriate abstract setting, this technical device enables us to reformulate also the computation within a membrane and proposes a unified view on several computational mechanisms initially inspired by biological processes. These theoretical tools are instantiated in MGS, an experimental programming language handling various types of membrane structures in a homogeneous and uniform syntax.

On a two-truths phenomenon in spectral graph clustering.

Abstract: Clustering is concerned with coherently grouping observations without any explicit concept of true groupings. Spectral graph clustering-clustering the vertices of a graph based on their spectral embedding-is commonly approached via K-means (or, more generally, Gaussian mixture model) clustering composed with either Laplacian spectral embedding (LSE) or adjacency spectral embedding (ASE). Recent theoretical results provide deeper understanding of the problem and solutions and lead us to a "two-truths" LSE vs. ASE spectral graph clustering phenomenon convincingly illustrated here via a diffusion MRI connectome dataset: The different embedding methods yield different clustering results, with LSE capturing left hemisphere/right hemisphere affinity structure and ASE capturing gray matter/white matter core-periphery structure.

CUDA Solutions for the SSSP Problem

Abstract: We present several algorithms that solve the single-source shortest-path problem using CUDA. We have run them on a database, composed of hundreds of large graphs represented by adjacency lists and adjacency matrices, achieving high speedups regarding a CPU implementation based on Fibonacci heaps. Concerning correctness, we outline why our solutions work, and show that a previous approach [10] is incorrect.