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 authors considered representations of graphs as rectanglevisibility graphs and as doubly linear graphs and proved that these graphs have at most 6n−20 edges for each n ≥ 8.
Abstract: This paper considers representations of graphs as rectanglevisibility graphs and as doubly linear graphs. These are, respectively, graphs whose vertices are isothetic rectangles in the plane with adjacency determined by horizontal and vertical visibility, and graphs that can be drawn as the union of two straight-edged planar graphs. We prove that these graphs have, with n vertices, at most 6n−20 (resp., 6n−18) edges, and we provide examples of these graphs with 6n−20 edges for each n≥8.
51 citations
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TL;DR: This work extends the RESCAL tensor factorization, which has shown state-of-the-art results for multi-relational learning, to account for the binary nature of adjacency tensors and shows that the logistic extension can improve the prediction results significantly.
Abstract: Tensor factorizations have become increasingly popular approaches for various learning tasks on structured data. In this work, we extend the RESCAL tensor factorization, which has shown state-of-the-art results for multi-relational learning, to account for the binary nature of adjacency tensors. We study the improvements that can be gained via this approach on various benchmark datasets and show that the logistic extension can improve the prediction results significantly.
51 citations
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TL;DR: This paper focuses on efficiently encoding and decoding the stitching information, and avoids encoding vertices (and properties bound to vertices) multiple times; thus a reduction of the size of the bit-stream of about 10% is obtained compared with encoding the model as a manifold.
Abstract: We present a method for compressing non-manifold polygonal meshes, i.e., polygonal meshes with singularities, which occur very frequently in the real-world. Most efficient polygonal compression methods currently available are restricted to a manifold mesh: they require converting a non-manifold mesh to a manifold mesh, and fail to retrieve the original model connectivity after decompression. The present method works by converting the original model to a manifold model, encoding the manifold model using an existing mesh compression technique, and clustering, or stitching together during the decompression process vertices that were duplicated earlier to faithfully recover the original connectivity. This paper focuses on efficiently encoding and decoding the stitching information. Using a naive method, the stitching information would incur a prohibitive cost, while our methods guarantee a worst case cost of O ( log m) bits per vertex replication, where m is the number of non-manifold vertices. Furthermore, when exploiting the adjacency between vertex replications, many replications can be encoded with an insignificant cost. By interleaving the connectivity, stitching information, geometry and properties, we can avoid encoding repeated vertices (and properties bound to vertices) multiple times; thus a reduction of the size of the bit-stream of about 10% is obtained compared with encoding the model as a manifold.
51 citations
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TL;DR: A graph-like data structure is constructed on these shape features, called the Characteristic Region Configuration Graph, which represents die surface in an effective and concise way.
Abstract: A method is described for the extraction of morphological information from a terrain approximated by a Delaunay triangulation, in order to find a combinatorial simpler surface description while maintaining its basic features. Characteristic regions (i.e., regions with concave, convex, planar or saddle shape) are considered the basic descriptive elements of the surface morphology, and are defined by taking into account the type of adjacency between triangles. Adjacencies between regions define the surface characteristic lines, which are classified as ridges, ravines or generic creases, and characteristic points, which are classified as maxima, minima or saddle points. A graph-like data structure is constructed on these shape features, called the Characteristic Region Configuration Graph, which represents die surface in an effective and concise way.
51 citations
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TL;DR: Six methods for implementing the widely used Clarke-Wright algorithm for the vehicle routing problem (VRP) are presented and compared and the results clearly establish methods of choice for VRP problems with given characteristics.
51 citations