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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: These results and methods are proved to be valid for various kinds of images (binary, gray-level, label), thus providing generic and efficient tools, which can be used in particular in the context of image registration and warping.
Abstract: We provide conditions under which 2D digital images preserve their topological properties under rigid transformations. We consider the two most common digital topology models, namely dual adjacency and well-composedness. This paper leads to the proposal of optimal preprocessing strategies that ensure the topological invariance of images under arbitrary rigid transformations. These results and methods are proved to be valid for various kinds of images (binary, gray-level, label), thus providing generic and efficient tools, which can be used in particular in the context of image registration and warping.

27 citations

Posted Content
TL;DR: In this paper, the authors presented a distance labeling scheme with label size (log 3)/2 + o(n) (logarithms are in base 2) and O(1) decoding time.
Abstract: We consider how to assign labels to any undirected graph with n nodes such that, given the labels of two nodes and no other information regarding the graph, it is possible to determine the distance between the two nodes. The challenge in such a distance labeling scheme is primarily to minimize the maximum label lenght and secondarily to minimize the time needed to answer distance queries (decoding). Previous schemes have offered different trade-offs between label lengths and query time. This paper presents a simple algorithm with shorter labels and shorter query time than any previous solution, thereby improving the state-of-the-art with respect to both label length and query time in one single algorithm. Our solution addresses several open problems concerning label length and decoding time and is the first improvement of label length for more than three decades. More specifically, we present a distance labeling scheme with label size (log 3)/2 + o(n) (logarithms are in base 2) and O(1) decoding time. This outperforms all existing results with respect to both size and decoding time, including Winkler's (Combinatorica 1983) decade-old result, which uses labels of size (log 3)n and O(n/log n) decoding time, and Gavoille et al. (SODA'01), which uses labels of size 11n + o(n) and O(loglog n) decoding time. In addition, our algorithm is simpler than the previous ones. In the case of integral edge weights of size at most W, we present almost matching upper and lower bounds for label sizes. For r-additive approximation schemes, where distances can be off by an additive constant r, we give both upper and lower bounds. In particular, we present an upper bound for 1-additive approximation schemes which, in the unweighted case, has the same size (ignoring second order terms) as an adjacency scheme: n/2. We also give results for bipartite graphs and for exact and 1-additive distance oracles.

27 citations

Journal ArticleDOI
TL;DR: A set of basic Euler operators based on the edge‐face adjacency relation is denned, which allow the incremental manipulation of boundary representations of solid objects.
Abstract: We propose a relational scheme for representing and modelling regular objects, which is based on the adjacency relations between faces and edges. In this structure, called edge-face graph, the nodes represent the faces and the arcs the edges of the corresponding object. Other topological entities, such as vertices, loops of edges, and shells, can be obtained from this relational scheme. We give a formal description of the edge-face graph, and the relationships between its properties and the topological entities of the object are analyzed in detail. Furthermore, a set of basic Euler operators based on the edge-face adjacency relation is denned, which allow the incremental manipulation of boundary representations of solid objects.

26 citations

Journal ArticleDOI
TL;DR: Several topology-based measures that characterise proximity relationships between regions in a spatial system are introduced, derived from a relative adjacency operator that is computed from the dual graph of aatial system.
Abstract: This paper introduces several topology-based measures that characterise proximity relationships between regions in a spatial system. These measures are derived from a relative adjacency operator that is computed from the dual graph of a spatial system. The operator is flexible as the respective importance of neighbouring and outlying regions can be parameterised. Given a reference region in a spatial system, we also show how the relative adjacency supports the analysis of the relative distribution of other regions, and how these regions are clustered with respect to that reference region. Extensions of the relative adjacency integrate additional spatial and thematic criteria. The properties of the relative adjacency are illustrated by means of reference examples and a case study.

26 citations

Posted Content
TL;DR: This paper presents a computationally tractable algorithm for estimating this graph structure from the available data, directed and weighted, possibly representing causation relations, not just correlations as in most existing approaches in the literature.
Abstract: Many big data applications collect a large number of time series, for example, the financial data of companies quoted in a stock exchange, the health care data of all patients that visit the emergency room of a hospital, or the temperature sequences continuously measured by weather stations across the US. A first task in the analytics of these data is to derive a low dimensional representation, a graph or discrete manifold, that describes well the interrelations among the time series and their intrarelations across time. This paper presents a computationally tractable algorithm for estimating this graph structure from the available data. This graph is directed and weighted, possibly representing causation relations, not just correlations as in most existing approaches in the literature. The algorithm is demonstrated on random graph and real network time series datasets, and its performance is compared to that of related methods. The adjacency matrices estimated with the new method are close to the true graph in the simulated data and consistent with prior physical knowledge in the real dataset tested.

26 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023209
2022439
2021283
2020280
2019296
2018232