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: A picture processing algorithm based on a line by line technique, designed to recognize and count the objects in a picture and to compute some of their geometrical and morphological properties is introduced.
33 citations
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25 Oct 2008TL;DR: This work considers the problem of online sublinear expander reconstruction and its relation to random walks in ``noisy" expanders, and shows that a random walk from almost any vertex in the expander part will have fast mixing properties in the general setting of irreducible finite Markov chains.
Abstract: We consider the problem of online sublinear expander reconstruction and its relation to random walks in ``noisy" expanders. Given access to an adjacency list representation of a bounded-degree graph G, we want to convert this graph into a bounded-degree expander G' changing G as little aspossible. The graph G' will be output by a distributed filter: this is sublinear time procedure that given a query vertex, outputs all its neighbors in G', and can do so even in a distributed manner, ensuring consistency in all the answers.One of the main tools in our analysis is a result on the behavior of random walks in graph that are almost expanders: graphs that are formed by arbitrarily connecting a small unknown graph (the noise) to a large expander. We show that a random walk from almost any vertex in the expander part will have fast mixing properties, in the general setting of irreducible finite Markov chains. We alsodesign sublinear time procedures to distinguish vertices of the expander part from those in the noise part, and use this procedure in the reconstruction algorithm.
33 citations
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TL;DR: This paper presents LF-GDPR, the first LDP-enabled graph metric estimation framework for graph analysis, and shows use cases on two common graph analysis tasks, namely, clustering coefficient estimation and community detection.
Abstract: Local differential privacy (LDP) is an emerging technique for privacy-preserving data collection without a trusted collector. Despite its strong privacy guarantee, LDP cannot be easily applied to real-world graph analysis tasks such as community detection and centrality analysis due to its high implementation complexity and low data utility. In this paper, we address these two issues by presenting LF-GDPR, the first LDP-enabled graph metric estimation framework for graph analysis. It collects two atomic graph metrics --- the adjacency bit vector and node degree --- from each node locally. LF-GDPR simplifies the job of implementing LDP-related steps (e.g., local perturbation, aggregation and calibration) for a graph metric estimation task by providing either a complete or a parameterized algorithm for each step. To address low data utility of LDP, it optimally allocates privacy budget between the two atomic metrics during data collection. To demonstrate the usage of LF-GDPR, we show use cases on two common graph analysis tasks, namely, clustering coefficient estimation and community detection. The privacy and utility achieved by LF-GDPR are verified through theoretical analysis and extensive experimental results.
33 citations
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TL;DR: This paper shows that kernels producing a slow reduction rate can be combined to speed up reduction, and proposes one sequential and one parallel algorithm to compute the contracted combinatorial maps.
33 citations
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14 May 2005TL;DR: A fairly simple and theoretically validated energy model for computing hierarchical graphs layouts, i.e. of positions of the nodes in two- or three-dimensional space, is presented.
Abstract: Hierarchical graphs are widely used as models of the structure of software systems. A central problem in the visualization of hierarchical graphs is the computation of layouts, i.e. of positions of the nodes in two- or three-dimensional space. We derive requirements for graph layouts from various software analysis questions, and classify the required layouts along three dimensions: layouts with meaningful distances between single nodes vs. layouts with meaningful distances between groups of nodes, layouts reflecting adjacency vs. layouts reflecting hierarchy, and layouts that faithfully reflect the size of subgraphs vs. layouts where certain subgraphs are magnified. We present a fairly simple and theoretically validated energy model for computing such layouts.
33 citations