We propose novel and exact algorithm for generating connected Erdős–Rényi random graphs G(n, p). Our approach exploits a link between the distribution of exploration process trajectories and an inhomogeneous ra...
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Fix a sequence of d-regular graphs (Gd)d∈N and denote by Gd,p the graph obtained from Gd after edge-percolation with probability p = c/d, for a constant c > 0. We prove a quantitative local convergence of (Gd,p)d...
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Causal discovery aims to infer causal graphs from observational or experimental data. Methods such as the popular PC algorithm are based on conditional independence testing and utilize enabling assumptions, such as th...
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The flip graph algorithm is a method for discovering new matrix multiplication schemes by following random walks on a graph. We introduce a version of the flip graph algorithm for matrix multiplication schemes that ad...
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Horizontal Visibility graphs establish a connection between time series and complex networks. As a feature, they have shown strong results in time series classification. For real-world applications, algorithms for com...
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Horizontal Visibility graphs establish a connection between time series and complex networks. As a feature, they have shown strong results in time series classification. For real-world applications, algorithms for computing HVGs are necessary that work efficiently on streamed data, that can be parallelized, and whose runtime is independent of the type of time series. Our proposed algorithm extends the fast horizontal visibility algorithm of Zhu et al. satisfying all these desirable properties. The extended version stays worst-case in O(n), works additionally efficiently on streamed data, and becomes parallelizable. Contrary to recent publications, it does not require a complex data structure. This approach enables the computation of HVGs with millions of vertices in a short period, opening up new application areas of HVGs for time series generated batch-wise or resulting from measurements with a high sampling rate.(c) 2023 Elsevier B.V. All rights reserved.
Given a static vertex-selection problem (e.g. independent set, dominating set) on a graph, we can define a corresponding temporal reconfiguration problem on a temporal graph which asks for a sequence of solutions to t...
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A recent breakthrough by [LNPSY STOC’21] showed that solving s-t vertex connectivity is sufficient (up to polylogarithmic factors) to solve (global) vertex connectivity in the sequential model. This raises a natural ...
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In this paper we present the notion of greyscale of a graph as a colouring of its vertices that uses colours from the real interval [0,1]. Any greyscale induces another colouring by assigning to each edge the non-nega...
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In this paper we present the notion of greyscale of a graph as a colouring of its vertices that uses colours from the real interval [0,1]. Any greyscale induces another colouring by assigning to each edge the non-negative difference between the colours of its vertices. These edge colours are ordered in lexicographical decreasing ordering and give rise to a new element of the graph: the gradation vector. We introduce the notion of minimum gradation vector as a new invariant for the graph and give polynomial algorithms to obtain it. These algorithms also output all greyscales that produce the minimum gradation vector. This way we tackle and solve a novel vectorial optimization problem in graphs that may generate more satisfactory solutions than those generated by known scalar optimization approaches.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).
Computing strongly connected components (SCC) is among the most fundamental problems in graph analytics. Given the large size of today's real-world graphs, parallel SCC implementation is increasingly important. SC...
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Computing strongly connected components (SCC) is among the most fundamental problems in graph analytics. Given the large size of today's real-world graphs, parallel SCC implementation is increasingly important. SCC is challenging in the parallel setting and is particularly hard on large-diameter graphs. Many existing parallel SCC implementations can be even slower than Tarjan's sequential algorithm on large-diameter *** tackle this challenge, we propose an efficient parallel SCC implementation using a new parallel reachability approach. Our solution is based on a novel idea referred to as vertical granularity control (VGC). It breaks the synchronization barriers to increase parallelism and hide scheduling overhead. To use VGC in our SCC algorithm, we also design an efficient data structure called the parallel hash bag. It uses parallel dynamic resizing to avoid redundant work in maintaining frontiers (vertices processed in a round).We implement the parallel SCC algorithm by Blelloch et al. (J. ACM, 2020) using our new parallel reachability approach. We compare our implementation to the state-of-the-art systems, including GBBS, iSpan, Multi-step, and our highly optimized Tarjan's (sequential) algorithm, on 18 graphs, including social, web, k-NN, and lattice graphs. On a machine with 96 cores, our implementation is the fastest on 16 out of 18 graphs. On average (geometric means) over all graphs, our SCC is 6.0× faster than the best previous parallel code (GBBS), 12.8× faster than Tarjan's sequential algorithms, and 2.7× faster than the best existing implementation on each *** believe that our techniques are of independent interest. We also apply our parallel hash bag and VGC scheme to other graph problems, including connectivity and least-element lists (LE-lists). Our implementations improve the performance of the state-of-the-art parallel implementations for these two problems.
A bipartite graph is a graph that consists of two disjoint sets of vertices and only edges between vertices from different vertex sets. In this paper, we study the counting problems of two common types of em motifs in...
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A bipartite graph is a graph that consists of two disjoint sets of vertices and only edges between vertices from different vertex sets. In this paper, we study the counting problems of two common types of em motifs in bipartite graphs: (i) butterflies (2x2 bicliques) and (ii) bi-triangles (length-6 cycles). Unlike most of the existing algorithms that aim to obtain exact counts, our goal is to obtain precise enough estimations of these counts in bipartite graphs, as such estimations are already sufficient and of great usefulness in various applications. While there exist approximate algorithms for butterfly counting, these algorithms are mainly based on the techniques designed for general graphs, and hence, they are less effective on bipartite graphs. Not to mention that there is still a lack of study on approximate bi-triangle counting. Motivated by this, we first propose a novel butterfly counting algorithm, called one-sided weighted sampling, which is tailored for bipartite graphs. The basic idea of this algorithm is to estimate the total butterfly count with the number of butterflies containing two randomly sampled vertices from the same side of the two vertex sets. We prove that our estimation is unbiased, and our technique can be further extended (non-trivially) for bi-triangle count estimation. Theoretical analyses under a power-law random bipartite graph model and extensive experiments on multiple large real datasets demonstrate that our proposed approximate counting algorithms can reach high accuracy, yet achieve up to three orders (resp. four orders) of magnitude speed-up over the state-of-the-art exact butterfly (resp. bi-triangle) counting algorithms. Additionally, we present an approximate clustering coefficient estimation framework for bipartite graphs, which shows a similar speed-up over the exact solutions with less than 1% relative error.
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