In this paper, due to the delay of communication and the time variability of the reference state, the traditional consistency algorithm is not very good at fitting the time-varying reference state, so this paper propo...
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This paper studies clustering algorithms for dynamically evolving graphs {Gt}, in which new edges (and potential new vertices) are added into a graph, and the underlying cluster structure of the graph can gradually ch...
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This paper studies clustering algorithms for dynamically evolving graphs {Gt}, in which new edges (and potential new vertices) are added into a graph, and the underlying cluster structure of the graph can gradually change. The paper proves that, under some mild condition on the cluster-structure, the clusters of the final graph GT of nT vertices at time T can be well approximated by a dynamic variant of the spectral clustering algorithm. The algorithm runs in amortised update time O(1) and query time o(nT). Experimental studies on both synthetic and real-world datasets further confirm the practicality of our designed algorithm. Copyright 2024 by the author(s)
In this paper we show that every graph G of bounded maximum average degree mad(G) and with maximum degree ∆ can be edge-colored using the optimal number of ∆ colors in quasilinear time, whenever ∆ ≥ 2 mad(G). The max...
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This study investigates the distributed fact-checking problem, where a series of fact-checkers (agents) with interconnected influence evaluate a sequence of statements from a source. Each statement has a hidden binary...
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We present a deterministic n2+o(1)-time algorithm that approximates the crossing number of any graph G of order n up to an additive error of o(n4), as well as a randomized polynomial-time algorithm that constructs a d...
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Counting and enumerating all occurrences of k-cliques, i.e., complete subgraphs with k vertices, in a large graph G is a fundamental problem with many applications. However, exact solutions are often infeasible due to...
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Counting and enumerating all occurrences of k-cliques, i.e., complete subgraphs with k vertices, in a large graph G is a fundamental problem with many applications. However, exact solutions are often infeasible due to the exponential growth in the number of k-cliques when k increases. Thus, a more practical approach is approximately counting and uniformly sampling k-cliques. Turán-Shadow and DP Color Path are two state-of-the-art algorithms for approximately counting k-cliques. The general idea is first constructing a sample space that is a superset of all k-cliques in G, and then sampling t elements uniformly-at-random (u.a.r.) from the sample space for a pre-determined t;the k-clique count is estimated as the sample space size multiplied by the ratio of k-cliques among the t samples. Although techniques have been proposed in Turán-Shadow for setting t to ensure the estimation accuracy, the theoretically chosen t is often too large to be practical. As a result, both of the existing algorithms used a fixed t in their implementations and thus do not offer accuracy guarantee. In this paper, we propose the first randomized algorithm that achieves the theoretical estimation accuracy and the practical efficiency at the same time. Different from the existing algorithms, we pre-determine the number s of k-clique samples that are required to achieve the estimation accuracy. Consequently, we can estimate the running time of the sampling stage (i.e., time taken to sample s k-cliques), for a given sample space. Then, we propose to balance the time of constructing/refining the sample space and the time of the sampling stage, by stopping the refinement of the sample space once the elapsed time is comparable to the estimated time of the sampling stage. Extensive empirical studies on large real graphs show that our algorithm SR-kCCE provides an accurate k-clique count estimation and also runs efficiently. As a by-product, our algorithm can also be used for efficiently sampling a c
To provide the industry with an algorithm capable of accurately calculating comment statement tags, this paper proposes a research method based on feature engineering and BILSTM technology. First, the paper uses big d...
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This paper comprehensively reviews the YOLO series algorithms in computer vision. It begins by emphasizing the significance of object detection in security, driving and image analysis, and then traces the evolution of...
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Most graphs are asymmetric, i.e. they lack any nontrivial automorphisms. Even in the case of highly symmetric graphs, removing just a single vertex from a graphical regular representation may result in a graph with a ...
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This empirical study demonstrate the effectiveness of correlation clustering that allows overlapping via graph-theoretic algorithms to cluster data collected by multiple monitoring & assessment stations of the US ...
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