We study the densest subgraph problem and give algorithms via multiplicative weights update and area convexity that converge in O(log m/ϵ2) and O (log m/ϵ) iterations, respectively, both with nearly-linear time per it...
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We study the densest subgraph problem and give algorithms via multiplicative weights update and area convexity that converge in O(log m/ϵ2) and O (log m/ϵ) iterations, respectively, both with nearly-linear time per iteration. Compared with the work by Bahmani et al. (2014), our MWU algorithm uses a very different and much simpler procedure for recovering the dense subgraph from the fractional solution and does not employ a binary search. Compared with the work by Boob et al. (2019), our algorithm via area convexity improves the iteration complexity by a factor ∆-the maximum degree in the graph, and matches the fastest theoretical runtime currently known via flows (Chekuri et al., 2022) in total time. Next, we study the dense subgraph decomposition problem and give the first practical iterative algorithm with linear convergence rate O (mn log 1/ϵ) via accelerated random coordinate descent. This significantly improves over O (m√mn∆/ϵ) time of the FISTA-based algorithm by Harb et al. (2022). In the high precision regime ϵ 1/n where we can even recover the exact solution, our algorithm has a total runtime of O (mn log n), matching the exact algorithm via parametric flows (Gallo et al., 1989). Empirically, we show that this algorithm is very practical and scales to very large graphs, and its performance is competitive with widely used methods that have significantly weaker theoretical guarantees. Copyright 2024 by the author(s)
Green supercomputing has been attracting more and more attention due to the acknowledgement of environmental issues. This is especially the case in the field of supercomputing: given the large number of compute nodes ...
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With the rapid development of e-commerce, online shopping has become an indispensable part of people's daily lives. However, in the face of vast amounts of product information, how to provide personalized product ...
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This article is a report by the challenge organizers on the 9th Parameterized algorithms and Computational Experiments Challenge (PACE 2024). As was common in previous iterations of the competition, this year’s itera...
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In today’s increasingly data- and AI-driven scientific research enterprise, the division of labor between computational methods development and usage poses great risks of misuse. Moreover, flaws in a method can be un...
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Music recommendation system (MRS) is a system that recommends music content for users based on their historical behavior and interests. Personalized algorithm is the core technology of MRS, which provides personalized...
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This paper addresses the direction-finding problem in passive localization systems and proposes a novel algorithm for direction finding passive localization using an improved weighted average method in spherical coord...
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In view of the limitations of traditional multidimensional analogy algorithms in the study of social media feature algorithms, a research scheme of media feature algorithm based on deep network was proposed. Firstly, ...
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This paper studies a few randomized algorithms (e.g., random walks, gossip) in peer-to-peer networks. We leverage the Docker virtual container technology to develop implementations of the peer-to-peer networks and of ...
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We present a polynomial-time pseudo-deterministic algorithm for constructing irreducible polynomial of degree d over finite field Fq. A pseudo-deterministic algorithm is allowed to use randomness, but with high probab...
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