{"title":"MHPD:超图上影响力最大化的高效评估方法","authors":"","doi":"10.1016/j.cnsns.2024.108268","DOIUrl":null,"url":null,"abstract":"<div><p>Influence maximization problem (IM) has been extensively applied in fields such as viral marketing, rumor control, and infectious disease prevention. However, research on the IM problem has primarily focused on ordinary networks, with limited attention devoted to hypergraphs. Firstly, we propose an efficient evaluation method, i.e., the multiple-hop probability dissemination method (MHPD), aiming to accurately and rapidly evaluate the propagation capacity of selected nodes. The MHPD method is a universal approach that is applicable to various network types, including hypergraphs, and it accommodates multiple probabilistic spreading models. Then, based on MHPD, we propose two novel algorithms for solving IM problem, i.e., MHPD-greedy and MHPD-heuristic. MHPD-greedy employs MHPD to evaluate the marginal benefits of nodes and iteratively adds nodes with the maximum marginal benefit to the seed set. MHPD-heuristic utilizes MHPD to evaluate the propagation capacity of each node and select the top-<span><math><mi>K</mi></math></span> nodes as the seeds. Experimental results on eight real-world hypergraphs and eight synthetic hypergraphs demonstrate that MHPD is capable of achieving near-identical accuracy in evaluating the propagation capability of both individual nodes and seed sets, while only incurring an average time overhead of merely <strong>0.25 %</strong> compared to Monte Carlo method. In comparison with seven cutting-edge algorithms, MHPD-heuristic demonstrates superior solution accuracy. Notably, MHPD-greedy maintains <strong>98.81 %</strong> of the solution accuracy while requiring only <strong>0.11 %</strong> of the time cost compared to the Greedy method. Furthermore, MHPD-greedy achieves an average performance improvement of <strong>23.4 %</strong> over the best baseline algorithm.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4000,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"MHPD: An efficient evaluation method for influence maximization on hypergraphs\",\"authors\":\"\",\"doi\":\"10.1016/j.cnsns.2024.108268\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Influence maximization problem (IM) has been extensively applied in fields such as viral marketing, rumor control, and infectious disease prevention. However, research on the IM problem has primarily focused on ordinary networks, with limited attention devoted to hypergraphs. Firstly, we propose an efficient evaluation method, i.e., the multiple-hop probability dissemination method (MHPD), aiming to accurately and rapidly evaluate the propagation capacity of selected nodes. The MHPD method is a universal approach that is applicable to various network types, including hypergraphs, and it accommodates multiple probabilistic spreading models. Then, based on MHPD, we propose two novel algorithms for solving IM problem, i.e., MHPD-greedy and MHPD-heuristic. MHPD-greedy employs MHPD to evaluate the marginal benefits of nodes and iteratively adds nodes with the maximum marginal benefit to the seed set. MHPD-heuristic utilizes MHPD to evaluate the propagation capacity of each node and select the top-<span><math><mi>K</mi></math></span> nodes as the seeds. Experimental results on eight real-world hypergraphs and eight synthetic hypergraphs demonstrate that MHPD is capable of achieving near-identical accuracy in evaluating the propagation capability of both individual nodes and seed sets, while only incurring an average time overhead of merely <strong>0.25 %</strong> compared to Monte Carlo method. In comparison with seven cutting-edge algorithms, MHPD-heuristic demonstrates superior solution accuracy. Notably, MHPD-greedy maintains <strong>98.81 %</strong> of the solution accuracy while requiring only <strong>0.11 %</strong> of the time cost compared to the Greedy method. Furthermore, MHPD-greedy achieves an average performance improvement of <strong>23.4 %</strong> over the best baseline algorithm.</p></div>\",\"PeriodicalId\":50658,\"journal\":{\"name\":\"Communications in Nonlinear Science and Numerical Simulation\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.4000,\"publicationDate\":\"2024-08-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Nonlinear Science and Numerical Simulation\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1007570424004532\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Nonlinear Science and Numerical Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1007570424004532","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
MHPD: An efficient evaluation method for influence maximization on hypergraphs
Influence maximization problem (IM) has been extensively applied in fields such as viral marketing, rumor control, and infectious disease prevention. However, research on the IM problem has primarily focused on ordinary networks, with limited attention devoted to hypergraphs. Firstly, we propose an efficient evaluation method, i.e., the multiple-hop probability dissemination method (MHPD), aiming to accurately and rapidly evaluate the propagation capacity of selected nodes. The MHPD method is a universal approach that is applicable to various network types, including hypergraphs, and it accommodates multiple probabilistic spreading models. Then, based on MHPD, we propose two novel algorithms for solving IM problem, i.e., MHPD-greedy and MHPD-heuristic. MHPD-greedy employs MHPD to evaluate the marginal benefits of nodes and iteratively adds nodes with the maximum marginal benefit to the seed set. MHPD-heuristic utilizes MHPD to evaluate the propagation capacity of each node and select the top- nodes as the seeds. Experimental results on eight real-world hypergraphs and eight synthetic hypergraphs demonstrate that MHPD is capable of achieving near-identical accuracy in evaluating the propagation capability of both individual nodes and seed sets, while only incurring an average time overhead of merely 0.25 % compared to Monte Carlo method. In comparison with seven cutting-edge algorithms, MHPD-heuristic demonstrates superior solution accuracy. Notably, MHPD-greedy maintains 98.81 % of the solution accuracy while requiring only 0.11 % of the time cost compared to the Greedy method. Furthermore, MHPD-greedy achieves an average performance improvement of 23.4 % over the best baseline algorithm.
期刊介绍:
The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity.
The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged.
Topics of interest:
Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity.
No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.