{"title":"最小成本定向完美感知问题:复杂性、算法和计算","authors":"Felipe de C. Pereira, Pedro J. de Rezende","doi":"10.1016/j.osnem.2023.100255","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we investigate the Least Cost Directed Perfect Awareness Problem (<span>LDPAP</span><span>), a combinatorial optimization problem that deals with the spread of information on social networks. The objective of </span><span>LDPAP</span> is to minimize the cost of recruiting individuals capable of starting a propagation of a given news so that it reaches everyone. By showing that <span>LDPAP</span> can be regarded as a generalization of the Perfect Awareness Problem, we establish that <span>LDPAP</span> is <span>NP</span>-hard and we then prove that it remains <span>NP</span><span>-hard even when restricted to directed acyclic graphs. Our contributions also include two integer programming<span> formulations, a heuristic based on the metaheuristic </span></span><span>GRASP</span> and a useful lower bound for the objective function. Lastly, we present extensive experiments comparing the efficiency and efficacy of our heuristic and mathematical models both on synthetic and on real-world datasets.</p></div>","PeriodicalId":52228,"journal":{"name":"Online Social Networks and Media","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Least Cost Directed Perfect Awareness Problem: complexity, algorithms and computations\",\"authors\":\"Felipe de C. Pereira, Pedro J. de Rezende\",\"doi\":\"10.1016/j.osnem.2023.100255\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we investigate the Least Cost Directed Perfect Awareness Problem (<span>LDPAP</span><span>), a combinatorial optimization problem that deals with the spread of information on social networks. The objective of </span><span>LDPAP</span> is to minimize the cost of recruiting individuals capable of starting a propagation of a given news so that it reaches everyone. By showing that <span>LDPAP</span> can be regarded as a generalization of the Perfect Awareness Problem, we establish that <span>LDPAP</span> is <span>NP</span>-hard and we then prove that it remains <span>NP</span><span>-hard even when restricted to directed acyclic graphs. Our contributions also include two integer programming<span> formulations, a heuristic based on the metaheuristic </span></span><span>GRASP</span> and a useful lower bound for the objective function. Lastly, we present extensive experiments comparing the efficiency and efficacy of our heuristic and mathematical models both on synthetic and on real-world datasets.</p></div>\",\"PeriodicalId\":52228,\"journal\":{\"name\":\"Online Social Networks and Media\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Online Social Networks and Media\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2468696423000149\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Social Sciences\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Online Social Networks and Media","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2468696423000149","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Social Sciences","Score":null,"Total":0}
The Least Cost Directed Perfect Awareness Problem: complexity, algorithms and computations
In this paper, we investigate the Least Cost Directed Perfect Awareness Problem (LDPAP), a combinatorial optimization problem that deals with the spread of information on social networks. The objective of LDPAP is to minimize the cost of recruiting individuals capable of starting a propagation of a given news so that it reaches everyone. By showing that LDPAP can be regarded as a generalization of the Perfect Awareness Problem, we establish that LDPAP is NP-hard and we then prove that it remains NP-hard even when restricted to directed acyclic graphs. Our contributions also include two integer programming formulations, a heuristic based on the metaheuristic GRASP and a useful lower bound for the objective function. Lastly, we present extensive experiments comparing the efficiency and efficacy of our heuristic and mathematical models both on synthetic and on real-world datasets.
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