{"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}
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Abstract
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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