{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T02:29:40Z","timestamp":1782959380958,"version":"3.54.5"},"reference-count":38,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2024,12,12]],"date-time":"2024-12-12T00:00:00Z","timestamp":1733961600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"crossref","award":["BK20242084"],"award-info":[{"award-number":["BK20242084"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["62402496"],"award-info":[{"award-number":["62402496"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Knowl. Discov. Data"],"published-print":{"date-parts":[[2025,1,31]]},"abstract":"<jats:p>Influence maximization (IM) aims to find a group of influential nodes as initial spreaders to maximize the influence spread over a network. Yet, traditional IM algorithms have not been designed with fairness in mind, resulting in discrimination against some groups, like LGBTQ communities and racial minorities. This issue has spurred research on Fair Influence Maximization (FIM). However, existing FIM studies come with some drawbacks. First, most proposed notions of fairness for FIM cannot adjust the tradeoff between fairness level and influence spread. Second, though a few specific notions of fairness allow such balancing, they are limited to a few specific concave functions, which may not be suitable for various real-world scenarios. Furthermore, none of them have studied the deep relations between the features of concave functions and the level of fairness. Third, existing fairness metrics are limited to their corresponding concepts of fairness. Comparing the level of fairness across different algorithms using existing metrics can be challenging. To tackle the above problems, this article first proposes a novel fairness notion named Poverty Reward (PR), which achieves fairness by rewarding the enrichment of groups with low utility. Based on PR, we further propose an algorithmic framework called Concave Fairness Framework (CFF) that allows any concave function that satisfies specific requirements. We also systematically clarify how fairness is improved by applying concave functions and provide an in-depth quantitative analysis of how to select appropriate concave functions for different utility distributions. Moreover, we propose the Reward of Fairness (RoF) metric that evaluates the disparity between groups. Based on RoF, an evaluation system is built to uniformly compare FIM algorithms from different fairness notions. Experiments in real-world datasets have demonstrated the validity of the CFF, as well as the proposed fairness notion.<\/jats:p>","DOI":"10.1145\/3701737","type":"journal-article","created":{"date-parts":[[2024,10,28]],"date-time":"2024-10-28T14:43:31Z","timestamp":1730126611000},"page":"1-23","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":6,"title":["A General Concave Fairness Framework for Influence Maximization Based on Poverty Reward"],"prefix":"10.1145","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4256-1477","authenticated-orcid":false,"given":"Zhixiao","family":"Wang","sequence":"first","affiliation":[{"name":"School of Computer Science, China University of Mining and Technology, Xuzhou, China and Mine Digitization Engineering Research Center of the Ministry of Education, Xuzhou, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0832-5822","authenticated-orcid":false,"given":"Jiayu","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Computer Science, China University of Mining and Technology, Xuzhou, China and Mine Digitization Engineering Research Center of the Ministry of Education, Xuzhou, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0995-9985","authenticated-orcid":false,"given":"Chengcheng","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Computer Science, China University of Mining and Technology, Xuzhou, China and Mine Digitization Engineering Research Center of the Ministry of Education, Xuzhou, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0951-1512","authenticated-orcid":false,"given":"Xiaobin","family":"Rui","sequence":"additional","affiliation":[{"name":"School of Computer Science, China University of Mining and Technology, Xuzhou, China and Mine Digitization Engineering Research Center of the Ministry of Education, Xuzhou, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3491-5968","authenticated-orcid":false,"given":"Philip S.","family":"Yu","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Illinois at Chicago, Chicago, IL, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2024,12,12]]},"reference":[{"key":"e_1_3_1_2_2","first-page":"1541","volume-title":"Proceedings of the IEEE International Conference on Data Engineering (ICDE \u201922)","author":"Ali Junaid","year":"2022","unstructured":"Junaid Ali, Mahmoudreza Babaei, Abhijnan Chakraborty, Baharan Mirzasoleiman, Krishna P. Gummadi, and Adish Singla. 2022. On the Fairness of Time-Critical Influence Maximization in Social Networks. In Proceedings of the IEEE International Conference on Data Engineering (ICDE \u201922), 1541\u20131542."},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10115-022-01696-3"},{"key":"e_1_3_1_4_2","first-page":"14684","volume-title":"Proceedings of the AAAI Conference on Artificial Intelligence (AAAI \u201921)","author":"Becker Ruben","year":"2021","unstructured":"Ruben Becker, Gianlorenzo D\u2019Angelo, Sajjad Ghobadi, and Hugo Gilbert. 2021. Fairness in Influence Maximization through Randomization. In Proceedings of the AAAI Conference on Artificial Intelligence (AAAI \u201921), 14684\u201314692."},{"key":"e_1_3_1_5_2","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1145\/3351095.3372864","volume-title":"Proceedings of the Conference on Fairness, Accountability, and Transparency (FAT* \u201920)","author":"Binns Reuben","year":"2020","unstructured":"Reuben Binns. 2020. On the Apparent Conflict between Individual and Group Fairness. In Proceedings of the Conference on Fairness, Accountability, and Transparency (FAT* \u201920), 514\u2013524."},{"key":"e_1_3_1_6_2","first-page":"57","volume-title":"Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD \u201901)","author":"Domingos Pedro","year":"2001","unstructured":"Pedro Domingos and Matthew Richardson. 2001. Mining the Network Value of Customers. In Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD \u201901), 57\u201366."},{"key":"e_1_3_1_7_2","doi-asserted-by":"publisher","DOI":"10.1145\/3447548.3467266"},{"key":"e_1_3_1_8_2","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2023.3265598"},{"key":"e_1_3_1_9_2","first-page":"214","article-title":"Fairness through Awareness","author":"Dwork Cynthia","year":"2012","unstructured":"Cynthia Dwork, Moritz Hardt, Toniann Pitassi, Omer Reingold, and Richard S. Zemel. 2012. Fairness through Awareness. In Innovations in Theoretical Computer Science 2012, 214\u2013226.","journal-title":"Innovations in Theoretical Computer Science 2012"},{"key":"e_1_3_1_10_2","doi-asserted-by":"crossref","first-page":"714","DOI":"10.1145\/3366424.3383555","volume-title":"Companion of the 2020 Web Conference 2020","author":"Farnadi Golnoosh","year":"2020","unstructured":"Golnoosh Farnadi, Behrouz Babaki, and Michel Gendreau. 2020. A Unifying Framework for Fairness-Aware Influence Maximization. In Companion of the 2020 Web Conference 2020, 714\u2013722."},{"key":"e_1_3_1_11_2","doi-asserted-by":"crossref","first-page":"480","DOI":"10.1145\/3308558.3313680","volume-title":"Proceedings of the World Wide Web Conference (WWW \u201919)","author":"Fish Benjamin","year":"2019","unstructured":"Benjamin Fish, Ashkan Bashardoust, danah boyd, Sorelle A. Friedler, Carlos Scheidegger, and Suresh Venkatasubramanian. 2019. Gaps in Information Access in Social Networks. In Proceedings of the World Wide Web Conference (WWW \u201919), 480\u2013490."},{"key":"e_1_3_1_12_2","doi-asserted-by":"publisher","DOI":"10.1145\/3447548.3467349"},{"key":"e_1_3_1_13_2","first-page":"284","volume-title":"Advances in Knowledge Discovery and Data Mining - 28th Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD \u201924)","volume":"14645","author":"Ghodsi Siamak","year":"2024","unstructured":"Siamak Ghodsi, Seyed Amjad Seyedi, and Eirini Ntoutsi. 2024. Towards Cohesion-Fairness Harmony: Contrastive Regularization in Individual Fair Graph Clustering. In Advances in Knowledge Discovery and Data Mining - 28th Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD \u201924), Vol. 14645, 284\u2013296."},{"key":"e_1_3_1_14_2","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2021.3058693"},{"key":"e_1_3_1_15_2","first-page":"3315","volume-title":"Advances in Neural Information Processing Systems 29: Annual Conference on Neural Information Processing Systems","author":"Hardt Moritz","year":"2016","unstructured":"Moritz Hardt, Eric Price, and Nati Srebro. 2016. Equality of Opportunity in Supervised Learning. In Advances in Neural Information Processing Systems 29: Annual Conference on Neural Information Processing Systems, 3315\u20133323."},{"key":"e_1_3_1_16_2","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1137\/1.9781611976236.69","volume-title":"Proceedings of the 2020 SIAM International Conference on Data Mining (SDM \u201920)","author":"Jalali Zeinab S.","year":"2020","unstructured":"Zeinab S. Jalali, Weixiang Wang, Myunghwan Kim, Hema Raghavan, and Sucheta Soundarajan. 2020. On the Information Unfairness of Social Networks. In Proceedings of the 2020 SIAM International Conference on Data Mining (SDM \u201920), 613\u2013521."},{"key":"e_1_3_1_17_2","doi-asserted-by":"publisher","DOI":"10.1145\/3394486.3403080"},{"key":"e_1_3_1_18_2","first-page":"137","volume-title":"Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD \u201903)","author":"Kempe David","year":"2003","unstructured":"David Kempe, Jon M. Kleinberg, and \u00c9va Tardos. 2003. Maximizing the Spread of Influence through a Social Network. In Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD \u201903), 137\u2013146."},{"key":"e_1_3_1_19_2","volume-title":"Proceedings of the 5th International Conference on Learning Representations (ICLR \u201917)","author":"Kipf Thomas N.","year":"2017","unstructured":"Thomas N. Kipf and Max Welling. 2017. Semi-Supervised Classification with Graph Convolutional Networks. In Proceedings of the 5th International Conference on Learning Representations (ICLR \u201917)."},{"key":"e_1_3_1_20_2","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2018.2807843"},{"key":"e_1_3_1_21_2","doi-asserted-by":"publisher","DOI":"10.5555\/2002472.2002537"},{"key":"e_1_3_1_22_2","doi-asserted-by":"publisher","DOI":"10.1613\/jair.1.14450"},{"key":"e_1_3_1_23_2","volume-title":"Fair Division and Collective Welfare","author":"Moulin Herv\u00e9","year":"2004","unstructured":"Herv\u00e9 Moulin. 2004. Fair Division and Collective Welfare, MIT press."},{"key":"e_1_3_1_24_2","first-page":"246","article-title":"Gatekeeper Training for Suicidal Behaviors: A Systematic Review","author":"Naohiro Yonemoto","year":"2019","unstructured":"Yonemoto Naohiro, Kawashima Yoshitaka, Endo Kaori, and Yamada Mitsuhiko. 2019. Gatekeeper Training for Suicidal Behaviors: A Systematic Review. Journal of Affective Disorders 246 (2019), 506\u2013514.","journal-title":"Journal of Affective Disorders"},{"key":"e_1_3_1_25_2","first-page":"3","volume-title":"Proceedings of the Conference on Fairness, Accountability and Transparency","volume":"1170","author":"Narayanan Arvind","year":"2018","unstructured":"Arvind Narayanan. 2018. Translation Tutorial: 21 Fairness Definitions and Their Politics. In Proceedings of the Conference on Fairness, Accountability and Transparency, Vol. 1170, 3."},{"key":"e_1_3_1_26_2","first-page":"5575","article-title":"Adaptive Influence Maximization with Myopic Feedback","volume":"32","author":"Peng Binghui","year":"2019","unstructured":"Binghui Peng and Wei Chen. 2019. Adaptive Influence Maximization with Myopic Feedback. In Advances in Neural Information Processing Systems (NeurIPS \u201919), Vol. 32, 5575\u20135584.","journal-title":"Advances in Neural Information Processing Systems (NeurIPS \u201919)"},{"key":"e_1_3_1_27_2","first-page":"7620","volume-title":"Proceedings of the 37th International Conference on Machine Learning (ICML \u201920)","volume":"119","author":"Perrault Pierre","year":"2020","unstructured":"Pierre Perrault, Jennifer Healey, Zheng Wen, and Michal Valko. 2020. Budgeted Online Influence Maximization. In Proceedings of the 37th International Conference on Machine Learning (ICML \u201920), Vol. 119, 7620\u20137631."},{"key":"e_1_3_1_28_2","first-page":"11630","volume-title":"Proceedings of the AAAI Conference on Artificial Intelligence (AAAI \u201921)","author":"Rahmattalabi Aida","year":"2021","unstructured":"Aida Rahmattalabi, Shahin Jabbari, Himabindu Lakkaraju, Phebe Vayanos, Max Izenberg, Ryan Brown, Eric Rice, and Milind Tambe. 2021. Fair Influence Maximization: A Welfare Optimization Approach. In Proceedings of the AAAI Conference on Artificial Intelligence (AAAI \u201921), 11630\u201311638."},{"key":"e_1_3_1_29_2","doi-asserted-by":"publisher","DOI":"10.2307\/j.ctvkjb25m"},{"key":"e_1_3_1_30_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCSS.2022.3198096"},{"key":"e_1_3_1_31_2","doi-asserted-by":"publisher","DOI":"10.1145\/775047.775057"},{"key":"e_1_3_1_32_2","first-page":"66675","volume-title":"Advances in Neural Information Processing Systems 36: Annual Conference on Neural Information Processing Systems","author":"Rui Xiaobin","year":"2023","unstructured":"Xiaobin Rui, Zhixiao Wang, Jiayu Zhao, Lichao Sun, and Wei Chen. 2023. Scalable Fair Influence Maximization. In Advances in Neural Information Processing Systems 36: Annual Conference on Neural Information Processing Systems, 66675\u201366691."},{"key":"e_1_3_1_33_2","doi-asserted-by":"publisher","DOI":"10.1145\/3366423.3380275"},{"key":"e_1_3_1_34_2","doi-asserted-by":"publisher","DOI":"10.1145\/3219819.3220101"},{"key":"e_1_3_1_35_2","first-page":"5997","volume-title":"Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI \u201919)","author":"Tsang Alan","year":"2019","unstructured":"Alan Tsang, Bryan Wilder, Eric Rice, Milind Tambe, and Yair Zick. 2019. Group-Fairness in Influence Maximization. In Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI \u201919), 5997\u20136005."},{"key":"e_1_3_1_36_2","doi-asserted-by":"publisher","DOI":"10.5555\/3237383.3237507"},{"key":"e_1_3_1_37_2","first-page":"5399","volume-title":"Proceedings of the 27th International Joint Conference on Artificial Intelligence (IJCAI \u201918)","author":"Yadav Amulya","year":"2018","unstructured":"Amulya Yadav, Bryan Wilder, Eric Rice, Robin Petering, Jaih Craddock, Amanda Yoshioka-Maxwell, Mary Hemler, Laura Onasch-Vera, Milind Tambe, and Darlene Woo. 2018. Bridging the Gap between Theory and Practice in Influence Maximization: Raising Awareness About HIV among Homeless Youth. In Proceedings of the 27th International Joint Conference on Artificial Intelligence (IJCAI \u201918), 5399\u20135403."},{"key":"e_1_3_1_38_2","doi-asserted-by":"publisher","DOI":"10.1086\/jar.33.4.3629752"},{"key":"e_1_3_1_39_2","first-page":"962","volume-title":"Proceedings of the International Conference on Artificial Intelligence and Statistics (AISTATS \u201917)","author":"Zafar Muhammad Bilal","year":"2017","unstructured":"Muhammad Bilal Zafar, Isabel Valera, Manuel Gomez-Rodriguez, and Krishna P. Gummadi. 2017. Fairness Constraints: Mechanisms for Fair Classification. In Proceedings of the International Conference on Artificial Intelligence and Statistics (AISTATS \u201917), 962\u2013970."}],"container-title":["ACM Transactions on Knowledge Discovery from Data"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3701737","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3701737","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T01:57:16Z","timestamp":1750298236000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3701737"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,12]]},"references-count":38,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1,31]]}},"alternative-id":["10.1145\/3701737"],"URL":"https:\/\/doi.org\/10.1145\/3701737","relation":{},"ISSN":["1556-4681","1556-472X"],"issn-type":[{"value":"1556-4681","type":"print"},{"value":"1556-472X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,12,12]]},"assertion":[{"value":"2024-02-15","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-10-12","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-12-12","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}