{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T19:48:22Z","timestamp":1774727302233,"version":"3.50.1"},"reference-count":15,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2026,2,9]],"date-time":"2026-02-09T00:00:00Z","timestamp":1770595200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,2,9]],"date-time":"2026-02-09T00:00:00Z","timestamp":1770595200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Comb Optim"],"published-print":{"date-parts":[[2026,3]]},"DOI":"10.1007\/s10878-026-01398-4","type":"journal-article","created":{"date-parts":[[2026,2,9]],"date-time":"2026-02-09T18:51:55Z","timestamp":1770663115000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On positive influence dominating sets with bi-directional weighted constraint in social networks"],"prefix":"10.1007","volume":"51","author":[{"given":"Qi","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8960-5521","authenticated-orcid":false,"given":"Hao","family":"Zhong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,2,9]]},"reference":[{"issue":"3","key":"1398_CR1","doi-asserted-by":"publisher","first-page":"79","DOI":"10.3390\/a14030079","volume":"14","author":"S Bouamama","year":"2021","unstructured":"Bouamama S, Blum C (2021) An improved greedy heuristic for the minimum positive influence dominating set problem in social networks. Algorithms 14(3):79","journal-title":"Algorithms"},{"issue":"1","key":"1398_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10878-021-00812-3","volume":"44","author":"W Chen","year":"2022","unstructured":"Chen W, Zhong H, Lidong W, Ding-Zhu D (2022) A general greedy approximation algorithm for finding minimum positive influence dominating sets in social networks. J Comb Optim 44(1):1\u201320","journal-title":"J Comb Optim"},{"key":"1398_CR3","doi-asserted-by":"crossref","unstructured":"Chen W, Yuan Y, Zhang L (2010) Scalable influence maximization in social networks under the linear threshold model. In 2010 IEEE International Conference on Data Mining, pages 88\u201397. IEEE","DOI":"10.1109\/ICDM.2010.118"},{"issue":"1","key":"1398_CR4","doi-asserted-by":"publisher","first-page":"348","DOI":"10.1137\/22M1526952","volume":"38","author":"Y Disser","year":"2024","unstructured":"Disser Y, Weckbecker D (2024) Unified greedy approximability beyond submodular maximization. SIAM J Discret Math 38(1):348\u2013379","journal-title":"SIAM J Discret Math"},{"key":"1398_CR5","doi-asserted-by":"crossref","unstructured":"Greetham DV, Charlton N, Poghosyan A (2019) Total positive influence domination on weighted networks. In International Conference on Complex Networks and Their Applications, pages 325\u2013336. Springer","DOI":"10.1007\/978-3-030-36687-2_27"},{"issue":"5","key":"1398_CR6","doi-asserted-by":"publisher","first-page":"956","DOI":"10.1109\/TCSS.2019.2937396","volume":"6","author":"D Hongwei","year":"2019","unstructured":"Hongwei D, Yuan C, Yuan H, Wei S, Wen X (2019) Identify connected positive influence dominating set in social networks using two-hop coverage. IEEE Trans Comput Soc Syst 6(5):956\u2013967","journal-title":"IEEE Trans Comput Soc Syst"},{"issue":"3","key":"1398_CR7","doi-asserted-by":"publisher","first-page":"830","DOI":"10.1109\/TCSS.2021.3096247","volume":"9","author":"Y Shan","year":"2022","unstructured":"Shan Y, Kang Q, Xiao R, Chen Y, Kang Y (2022) An iterated carousel greedy algorithm for finding minimum positive influence dominating sets in social networks. IEEE Trans Comput Soc Syst 9(3):830\u2013838","journal-title":"IEEE Trans Comput Soc Syst"},{"issue":"1","key":"1398_CR8","doi-asserted-by":"publisher","first-page":"2330","DOI":"10.1038\/srep02330","volume":"3","author":"Pramesh Singh","year":"2013","unstructured":"Singh Pramesh, Sreenivasan Sameet, Szymanski Boleslaw K, Korniss Gyorgy (2013) Threshold-limited spreading in social networks with multiple initiators. Scientific reports 3(1):2330","journal-title":"Scientific reports"},{"key":"1398_CR9","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2023.106197","volume":"154","author":"R Sun","year":"2023","unstructured":"Sun R, Jieyu W, Jin C, Wang Y, Zhou W, Yin M (2023) An efficient local search algorithm for minimum positive influence dominating set problem. Comput & Operat Res 154:106197","journal-title":"Comput & Operat Res"},{"issue":"2","key":"1398_CR10","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1007\/s11590-015-0938-8","volume":"11","author":"G Tong","year":"2017","unstructured":"Tong G, Weili W, Pardalos PM, Ding-Zhu D (2017) On positive-influence target-domination. Optim Letters 11(2):419\u2013427","journal-title":"Optim Letters"},{"issue":"3","key":"1398_CR11","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1016\/j.tcs.2009.10.001","volume":"412","author":"F Wang","year":"2011","unstructured":"Wang F, Du Hongwei D, Camacho E, Xu K, Lee W, Shi Y, Shan S (2011) On positive influence dominating sets in social networks. Theor Comput Sci 412(3):265\u2013269","journal-title":"Theor Comput Sci"},{"issue":"1","key":"1398_CR12","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/s13278-011-0033-9","volume":"2","author":"W Zhang","year":"2012","unstructured":"Zhang W, Weili W, Wang F, Kuai X (2012) Positive influence dominating sets in power-law graphs. Soc Netw Anal Min 2(1):31\u201337","journal-title":"Soc Netw Anal Min"},{"key":"1398_CR13","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2023.114069","volume":"973","author":"H Zhong","year":"2023","unstructured":"Zhong H, Tang Y, Zhang Q, Lin R, Li W (2023) A unified greedy approximation for several dominating set problems. Theoret Comput Sci 973:114069","journal-title":"Theoret Comput Sci"},{"issue":"5","key":"1398_CR14","doi-asserted-by":"publisher","first-page":"2930","DOI":"10.1109\/TCSS.2025.3541230","volume":"12","author":"H Zhong","year":"2025","unstructured":"Zhong H, Li W, Zhang Q, Lin R, Tang Y (2025) Efficient approximation algorithms for several positive influence dominating set problems in social networks. IEEE Trans Comput Soc Syst 12(5):2930\u20132939","journal-title":"IEEE Trans Comput Soc Syst"},{"issue":"4","key":"1398_CR15","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1007\/s10898-009-9511-2","volume":"48","author":"X Zhu","year":"2010","unstructured":"Zhu X, Jieun Yu, Lee W, Kim D, Shan S, Ding-Zhu D (2010) New dominating sets in social networks. J Global Optim 48(4):633\u2013642","journal-title":"J Global Optim"}],"container-title":["Journal of Combinatorial Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-026-01398-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10878-026-01398-4","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-026-01398-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T18:59:42Z","timestamp":1774724382000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10878-026-01398-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,9]]},"references-count":15,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,3]]}},"alternative-id":["1398"],"URL":"https:\/\/doi.org\/10.1007\/s10878-026-01398-4","relation":{},"ISSN":["1382-6905","1573-2886"],"issn-type":[{"value":"1382-6905","type":"print"},{"value":"1573-2886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,9]]},"assertion":[{"value":"3 June 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 January 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 February 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that this paper is original and has not been published elsewhere previously.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval"}},{"value":"The authors declare that they have no competing interests.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing Interests"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Research involving human participants and\/or animals"}}],"article-number":"17"}}