{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:20:39Z","timestamp":1740122439447,"version":"3.37.3"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2024,4,26]],"date-time":"2024-04-26T00:00:00Z","timestamp":1714089600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,4,26]],"date-time":"2024-04-26T00:00:00Z","timestamp":1714089600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U20A2068"],"award-info":[{"award-number":["U20A2068"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Comb Optim"],"published-print":{"date-parts":[[2024,5]]},"DOI":"10.1007\/s10878-024-01124-y","type":"journal-article","created":{"date-parts":[[2024,4,26]],"date-time":"2024-04-26T14:02:10Z","timestamp":1714140130000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Approximation algorithm for the minimum partial connected Roman dominating set problem"],"prefix":"10.1007","volume":"47","author":[{"given":"Yaoyao","family":"Zhang","sequence":"first","affiliation":[]},{"given":"Zhao","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Ding-Zhu","family":"Du","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,4,26]]},"reference":[{"key":"1124_CR1","volume":"391","author":"HA Ahangar","year":"2021","unstructured":"Ahangar HA, \u00c1lvarez MP, Chellali M, Sheikholeslami SM, Valenzuela-Tripodoro JC (2021) Triple roman domination in graphs. Appl Math Comput 391:125444","journal-title":"Appl Math Comput"},{"issue":"4","key":"1124_CR2","doi-asserted-by":"publisher","first-page":"787","DOI":"10.7151\/dmgt.2108","volume":"39","author":"HA Ahangar","year":"2019","unstructured":"Ahangar HA, Amjadi J, Chellali M, Nazari-Moghaddam S, Sheikholeslami SM (2019) Total roman reinforcement in graphs. Discuss Math Graph Theory 39(4):787\u2013803","journal-title":"Discuss Math Graph Theory"},{"key":"1124_CR3","first-page":"2017","volume":"103","author":"HA Ahangar","year":"2017","unstructured":"Ahangar HA, Bahremandpour A, Sheikholeslami SM, Soner ND, Tahmasbzadehbaee Z, Volkmann L (2017) Maximal roman domination numbers in graphs. Util Math 103:2017","journal-title":"Util Math"},{"key":"1124_CR4","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1016\/j.dam.2016.03.017","volume":"211","author":"RA Beeler","year":"2016","unstructured":"Beeler RA, Haynes TW, Hedetniemi ST (2016) Double roman domination. Discrete Appl Math 211:23\u201329","journal-title":"Discrete Appl Math"},{"issue":"1\u20132","key":"1124_CR5","first-page":"89","volume":"64","author":"P Chakradhar","year":"2020","unstructured":"Chakradhar P, Reddy PVS (2020) Algorithmic aspects of roman domination in graphs. J Appl Math Comput 64(1\u20132):89\u2013102","journal-title":"J Appl Math Comput"},{"issue":"05","key":"1124_CR6","doi-asserted-by":"publisher","first-page":"2150063","DOI":"10.1142\/S1793830921500634","volume":"13","author":"P Chakradhar","year":"2021","unstructured":"Chakradhar P, Reddy PVS (2021) Algorithmic aspects of total roman $$\\{3\\}$$-domination in graphs. Discrete Math Algorithms Appl 13(05):2150063","journal-title":"Discrete Math Algorithms Appl"},{"key":"1124_CR7","first-page":"183","volume":"7","author":"P Chakradhar","year":"2022","unstructured":"Chakradhar P, Reddy PVS (2022) Algorithmic aspects of total roman $$\\{2\\}$$-domination in graphs. Commun Comb Optim 7:183\u2013192","journal-title":"Commun Comb Optim"},{"key":"1124_CR8","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1016\/j.dam.2015.11.013","volume":"204","author":"M Chellali","year":"2016","unstructured":"Chellali M, Haynes TW, Hedetniemi ST, McRae A (2016) Roman 2-domination. Discrete Appl Math 204:22\u201328","journal-title":"Discrete Appl Math"},{"key":"1124_CR9","first-page":"273","volume-title":"Varieties of Roman domination","author":"M Chellali","year":"2021","unstructured":"Chellali M, JafariRad N, Sheikholeslami SM, Volkmann L (2021) Varieties of Roman domination. Springer, Cham, pp 273\u2013307"},{"issue":"1\u20133","key":"1124_CR10","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1016\/j.disc.2003.06.004","volume":"278","author":"EJ Cockayne","year":"2004","unstructured":"Cockayne EJ, Dreyer PA Jr, Hedetniemi SM, Hedetniemi ST (2004) Roman domination in graphs. Discrete Math 278(1\u20133):11\u201322","journal-title":"Discrete Math"},{"key":"1124_CR11","volume-title":"Applications and variations of domination in graphs","author":"PA Dreyer Jr","year":"2000","unstructured":"Dreyer PA Jr (2000) Applications and variations of domination in graphs. Rutgers The State University of New Jersey, School of Graduate Studies, New Brunswick"},{"key":"1124_CR12","volume-title":"Topics in domination in graphs","author":"TW Haynes","year":"2010","unstructured":"Haynes TW, Hedetniemi ST, Henning MA (2010) Topics in domination in graphs. Springer, Cham"},{"issue":"2","key":"1124_CR13","doi-asserted-by":"publisher","first-page":"325","DOI":"10.7151\/dmgt.1178","volume":"22","author":"MA Henning","year":"2002","unstructured":"Henning MA (2002) A characterization of roman trees. Discuss Math Graph Theory 22(2):325\u2013334","journal-title":"Discuss Math Graph Theory"},{"issue":"1","key":"1124_CR14","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1137\/18M1212094","volume":"34","author":"S Khuller","year":"2020","unstructured":"Khuller S, Purohit M, Sarpatwar KK (2020) Analyzing the optimal neighborhood: algorithms for partial and budgeted connected dominating set problems. SIAM J Discrete Math 34(1):251\u2013270","journal-title":"SIAM J Discrete Math"},{"issue":"8","key":"1124_CR15","doi-asserted-by":"publisher","first-page":"2261","DOI":"10.1007\/s11590-022-01862-0","volume":"16","author":"K Li","year":"2022","unstructured":"Li K, Ran Y, Zhang Z, Ding-Zhu D (2022) Nearly tight approximation algorithm for (connected) roman dominating set. Optim Lett 16(8):2261\u20132276","journal-title":"Optim Lett"},{"key":"1124_CR16","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1016\/j.dam.2023.08.006","volume":"341","author":"K Li","year":"2023","unstructured":"Li K, Zhang Z (2023) Approximation algorithm for (connected) Italian dominating function. Discrete Appl Math 341:169\u2013179","journal-title":"Discrete Appl Math"},{"key":"1124_CR17","doi-asserted-by":"crossref","unstructured":"Liedloff M, Kloks T, Liu, J and Peng S-L (2005) Roman domination over some graph classes. In: International workshop on graph-theoretic concepts in computer science (WG 2005). Springer Berlin Heidelberg, pp 103\u2013114","DOI":"10.1007\/11604686_10"},{"issue":"2","key":"1124_CR18","doi-asserted-by":"publisher","first-page":"460","DOI":"10.1137\/S0097539702420474","volume":"37","author":"A Moss","year":"2007","unstructured":"Moss A, Rabani Y (2007) Approximation algorithms for constrained node weighted Steiner tree problems. SIAM J Comput 37(2):460\u2013481","journal-title":"SIAM J Comput"},{"issue":"01","key":"1124_CR19","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1142\/S1793830910000504","volume":"2","author":"W Shang","year":"2010","unstructured":"Shang W, Wang X, Xiaodong H (2010) Roman domination and its variants in unit disk graphs. Discrete Math Algorithms Appl 2(01):99\u2013105","journal-title":"Discrete Math Algorithms Appl"},{"issue":"6","key":"1124_CR20","doi-asserted-by":"publisher","first-page":"136","DOI":"10.1038\/scientificamerican1299-136","volume":"281","author":"I Stewart","year":"1999","unstructured":"Stewart I (1999) Defend the roman empire! Sci Am 281(6):136\u2013138","journal-title":"Sci Am"},{"issue":"1","key":"1124_CR21","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1007\/s10878-019-00459-1","volume":"39","author":"L Wang","year":"2020","unstructured":"Wang L, Shi Y, Zhang Z, Zhang Z-B, Zhang X (2020) Approximation algorithm for a generalized roman domination problem in unit ball graphs. J Comb Optim 39(1):138\u2013148","journal-title":"J Comb Optim"}],"container-title":["Journal of Combinatorial Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-024-01124-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10878-024-01124-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-024-01124-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,17]],"date-time":"2024-05-17T13:11:17Z","timestamp":1715951477000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10878-024-01124-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,26]]},"references-count":21,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,5]]}},"alternative-id":["1124"],"URL":"https:\/\/doi.org\/10.1007\/s10878-024-01124-y","relation":{},"ISSN":["1382-6905","1573-2886"],"issn-type":[{"type":"print","value":"1382-6905"},{"type":"electronic","value":"1573-2886"}],"subject":[],"published":{"date-parts":[[2024,4,26]]},"assertion":[{"value":"28 February 2024","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 April 2024","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no relevant financial or non-financial interests to disclose.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"62"}}