{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T11:52:17Z","timestamp":1778500337227,"version":"3.51.4"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,5,22]],"date-time":"2023-05-22T00:00:00Z","timestamp":1684713600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,5,22]],"date-time":"2023-05-22T00:00:00Z","timestamp":1684713600000},"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"}]},{"name":"Zhejiang Provincial Natural Science Foundation of China","award":["LD19A010001"],"award-info":[{"award-number":["LD19A010001"]}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["III-1907472"],"award-info":[{"award-number":["III-1907472"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Optim Lett"],"published-print":{"date-parts":[[2024,3]]},"DOI":"10.1007\/s11590-023-02008-6","type":"journal-article","created":{"date-parts":[[2023,5,22]],"date-time":"2023-05-22T18:02:44Z","timestamp":1684778564000},"page":"575-589","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A unified approach to approximate partial, prize-collecting, and budgeted sweep cover problems"],"prefix":"10.1007","volume":"18","author":[{"given":"Wei","family":"Liang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhao","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ding-Zhu","family":"Du","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,5,22]]},"reference":[{"issue":"2","key":"2008_CR1","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1137\/090771429","volume":"40","author":"A Archer","year":"2011","unstructured":"Archer, A., Bateni, M.H., Hajiaghayi, M.T., Karloff, H.: Improved approximation algorithms for prize-collecting steiner tree and tsp. SIAM J. Comput. 40(2), 309\u2013332 (2011)","journal-title":"SIAM J. Comput."},{"issue":"3","key":"2008_CR2","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1007\/s10107-005-0693-1","volume":"107","author":"S Arora","year":"2006","unstructured":"Arora, S., Karakostas, G.: A 2+$$\\epsilon $$ approximation algorithm for the k-mst problem. Math. Program. 107(3), 491\u2013504 (2006)","journal-title":"Math. Program."},{"issue":"3","key":"2008_CR3","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1016\/S0020-0190(98)00010-6","volume":"65","author":"S Arya","year":"1998","unstructured":"Arya, S., Ramesh, H.: A 2.5-factor approximation algorithm for the k-mst problem. Inf. Process. Lett. 65(3), 117\u2013118 (1998)","journal-title":"Inf. Process. Lett."},{"issue":"1","key":"2008_CR4","doi-asserted-by":"publisher","first-page":"254","DOI":"10.1137\/S009753979528826X","volume":"28","author":"BAY Azar","year":"1998","unstructured":"Azar, B.A.Y., Blum, A., Vempala, S.: New approximation guarantees for minimum-weight $$k$$-trees and prize-collecting salesmen. SIAM J. Comput. 28(1), 254\u2013262 (1998)","journal-title":"SIAM J. Comput."},{"issue":"6","key":"2008_CR5","doi-asserted-by":"publisher","first-page":"621","DOI":"10.1002\/net.3230190602","volume":"19","author":"E Balas","year":"1989","unstructured":"Balas, E.: The prize collecting traveling salesman problem. Networks 19(6), 621\u2013636 (1989)","journal-title":"Networks"},{"issue":"1","key":"2008_CR6","first-page":"254","volume":"28","author":"A Baruch","year":"1999","unstructured":"Baruch, A., Yossi, A., Avrim, B., Vempala, S.: Improved approximation guarantees for minimum-weight $$k$$-trees and prize-collecting salesmen. SIAM J. Comput. 28(1), 254\u2013262 (1999)","journal-title":"SIAM J. Comput."},{"issue":"1","key":"2008_CR7","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1007\/BF01581256","volume":"59","author":"D Bienstock","year":"1993","unstructured":"Bienstock, D., Goemans, M.X., Simchi-Levi, D., Williamson, D.: A note on the prize collecting traveling salesman problem. Math. Program. 59(1), 413\u2013420 (1993)","journal-title":"Math. Program."},{"key":"2008_CR8","doi-asserted-by":"crossref","unstructured":"Blum, A., Ravi, R., Vempala, S.: A constant-factor approximation algorithm for the k mst problem. In: Proceedings of the Twenty-eighth Annual ACM Symposium on Theory of Computing, pp. 442\u2013448 (1996)","DOI":"10.1145\/237814.237992"},{"key":"2008_CR9","doi-asserted-by":"crossref","unstructured":"Chen, Z., Zhu, X., Gao, X., Wu, F., Gu, J., Chen, G.: Efficient scheduling strategies for mobile sensors in sweep coverage problem. In: 2016 13th Annual IEEE International Conference on Sensing, Communication, and Networking (SECON), pp. 1\u20134 (2016)","DOI":"10.1109\/SAHCN.2016.7732985"},{"issue":"05","key":"2008_CR10","doi-asserted-by":"publisher","first-page":"1850064","DOI":"10.1142\/S1793830918500647","volume":"10","author":"Qingqing Chen","year":"2018","unstructured":"Chen, Qingqing, Huang, Xiaohui, Ran, Yingli: Approximation algorithm for distance constraint sweep coverage without predetermined base stations. Discrete Math. Algorithms Appl. 10(05), 1850064 (2018)","journal-title":"Discrete Math. Algorithms Appl."},{"key":"2008_CR11","doi-asserted-by":"crossref","unstructured":"Cheng, W., Li, M., Liu, K., Liu, Y., Li, X., Liao, X.: Sweep coverage with mobile sensors. In: 2008 IEEE International Symposium on Parallel and Distributed Processing, pp. 1\u20139 (2008)","DOI":"10.1109\/IPDPS.2008.4536245"},{"issue":"2","key":"2008_CR12","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1007\/s10107-003-0479-2","volume":"100","author":"FA Chudak","year":"2004","unstructured":"Chudak, F.A., Roughgarden, T., Williamson, D.P.: Approximate $$k$$-msts and $$k$$-steiner trees via the primal-dual method and lagrangean relaxation. Math. Program. 100(2), 411\u2013421 (2004)","journal-title":"Math. Program."},{"key":"2008_CR13","doi-asserted-by":"crossref","unstructured":"Feng, Y., Gao, X., Wu, F., Chen, G.: Shorten the trajectory of mobile sensors in sweep coverage problem. In: 2015 IEEE Global Communications Conference (GLOBECOM), pp. 1\u20136 (2015)","DOI":"10.1109\/GLOCOM.2015.7417353"},{"key":"2008_CR14","doi-asserted-by":"crossref","unstructured":"Gage, D.W.: Command Control for Many-robot Systems. Technical Report, Naval Command Control and Ocean Surveillance Center Rdt and E Div San Diego CA (1992)","DOI":"10.21236\/ADA422540"},{"key":"2008_CR15","unstructured":"Gao, X., Fan, J., Wu, F., Chen, G.: Cooperative sweep coverage problem with mobile sensors. IEEE Trans. Mob. Comput 1\u20131 (2020)"},{"issue":"2","key":"2008_CR16","doi-asserted-by":"publisher","first-page":"990","DOI":"10.1109\/TNET.2018.2815630","volume":"26","author":"X Gao","year":"2018","unstructured":"Gao, X., Fan, J., Fan, W., Chen, G.: Approximation algorithms for sweep coverage problem with multiple mobile sensors. IEEE\/ACM Trans. Netw. 26(2), 990\u20131003 (2018)","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"2008_CR17","doi-asserted-by":"crossref","unstructured":"Garg, N.: A 3-approximation for the minimum tree spanning $$k$$ vertices. In: Proceedings of 37th Conference on Foundations of Computer Science. pp. 302\u2013309. IEEE (1996)","DOI":"10.1109\/SFCS.1996.548489"},{"key":"2008_CR18","doi-asserted-by":"crossref","unstructured":"Garg, N.: Saving an epsilon: a 2-approximation for the $$k$$-mst problem in graphs. In: Proceedings of the thirty-seventh annual ACM symposium on Theory of computing, pp. 396\u2013402 (2005)","DOI":"10.1145\/1060590.1060650"},{"issue":"2","key":"2008_CR19","doi-asserted-by":"publisher","first-page":"296","DOI":"10.1137\/S0097539793242618","volume":"24","author":"MX Goemans","year":"1995","unstructured":"Goemans, M.X., Williamson, D.P.: A general approximation technique for constrained forest problems. SIAM J. Comput. 24(2), 296 (1995)","journal-title":"SIAM J. Comput."},{"issue":"9","key":"2008_CR20","doi-asserted-by":"publisher","first-page":"712","DOI":"10.1016\/j.ipl.2015.03.011","volume":"115","author":"B Gorain","year":"2015","unstructured":"Gorain, B., Mandal, P.S.: Approximation algorithm for sweep coverage on graph. Inf. Process. Lett. 115(9), 712\u2013718 (2015)","journal-title":"Inf. Process. Lett."},{"key":"2008_CR21","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1016\/j.dam.2016.09.028","volume":"228","author":"B Gorain","year":"2017","unstructured":"Gorain, B., Mandal, P.S.: Solving energy issues for sweep coverage in wireless sensor networks. Discrets Appl. Math. 228, 130\u2013139 (2017)","journal-title":"Discrets Appl. Math."},{"key":"2008_CR22","doi-asserted-by":"publisher","first-page":"50055","DOI":"10.1109\/ACCESS.2018.2868931","volume":"6","author":"P Huang","year":"2018","unstructured":"Huang, P., Zhu, W., Liao, K., Sellis, T., Zhiyong, Y., Guo, L.: Efficient algorithms for flexible sweep coverage in crowdsensing. IEEE Access 6, 50055\u201350065 (2018)","journal-title":"IEEE Access"},{"key":"2008_CR23","unstructured":"Johnson, D.S., Minkoff, M., & Phillips, S.: The prize collecting steiner tree problem: theory and practice. In: Proceedings of the Eleventh Annual ACM-SIAM Symposium on Discrete Algorithms, SODA \u201900, pp. 760\u2013769. Society for Industrial and Applied Mathematics (2000)"},{"issue":"4","key":"2008_CR24","doi-asserted-by":"publisher","first-page":"316","DOI":"10.1016\/j.orl.2003.11.002","volume":"32","author":"A Levin","year":"2004","unstructured":"Levin, A.: A better approximation algorithm for the budget prize collecting tree problem. Oper. Res. Lett. 32(4), 316\u2013319 (2004)","journal-title":"Oper. Res. Lett."},{"issue":"11","key":"2008_CR25","doi-asserted-by":"publisher","first-page":"1534","DOI":"10.1109\/TMC.2010.237","volume":"10","author":"M Li","year":"2011","unstructured":"Li, M., Cheng, W., Liu, K., He, Y., Li, X., Liao, X.: Sweep coverage with mobile sensors. IEEE Trans. Mob. Comput. 10(11), 1534\u20131545 (2011)","journal-title":"IEEE Trans. Mob. Comput."},{"key":"2008_CR26","unstructured":"Liang, D., Shen, H.: Chargeable sweep coverage problem. arXiv e-prints, arXiv:2105.06030 (2021)"},{"key":"2008_CR27","doi-asserted-by":"crossref","unstructured":"Liang, W., Zhang, Z.: Approximation algorithm for prize-collecting sweep cover with base stations. Theor. Comput. Sci., a preliminary version was presented in AAIM2020 (2022)","DOI":"10.1016\/j.tcs.2022.06.026"},{"issue":"4","key":"2008_CR28","doi-asserted-by":"publisher","first-page":"1457","DOI":"10.3390\/s21041457","volume":"21","author":"D Liang","year":"2021","unstructured":"Liang, D., Shen, H.: Efficient algorithms for max-weighted point sweep coverage on lines. Sensors (Basel, Switzerland) 21(4), 1457 (2021)","journal-title":"Sensors (Basel, Switzerland)"},{"issue":"4","key":"2008_CR29","doi-asserted-by":"publisher","first-page":"1111","DOI":"10.1007\/s10878-018-0341-3","volume":"37","author":"J Liang","year":"2019","unstructured":"Liang, J., Huang, X., Zhang, Z.: Approximation algorithms for distance constraint sweep coverage with base stations. J. Comb. Optim. 37(4), 1111\u20131125 (2019)","journal-title":"J. Comb. Optim."},{"key":"2008_CR30","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.tcs.2020.05.012","volume":"836","author":"C Liu","year":"2020","unstructured":"Liu, C., Hongwei, D., Ye, Q., Wen, X.: Group sweep coverage with guaranteed approximation ratio. Theoret. Comput. Sci. 836, 1\u201315 (2020)","journal-title":"Theoret. Comput. Sci."},{"key":"2008_CR31","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/j.tcs.2021.02.028","volume":"864","author":"Z Nie","year":"2021","unstructured":"Nie, Z., Hongwei, D.: An approximation algorithm for general energy restricted sweep coverage problem. Theoret. Comput. Sci. 864, 70\u201379 (2021)","journal-title":"Theoret. Comput. Sci."},{"issue":"2","key":"2008_CR32","doi-asserted-by":"publisher","first-page":"576","DOI":"10.1287\/moor.2019.1002","volume":"45","author":"A Paul","year":"2020","unstructured":"Paul, A., Freund, D., Ferber, A., Shmoys, D.B., Williamson, D.P.: Budgeted prize-collecting traveling salesman and minimum spanning tree problems. Math. Oper. Res. 45(2), 576\u2013590 (2020)","journal-title":"Math. Oper. Res."},{"issue":"2","key":"2008_CR33","doi-asserted-by":"publisher","first-page":"178","DOI":"10.1137\/S0895480194266331","volume":"9","author":"R Ravi","year":"1996","unstructured":"Ravi, R., Sundaram, R., Marathe, M.V., Rosenkrantz, D.J., Ravi, S.S.: Spanning trees\u2013short or small. SIAM J. Discrete Math. 9(2), 178\u2013200 (1996)","journal-title":"SIAM J. Discrete Math."},{"key":"2008_CR34","volume-title":"Approximation Algoritms","author":"VV Vazirani","year":"2001","unstructured":"Vazirani, V.V.: Approximation Algoritms. Springer, New York (2001)"},{"key":"2008_CR35","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-52824-9","volume-title":"Optimal Coverage in Wireless Sensor Networks","author":"W Wu","year":"2020","unstructured":"Wu, W., Zhang, Z., Lee, W., Du, D.: Optimal Coverage in Wireless Sensor Networks. Springer, New York (2020)"},{"issue":"17","key":"2008_CR36","doi-asserted-by":"publisher","first-page":"3449","DOI":"10.1016\/j.comnet.2006.01.008","volume":"50","author":"G Yaoyao","year":"2006","unstructured":"Yaoyao, G., Bozda, D., Brewer, R.W., Ekici, E.: Data harvesting with mobile elements in wireless sensor networks. Comput. Netw. 50(17), 3449\u20133465 (2006)","journal-title":"Comput. Netw."},{"key":"2008_CR37","doi-asserted-by":"crossref","unstructured":"Zhao, D., Ma, H., Liu, L.: Mobile sensor scheduling for timely sweep coverage. In: IEEE Wireless Communications and Networking Conference, WCNC, pp. 1771\u20131776, 04 (2012)","DOI":"10.1109\/WCNC.2012.6214071"},{"key":"2008_CR38","doi-asserted-by":"crossref","unstructured":"Zixiong, N., Chuang, L., Hongwei, D.: Data sensing with limited mobile sensors in sweep coverage. In: International Conference on Combinatorial Optimization and Applications, pp. 669\u2013680. Springer (2020)","DOI":"10.1007\/978-3-030-64843-5_45"}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-023-02008-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11590-023-02008-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-023-02008-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,20]],"date-time":"2024-10-20T21:59:59Z","timestamp":1729461599000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11590-023-02008-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,22]]},"references-count":38,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,3]]}},"alternative-id":["2008"],"URL":"https:\/\/doi.org\/10.1007\/s11590-023-02008-6","relation":{},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"value":"1862-4472","type":"print"},{"value":"1862-4480","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,22]]},"assertion":[{"value":"1 November 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 April 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 May 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}