{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T22:21:42Z","timestamp":1742941302580,"version":"3.40.3"},"publisher-location":"Cham","reference-count":18,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030692438"},{"type":"electronic","value":"9783030692445"}],"license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021]]},"DOI":"10.1007\/978-3-030-69244-5_33","type":"book-chapter","created":{"date-parts":[[2021,2,20]],"date-time":"2021-02-20T16:36:12Z","timestamp":1613838972000},"page":"371-378","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Prize-Collecting k-Steiner Tree Problem"],"prefix":"10.1007","author":[{"given":"Lu","family":"Han","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Changjun","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dachuan","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dongmei","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,2,21]]},"reference":[{"key":"33_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, 309\u2013332 (2011)","journal-title":"SIAM J. Comput."},{"key":"33_CR2","unstructured":"Arora, S., Karakostas, G.: A $$2+\\varepsilon $$ approximation algorithm for the $$k$$-MST problem. In: Proceedings of the 11th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 754\u2013759 (2000)"},{"key":"33_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, 117\u2013118 (1998)","journal-title":"Inf. Process. Lett."},{"key":"33_CR4","doi-asserted-by":"publisher","first-page":"254","DOI":"10.1137\/S009753979528826X","volume":"28","author":"B Awerbuch","year":"1999","unstructured":"Awerbuch, B., Azar, Y., Blum, A., Vempala, S.: Improved approximation guarantees for minimum-weight $$k$$-trees and prize-collecting salesmen. SIAM J. Comput. 28, 254\u2013262 (1999)","journal-title":"SIAM J. Comput."},{"key":"33_CR5","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.P.: A note on the prize collecting traveling salesman problem. Math. Program. 59, 413\u2013420 (1993)","journal-title":"Math. Program."},{"key":"33_CR6","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 28th Annual ACM Symposium on Theory of Computing, pp. 442\u2013448 (1996)","DOI":"10.1145\/237814.237992"},{"key":"33_CR7","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, 411\u2013421 (2004)","journal-title":"Math. Program."},{"key":"33_CR8","doi-asserted-by":"crossref","unstructured":"Fischetti, M., Hamacher, H.W., J\u00f8rnsten, K., Maffioli, F.: Weighted $$k$$-cardinality trees: complexity and polyhedral structure. Networks 24, 11\u201321 (1994)","DOI":"10.1002\/net.3230240103"},{"key":"33_CR9","unstructured":"Garg, N.: A $$3$$-approximation for the minimum tree spanning $$k$$ vertices. In: Proceedings of the 37th Annual Symposium on Foundations of Computer Science, pp. 302\u2013309 (1996)"},{"key":"33_CR10","doi-asserted-by":"crossref","unstructured":"Garg, N.: Saving an epsilon: a $$2$$-approximation for the $$k$$-MST problem in graphs. In: Proceedings of the 37th Annual ACM Symposium on Theory of Computing, pp. 396\u2013402 (2005)","DOI":"10.1145\/1060590.1060650"},{"key":"33_CR11","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, 296\u2013317 (1995)","journal-title":"SIAM J. Comput."},{"key":"33_CR12","doi-asserted-by":"publisher","first-page":"573","DOI":"10.1007\/s11590-017-1135-8","volume":"13","author":"L Han","year":"2019","unstructured":"Han, L., Xu, D., Du, D., Wu, C.: A $$5$$-approximation algorithm for the $$k$$-prize-collecting Steiner tree problem. Optim. Lett. 13, 573\u2013585 (2019)","journal-title":"Optim. Lett."},{"key":"33_CR13","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/s40305-017-0164-4","volume":"5","author":"L Han","year":"2017","unstructured":"Han, L., Xu, D., Du, D., Wu, C.: A primal-dual algorithm for the generalized prize-collecting Steiner forest problem. J. Oper. Res. Soc. China 5, 219\u2013231 (2017)","journal-title":"J. Oper. Res. Soc. China"},{"key":"33_CR14","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1007\/s11590-018-1367-2","volume":"13","author":"Y Matsuda","year":"2019","unstructured":"Matsuda, Y., Takahashi, S.: A $$4$$-approximation algorithm for $$k$$-prize collecting Steiner tree problems. Optim. Lett. 13, 341\u2013348 (2019)","journal-title":"Optim. Lett."},{"key":"33_CR15","unstructured":"Rajagopalan, S., Vazirani, V.V.: Logarithmic approximation of minimum weight $$k$$ trees. Unpublished manuscript (1995)"},{"key":"33_CR16","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 short or small. SIAM J. Discrete Math. 9, 178\u2013200 (1996)","journal-title":"SIAM J. Discrete Math."},{"key":"33_CR17","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1016\/j.tcs.2017.03.014","volume":"774","author":"Y Xu","year":"2019","unstructured":"Xu, Y., Xu, D., Du, D., Wu, C.: Improved approximation algorithm for universal facility location problem with linear penalties. Theor. Comput. Sci. 774, 143\u2013151 (2019)","journal-title":"Theor. Comput. Sci."},{"key":"33_CR18","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1016\/j.dam.2019.03.013","volume":"264","author":"Y Xu","year":"2019","unstructured":"Xu, Y., Xu, D., Du, D., Zhang, D.: Approximation algorithm for squared metric facility location problem with non uniform capacities. Discrete Appl. Math. 264, 208\u2013217 (2019)","journal-title":"Discrete Appl. Math."}],"container-title":["Lecture Notes in Computer Science","Parallel and Distributed Computing, Applications and Technologies"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-69244-5_33","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,20]],"date-time":"2021-02-20T16:49:52Z","timestamp":1613839792000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-030-69244-5_33"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"ISBN":["9783030692438","9783030692445"],"references-count":18,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-69244-5_33","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2021]]},"assertion":[{"value":"21 February 2021","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"PDCAT","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Parallel and Distributed Computing: Applications and Technologies","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Shenzhen","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"China","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2020","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"28 December 2020","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"30 December 2020","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"21","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"pdcat2020","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/hpcc.siat.ac.cn\/meeting\/pdcat-paap2020\/index.html","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"OCS","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"109","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"34","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"31% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"6","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}