{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T17:34:25Z","timestamp":1790184865782,"version":"4.1.0"},"publisher-location":"Cham","reference-count":28,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031496103","type":"print"},{"value":"9783031496110","type":"electronic"}],"license":[{"start":{"date-parts":[[2023,12,9]],"date-time":"2023-12-09T00:00:00Z","timestamp":1702080000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,12,9]],"date-time":"2023-12-09T00:00:00Z","timestamp":1702080000000},"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":[],"published-print":{"date-parts":[[2024]]},"DOI":"10.1007\/978-3-031-49611-0_21","type":"book-chapter","created":{"date-parts":[[2023,12,8]],"date-time":"2023-12-08T14:02:45Z","timestamp":1702044165000},"page":"287-299","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Greedy+Max: An Efficient Approximation Algorithm for\u00a0k-Submodular Knapsack Maximization"],"prefix":"10.1007","author":[{"given":"Zhongzheng","family":"Tang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jingwen","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chenhao","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tian","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Weijia","family":"Jia","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,12,9]]},"reference":[{"key":"21_CR1","doi-asserted-by":"crossref","unstructured":"Buchbinder, N., Feldman, M., Naor, J., Schwartz, R.: Submodular maximization with cardinality constraints. In Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1433\u20131452. SIAM (2014)","DOI":"10.1137\/1.9781611973730.80"},{"key":"21_CR2","doi-asserted-by":"publisher","unstructured":"Chen, J., Tang, Z., Wang, C.: Monotone $$k$$-submodular knapsack maximization: an analysis of the Greedy+Singleton algorithm. In: Ni, Q., Wu, W. (eds.) Algorithmic Aspects in Information and Management. AAIM 2022. LNCS, vol. 13513. Springer, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-031-16081-3_13","DOI":"10.1007\/978-3-031-16081-3_13"},{"issue":"4","key":"21_CR3","doi-asserted-by":"publisher","first-page":"634","DOI":"10.1145\/285055.285059","volume":"45","author":"U Feige","year":"1998","unstructured":"Feige, U.: A threshold of $$\\ln n$$ for approximating set cover. J. ACM 45(4), 634\u2013652 (1998)","journal-title":"J. ACM"},{"key":"21_CR4","doi-asserted-by":"crossref","unstructured":"Gridchyn, I., Kolmogorov, V.: Potts model, parametric maxflow and $$k$$-submodular functions. In: Proceedings of the IEEE International Conference on Computer Vision (ICCV), pp. 2320\u20132327 (2013)","DOI":"10.1109\/ICCV.2013.288"},{"issue":"3","key":"21_CR5","doi-asserted-by":"publisher","first-page":"1726","DOI":"10.1137\/15M101926X","volume":"30","author":"H Hirai","year":"2016","unstructured":"Hirai, H., Iwamasa, Y.: On $$k$$-submodular relaxation. SIAM J. Discret. Math. 30(3), 1726\u20131736 (2016)","journal-title":"SIAM J. Discret. Math."},{"key":"21_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1007\/978-3-642-32147-4_40","volume-title":"Combinatorial Optimization","author":"A Huber","year":"2012","unstructured":"Huber, A., Kolmogorov, V.: Towards minimizing k-submodular functions. In: Mahjoub, A.R., Markakis, V., Milis, I., Paschos, V.T. (eds.) ISCO 2012. LNCS, vol. 7422, pp. 451\u2013462. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-32147-4_40"},{"key":"21_CR7","doi-asserted-by":"crossref","unstructured":"Iwata, S., Orlin, J.B.: A simple combinatorial algorithm for submodular function minimization. In: Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1230\u20131237. SIAM (2009)","DOI":"10.1137\/1.9781611973068.133"},{"key":"21_CR8","doi-asserted-by":"crossref","unstructured":"Iwata, S., Tanigawa, S., Yoshida, Y.: Improved approximation algorithms for $$k$$-submodular function maximization. In: Proceedings of the 27th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 404\u2013413 (2016)","DOI":"10.1137\/1.9781611974331.ch30"},{"key":"21_CR9","unstructured":"Lin, H., Bilmes, J.: Multi-document summarization via budgeted maximization of submodular functions. In: Human Language Technologies: The 2010 Annual Conference of the North American Chapter of the Association for Computational Linguistics, pp. 912\u2013920 (2010)"},{"key":"21_CR10","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1007\/978-3-642-68874-4_10","volume":"1982","author":"L Lov\u00e1sz","year":"1983","unstructured":"Lov\u00e1sz, L.: Submodular functions and convexity. Math. Program. State Art: Bonn 1982, 235\u2013257 (1983)","journal-title":"Math. Program. State Art: Bonn"},{"key":"21_CR11","doi-asserted-by":"crossref","unstructured":"Nemhauser, G.L., Wolsey, L.A., Fisher, M.L.: An analysis of approximations for maximizing submodular set functions\u2013I. Math. Program. 14, 265\u2013294 (1978)","DOI":"10.1007\/BF01588971"},{"key":"21_CR12","unstructured":"Nguyen, L., Thai, M.T.: Streaming $$k$$-submodular maximization under noise subject to size constraint. In: Proceedings of the 37th International Conference on Machine Learning (ICML), pp. 7338\u20137347. PMLR (2020)"},{"key":"21_CR13","unstructured":"Ohsaka, N., Yoshida, Y.: Monotone $$k$$-submodular function maximization with size constraints. In: Proceedings of the 28th International Conference on Neural Information Processing Systems (NeurIPS), vol. 1, pp. 694\u2013702 (2015)"},{"issue":"1","key":"21_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1137\/19M1277692","volume":"35","author":"H Oshima","year":"2021","unstructured":"Oshima, H.: Improved randomized algorithm for $$k$$-submodular function maximization. SIAM J. Discret. Math. 35(1), 1\u201322 (2021)","journal-title":"SIAM J. Discret. Math."},{"key":"21_CR15","doi-asserted-by":"crossref","unstructured":"Pham, C.V., Ha, D.K.T., Hoang, H.X., Tran, T.D.: Fast streaming algorithms for $$k$$-submodular maximization under a knapsack constraint. In Proceedings of the IEEE 9th International Conference on Data Science and Advanced Analytics (DSAA), pp. 1\u201310. IEEE (2022)","DOI":"10.1109\/DSAA54385.2022.10032383"},{"key":"21_CR16","doi-asserted-by":"crossref","unstructured":"Pham, C.V., Vu, Q.C., Ha, D.K.T., Nguyen, T.T., Le, N.D.: Maximizing k-submodular functions under budget constraint: applications and streaming algorithms. J. Comb. Optim. 44(1), 723\u2013751 (2022)","DOI":"10.1007\/s10878-022-00858-x"},{"key":"21_CR17","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1016\/j.disopt.2017.01.003","volume":"23","author":"S Sakaue","year":"2017","unstructured":"Sakaue, S.: On maximizing a monotone $$k$$-submodular function subject to a matroid constraint. Discret. Optim. 23, 105\u2013113 (2017)","journal-title":"Discret. Optim."},{"key":"21_CR18","doi-asserted-by":"publisher","unstructured":"Schrijver, A.: Combinatorial optimization: polyhedra and efficiency, volume 24. Springer (2003). https:\/\/doi.org\/10.1007\/s10288-004-0035-9","DOI":"10.1007\/s10288-004-0035-9"},{"key":"21_CR19","unstructured":"Soma, T.: No-regret algorithms for online $$ k $$-submodular maximization. In: Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS), pp. 1205\u20131214. PMLR (2019)"},{"key":"21_CR20","doi-asserted-by":"publisher","unstructured":"Sun, Y., Liu, Y., Li, M.: Maximization of $$k$$-submodular function with a matroid constraint. In: Du, DZ., Du, D., Wu, C., Xu, D. (eds.) Theory and Applications of Models of Computation. TAMC 2022. LNCS, vol. 13571. Springer, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-031-20350-3_1","DOI":"10.1007\/978-3-031-20350-3_1"},{"issue":"1","key":"21_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/3447386","volume":"5","author":"J Tang","year":"2021","unstructured":"Tang, J., Tang, X., Lim, A., Han, K., Li, C., Yuan, J.: Revisiting modified greedy algorithm for monotone submodular maximization with a knapsack constraint. Proc. ACM Measur. Anal. Comput. Syst. 5(1), 1\u201322 (2021)","journal-title":"Proc. ACM Measur. Anal. Comput. Syst."},{"key":"21_CR22","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1016\/j.tcs.2022.04.003","volume":"921","author":"Z Tang","year":"2022","unstructured":"Tang, Z., Wang, C., Chan, H.: Monotone $$k$$-submodular secretary problems: cardinality and knapsack constraints. Theoret. Comput. Sci. 921, 86\u201399 (2022)","journal-title":"Theoret. Comput. Sci."},{"issue":"1","key":"21_CR23","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1016\/j.orl.2021.11.010","volume":"50","author":"Z Tang","year":"2022","unstructured":"Tang, Z., Wang, C., Chan, H.: On maximizing a monotone $$k$$-submodular function under a knapsack constraint. Oper. Res. Lett. 50(1), 28\u201331 (2022)","journal-title":"Oper. Res. Lett."},{"key":"21_CR24","unstructured":"Wang, B., Zhou, H.: Multilinear extension of $$ k $$-submodular functions. arXiv preprint:2107.07103 (2021)"},{"issue":"4","key":"21_CR25","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/2850419","volume":"12","author":"J Ward","year":"2016","unstructured":"Ward, J., \u017divn\u1ef3, S.: Maximizing $$k$$-submodular functions and beyond. ACM Trans. Algorithms 12(4), 1\u201326 (2016)","journal-title":"ACM Trans. Algorithms"},{"key":"21_CR26","doi-asserted-by":"crossref","unstructured":"Xiao, H., Liu, Q., Zhou, Y., Li, M.: Approximation algorithms for $$k$$-submodular maximization subject to a knapsack constraint. arXiv preprint:2306.14520 (2023)","DOI":"10.1007\/s40305-024-00539-y"},{"key":"21_CR27","unstructured":"Yaroslavtsev, G., Zhou, S., Avdiukhin, D.: \u201cbring your own greedy\u201d+ max: near-optimal 1\/2-approximations for submodular knapsack. In: International Conference on Artificial Intelligence and Statistics, pp. 3263\u20133274. PMLR (2020)"},{"key":"21_CR28","doi-asserted-by":"publisher","unstructured":"Yu, K., Li, M., Zhou, Y., Liu, Q.: Guarantees for maximization of $$k$$-submodular functions with a knapsack and a matroid constraint. In: Ni, Q., Wu, W. (eds.) Algorithmic Aspects in Information and Management. AAIM 2022. LNCS, vol. 13513. Springer, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-031-16081-3_14","DOI":"10.1007\/978-3-031-16081-3_14"}],"container-title":["Lecture Notes in Computer Science","Combinatorial Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-49611-0_21","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,5]],"date-time":"2024-11-05T16:51:36Z","timestamp":1730825496000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-49611-0_21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,9]]},"ISBN":["9783031496103","9783031496110"],"references-count":28,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-49611-0_21","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,9]]},"assertion":[{"value":"9 December 2023","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"COCOA","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Combinatorial Optimization and Applications","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Hawai, HI","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"USA","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2023","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"15 December 2023","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17 December 2023","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"16","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"cocoa2023","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/theory.utdallas.edu\/COCOA2023\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Double-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EquinOCS","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"117","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":"73","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":"62% - 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)"}}]}}