{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T20:09:06Z","timestamp":1757621346071,"version":"3.44.0"},"publisher-location":"Singapore","reference-count":27,"publisher":"Springer Nature Singapore","isbn-type":[{"type":"print","value":"9789819502172"},{"type":"electronic","value":"9789819502189"}],"license":[{"start":{"date-parts":[[2025,8,3]],"date-time":"2025-08-03T00:00:00Z","timestamp":1754179200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,8,3]],"date-time":"2025-08-03T00:00:00Z","timestamp":1754179200000},"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":[[2026]]},"DOI":"10.1007\/978-981-95-0218-9_5","type":"book-chapter","created":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T21:09:13Z","timestamp":1754168953000},"page":"53-67","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Sum-of-Max Chain Partition of\u00a0a\u00a0Tree"],"prefix":"10.1007","author":[{"given":"Ruixi","family":"Luo","sequence":"first","affiliation":[]},{"given":"Taikun","family":"Zhu","sequence":"additional","affiliation":[]},{"given":"Kai","family":"Jin","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,8,3]]},"reference":[{"key":"5_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/3-540-63307-3_47","volume-title":"Algorithms and Data Structures","author":"S Alstrup","year":"1997","unstructured":"Alstrup, S., Lauridsen, P.W., Sommerlund, P., Thorup, M.: Finding cores of limited length. In: Dehne, F., Rau-Chaplin, A., Sack, J.-R., Tamassia, R. (eds.) WADS 1997. LNCS, vol. 1272, pp. 45\u201354. Springer, Heidelberg (1997). https:\/\/doi.org\/10.1007\/3-540-63307-3_47"},{"key":"5_CR2","doi-asserted-by":"crossref","unstructured":"Bagheri, A., Keshavarz-Kohjerdi, F., Razzazi, M.: A linear-time approximation algorithm for the minimum-length geometric embedding of trees. Optimization 1\u201316 (2024)","DOI":"10.1080\/02331934.2024.2335946"},{"key":"5_CR3","unstructured":"Bagheri, A., Razzazi, M.: Minimum height path partitioning of trees. Sci. Iranica 17(2) (2010)"},{"issue":"1","key":"5_CR4","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1016\/j.tcs.2003.05.002","volume":"321","author":"M Bender","year":"2004","unstructured":"Bender, M., Farach-Colton, M.: The level ancestor problem simplified. Theoret. Comput. Sci. 321(1), 5\u201312 (2004)","journal-title":"Theoret. Comput. Sci."},{"key":"5_CR5","doi-asserted-by":"crossref","unstructured":"Boesch, F., Chen, S., McHugh, J.: On covering the points of a graph with point disjoint paths. In: Graphs and Combinatorics: Proceedings of the Capital Conference on Graph Theory and Combinatorics at the George Washington University June 18\u201322, 1973, pp. 201\u2013212. Springer (1974)","DOI":"10.1007\/BFb0066442"},{"key":"5_CR6","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1016\/j.dam.2017.01.013","volume":"223","author":"C Brause","year":"2017","unstructured":"Brause, C., Krivo\u0161-Bellu\u0161, R.: On a relation between $$k$$-path partition and $$k$$-path vertex cover. Discret. Appl. Math. 223, 28\u201338 (2017)","journal-title":"Discret. Appl. Math."},{"key":"5_CR7","unstructured":"Buchsbaum, A., Westbrook, J.: Maintaining hierarchical graph views. In: Proceedings of the Eleventh Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 566\u2013575 (2000)"},{"key":"5_CR8","unstructured":"Cai, Y., Zhang, X., Qian, J., Sun, Y.: An $$O(n)$$ Algorithm for $$\\omega $$-Path Partition of Edge-Weighted Forests. Ph.D. thesis (2003)"},{"issue":"1","key":"5_CR9","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1007\/s10878-018-00372-z","volume":"38","author":"Y Chen","year":"2019","unstructured":"Chen, Y., Goebel, R., Lin, G., Su, B., Xu, Y., Zhang, A.: An improved approximation algorithm for the minimum 3-path partition problem. J. Comb. Optim. 38(1), 150\u2013164 (2019). https:\/\/doi.org\/10.1007\/s10878-018-00372-z","journal-title":"J. Comb. Optim."},{"key":"5_CR10","doi-asserted-by":"crossref","unstructured":"Goodman, S., Hedetniemi, S.: On the Hamiltonian completion problem. In: Graphs and Combinatorics: Proceedings of the Capital Conference on Graph Theory and Combinatorics at the George Washington University June 18\u201322, 1973, pp. 262\u2013272. Springer (1974)","DOI":"10.1007\/BFb0066448"},{"issue":"2","key":"5_CR11","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1137\/0213024","volume":"13","author":"D Harel","year":"1984","unstructured":"Harel, D., Tarjan, R.: Fast algorithms for finding nearest common ancestors. SIAM J. Comput. 13(2), 338\u2013355 (1984)","journal-title":"SIAM J. Comput."},{"key":"5_CR12","doi-asserted-by":"crossref","unstructured":"Hartmanis, J.: Computers and intractability: a guide to the theory of NP-completeness (Michael R. Garey and David S. Johnson). SIAM Rev. 24(1), 90 (1982)","DOI":"10.1137\/1024022"},{"key":"5_CR13","doi-asserted-by":"publisher","DOI":"10.1016\/j.compeleceng.2022.108521","volume":"105","author":"K Jin","year":"2023","unstructured":"Jin, K., Zhang, D., Zhang, C.: Sum-of-max partition under a knapsack constraint. Comput. Electr. Eng. 105, 108521 (2023)","journal-title":"Comput. Electr. Eng."},{"issue":"1","key":"5_CR14","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1007\/s11766-008-0117-0","volume":"23","author":"Z Jin","year":"2008","unstructured":"Jin, Z., Li, X.: Vertex partitions of $$r$$-edge-colored graphs. Appl. Math.-A J. Chin. Univ. 23(1), 120\u2013126 (2008)","journal-title":"Appl. Math.-A J. Chin. Univ."},{"key":"5_CR15","doi-asserted-by":"crossref","unstructured":"Klein, P.: Computing the edit-distance between unrooted ordered trees. In: European Symposium on Algorithms, pp. 91\u2013102. Springer (1998)","DOI":"10.1007\/3-540-68530-8_8"},{"key":"5_CR16","unstructured":"Li, S., Yu, W., Liu, Z.: Improved approximation algorithms for the $$k$$-path partition problem. J. Global Optim. pp. 1\u201324 (2024)"},{"issue":"13\u201314","key":"5_CR17","doi-asserted-by":"publisher","first-page":"2062","DOI":"10.1016\/j.dam.2013.02.020","volume":"161","author":"C Lu","year":"2013","unstructured":"Lu, C., Zhou, Q.: Path covering number and $$l(2,1)$$-labeling number of graphs. Discret. Appl. Math. 161(13\u201314), 2062\u20132074 (2013)","journal-title":"Discret. Appl. Math."},{"key":"5_CR18","doi-asserted-by":"crossref","unstructured":"Luo, R., Zhu, T., Jin, K.: Sum-of-max chain partition of a tree (2025). https:\/\/arxiv.org\/abs\/2503.11526","DOI":"10.1007\/978-981-95-0218-9_5"},{"key":"5_CR19","unstructured":"Manuel, P.: Revisiting path-type covering and partitioning problems. arXiv preprint arXiv:1807.10613 (2018)"},{"key":"5_CR20","doi-asserted-by":"publisher","DOI":"10.1201\/9781420035179","volume-title":"Handbook of Data Structures and Applications","author":"D Mehta","year":"2004","unstructured":"Mehta, D., Sahni, S.: Handbook of Data Structures and Applications. Chapman and Hall\/CRC, New York (2004)"},{"issue":"1","key":"5_CR21","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1016\/0020-0190(75)90057-5","volume":"4","author":"J Misra","year":"1975","unstructured":"Misra, J., Tarjan, R.: Optimal chain partitions of trees. Inf. Process. Lett. 4(1), 24\u201326 (1975)","journal-title":"Inf. Process. Lett."},{"issue":"5","key":"5_CR22","doi-asserted-by":"publisher","first-page":"677","DOI":"10.1016\/j.orl.2006.12.004","volume":"35","author":"J Monnot","year":"2007","unstructured":"Monnot, J., Toulouse, S.: The path partition problem and related problems in bipartite graphs. Oper. Res. Lett. 35(5), 677\u2013684 (2007)","journal-title":"Oper. Res. Lett."},{"issue":"8","key":"5_CR23","doi-asserted-by":"publisher","first-page":"974","DOI":"10.1016\/j.jpdc.2004.05.003","volume":"64","author":"A P\u0131nar","year":"2004","unstructured":"P\u0131nar, A., Aykanat, C.: Fast optimal load balancing algorithms for 1D partitioning. J. Parallel Distrib. Comput. 64(8), 974\u2013996 (2004)","journal-title":"J. Parallel Distrib. Comput."},{"issue":"1","key":"5_CR24","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/0012-365X(79)90153-5","volume":"25","author":"P Slater","year":"1979","unstructured":"Slater, P.: Path coverings of the vertices of a tree. Discret. Math. 25(1), 65\u201374 (1979)","journal-title":"Discret. Math."},{"key":"5_CR25","doi-asserted-by":"crossref","unstructured":"Sleator, D., Tarjan, R.: A data structure for dynamic trees. In: Proceedings of the Thirteenth Annual ACM Symposium on Theory of Computing, pp. 114\u2013122 (1981)","DOI":"10.1145\/800076.802464"},{"issue":"4","key":"5_CR26","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1145\/359460.359478","volume":"21","author":"J Vuillemin","year":"1978","unstructured":"Vuillemin, J.: A data structure for manipulating priority queues. Commun. ACM 21(4), 309\u2013315 (1978)","journal-title":"Commun. ACM"},{"issue":"1\u20133","key":"5_CR27","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1016\/S0166-218X(97)00012-7","volume":"78","author":"J Yan","year":"1997","unstructured":"Yan, J., Chang, G., Hedetniemi, S., Hedetniemi, S.: $$k$$-path partitions in trees. Discret. Appl. Math. 78(1\u20133), 227\u2013233 (1997)","journal-title":"Discret. Appl. Math."}],"container-title":["Lecture Notes in Computer Science","Computing and Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-981-95-0218-9_5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T12:46:49Z","timestamp":1757335609000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-981-95-0218-9_5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,3]]},"ISBN":["9789819502172","9789819502189"],"references-count":27,"URL":"https:\/\/doi.org\/10.1007\/978-981-95-0218-9_5","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2025,8,3]]},"assertion":[{"value":"3 August 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"COCOON","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Computing and Combinatorics Conference","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Chengdu","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":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"15 August 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17 August 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"31","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"cocoon0","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/tcsuestc.com\/cocoon2025\/index.html","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}