{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T02:10:39Z","timestamp":1773281439832,"version":"3.50.1"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,11,20]],"date-time":"2025-11-20T00:00:00Z","timestamp":1763596800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,11,20]],"date-time":"2025-11-20T00:00:00Z","timestamp":1763596800000},"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":["12261019"],"award-info":[{"award-number":["12261019"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Basic Research Program Project of Shaanxi Province","award":["2024JC-YBMS-019"],"award-info":[{"award-number":["2024JC-YBMS-019"]}]},{"name":"Guizhou Provincial Science and Technology Projects","award":["QHKJC-ZK[2022]YB084"],"award-info":[{"award-number":["QHKJC-ZK[2022]YB084"]}]},{"name":"the Project of Science and Technology on Reliability Physics and Application Technology of Electronic Component Laboratory","award":["6142806230302"],"award-info":[{"award-number":["6142806230302"]}]},{"name":"the Science and Technology Development Program of Shaanxi","award":["2023-YBGY-273"],"award-info":[{"award-number":["2023-YBGY-273"]}]},{"name":"the Fundamental Research Funds for the Central Universities and the Innovation Fund of Xidian University","award":["YJSJ25009"],"award-info":[{"award-number":["YJSJ25009"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2026,4]]},"DOI":"10.1007\/s10589-025-00749-x","type":"journal-article","created":{"date-parts":[[2025,11,20]],"date-time":"2025-11-20T09:28:37Z","timestamp":1763630917000},"page":"1069-1105","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multi-objective k-way parallel hypergraph partitioning with proximal gradient algorithm"],"prefix":"10.1007","volume":"93","author":[{"given":"Yingying","family":"Li","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8672-914X","authenticated-orcid":false,"given":"Hongwei","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Hailong","family":"You","sequence":"additional","affiliation":[]},{"given":"Zexian","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Fang","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,11,20]]},"reference":[{"key":"749_CR1","doi-asserted-by":"crossref","unstructured":"Caldwell, A.E., Kahang, A.B., Kennings, A.A., Markov, I.L.: Hypergraph partitioning for vlsi cad: methodology for heuristic development, experimentation and reporting. In: Proceedings 1999 Design Automation Conference (Cat. No. 99CH36361), pp. 349\u2013354 (1999)","DOI":"10.1109\/DAC.1999.781340"},{"issue":"4","key":"749_CR2","doi-asserted-by":"publisher","first-page":"1154","DOI":"10.1109\/TPDS.2014.2318697","volume":"26","author":"G Qu","year":"2015","unstructured":"Qu, G., Fang, Z., Zhang, J., Zheng, S.-Q.: Switch-centric data center network structures based on hypergraphs and combinatorial block designs. IEEE Trans. Parallel Distrib. Syst. 26(4), 1154\u20131164 (2015)","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"issue":"11","key":"749_CR3","doi-asserted-by":"publisher","first-page":"1418","DOI":"10.14778\/3137628.3137650","volume":"10","author":"I Kabiljo","year":"2017","unstructured":"Kabiljo, I., Karrer, B., Pundir, M., Pupyrev, S., Shalita, A.: Social hash partitioner: a scalable distributed hypergraph partitioner. Proc. VLDB Endowment 10(11), 1418\u20131429 (2017)","journal-title":"Proc. VLDB Endowment"},{"issue":"7","key":"749_CR4","doi-asserted-by":"publisher","first-page":"1857","DOI":"10.1109\/TC.2014.2345409","volume":"64","author":"F Xia","year":"2015","unstructured":"Xia, F., Ahmed, A.M., Yang, L.T., Luo, Z.: Community-based event dissemination with optimal load balancing. IEEE Trans. Comput. 64(7), 1857\u20131869 (2015)","journal-title":"IEEE Trans. Comput."},{"issue":"2","key":"749_CR5","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1002\/j.1538-7305.1970.tb01770.x","volume":"49","author":"BW Kernighan","year":"1970","unstructured":"Kernighan, B.W., Lin, S.: An efficient heuristic procedure for partitioning graphs. Bell Syst. Tech. J. 49(2), 291\u2013307 (1970)","journal-title":"Bell Syst. Tech. J."},{"key":"749_CR6","doi-asserted-by":"crossref","unstructured":"Fiduccia, C.M., Mattheyses, R.M.: A linear-time heuristic for improving network partitions. In: 19th Design Automation Conference, pp. 175\u2013181 (1982)","DOI":"10.1109\/DAC.1982.1585498"},{"issue":"2","key":"749_CR7","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1109\/43.573831","volume":"16","author":"A Dasdan","year":"1997","unstructured":"Dasdan, A., Aykanat, C.: Two novel multiway circuit partitioning algorithms using relaxed locking. IEEE Trans. Comput. Aided Des. Integr. Circ. Syst. 16(2), 169\u2013178 (1997)","journal-title":"IEEE Trans. Comput. Aided Des. Integr. Circ. Syst."},{"key":"749_CR8","doi-asserted-by":"crossref","unstructured":"Eem, C., CHong, J.: An efficient iterative improvement technique for vlsi circuit partitioning using hybrid bucket structures. In: Proceedings of the ASP-DAC\u201999 Asia and South Pacific Design Automation Conference 1999 (Cat. No. 99EX198), pp. 73\u201376 (1999)","DOI":"10.1109\/ASPDAC.1999.759713"},{"issue":"1","key":"749_CR9","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1145\/504914.504918","volume":"7","author":"S Dutt","year":"2002","unstructured":"Dutt, S., Deng, W.: Cluster-aware iterative improvement techniques for partitioning large vlsi circuits. ACM Trans. Design Autom. Electron. Syst. 7(1), 91\u2013121 (2002)","journal-title":"ACM Trans. Design Autom. Electron. Syst."},{"issue":"1","key":"749_CR10","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1109\/12.8730","volume":"38","author":"LA Sanchis","year":"1989","unstructured":"Sanchis, L.A.: Multiple-way network partitioning. IEEE Trans. Comput. 38(1), 62\u201381 (1989)","journal-title":"IEEE Trans. Comput."},{"key":"749_CR11","doi-asserted-by":"crossref","unstructured":"Tang, J., Bi, S., Wu, H., You, H.: Tbpart: An effective topological order balanced hypergraph partitioning algorithm for vlsi processor-based hardware emulation. In: 2024 2nd International Symposium of Electronics Design Automation, pp. 300\u2013305 (2024)","DOI":"10.1109\/ISEDA62518.2024.10618032"},{"issue":"1","key":"749_CR12","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1109\/92.748202","volume":"7","author":"G Karypis","year":"1999","unstructured":"Karypis, G., Aggarwal, R., Kumar, V., Shekhar, S.: Multilevel hypergraph partitioning: applications in vlsi domain. IEEE Trans. Very Large Scale Integration (VLSI) Syst. 7(1), 69\u201379 (1999)","journal-title":"IEEE Trans. Very Large Scale Integration (VLSI) Syst."},{"key":"749_CR13","doi-asserted-by":"crossref","unstructured":"Karypis, G., Kumar, V.: Multilevel k-way hypergraph partitioning. In: Proceedings of the 36th Annual ACM\/IEEE Design Automation Conference, pp. 343\u2013348 (1999)","DOI":"10.1145\/309847.309954"},{"key":"749_CR14","unstructured":"\u00c7ataly\u00fcrek, \u00dc.V., Aykanat, C.: Patoh (partitioning tool for hypergraphs). In: Encyclopedia of Parallel Computing (2011)"},{"key":"749_CR15","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1090\/conm\/588\/11704","volume":"588","author":"UV \u00c7atalyiirek","year":"2013","unstructured":"\u00c7atalyiirek, U.V., Deveci, M., Kaya, K., U\u00e7ar, B.: Umpa: A multi-objective multi-level partitioner for communication minimization umit v. catalyiirek mehmet deveci kamer kaya and bora ucar. Graph Partition. Graph Clust. 588, 53 (2013)","journal-title":"Graph Partition. Graph Clust."},{"key":"749_CR16","doi-asserted-by":"crossref","unstructured":"Akhremtsev, Y., Heuer, T., Sanders, P., Schlag, S.: Engineering a direct k-way hypergraph partitioning algorithm. In: 2017 Proceedings of the Ninteenth Workshop on Algorithm Engineering and Experiments, pp. 28\u201342 (2017)","DOI":"10.1137\/1.9781611974768.3"},{"key":"749_CR17","unstructured":"Gottesb\u00fcren, L., Hamann, M., Schlag, S., Wagner, D.: Advanced Flow-Based Multilevel Hypergraph Partitioning. In: 18th International Symposium on Experimental Algorithms. Leibniz International Proceedings in Informatics, vol. 160, pp. 1\u201315 (2020)"},{"key":"749_CR18","unstructured":"Gottesb\u00fcren, L., Heuer, T., Sanders, P.: Parallel flow-based hypergraph partitioning. In: 20th International Symposium on Experimental Algorithms. Leibniz International Proceedings in Informatics, vol. 233, pp. 1\u201321 (2022)"},{"key":"749_CR19","first-page":"1","volume":"27","author":"S Schlag","year":"2023","unstructured":"Schlag, S., Heuer, T., Gottesb\u00fcren, L., Akhremtsev, Y., Schulz, C., Sanders, P.: High-quality hypergraph partitioning. ACM J. Exp. Algorithm. 27, 1\u201339 (2023)","journal-title":"ACM J. Exp. Algorithm."},{"issue":"5","key":"749_CR20","doi-asserted-by":"publisher","first-page":"420","DOI":"10.1147\/rd.175.0420","volume":"17","author":"WE Donath","year":"1973","unstructured":"Donath, W.E., Hoffman, A.J.: Lower bounds for the partitioning of graphs. IBM J. Res. Dev. 17(5), 420\u2013425 (1973)","journal-title":"IBM J. Res. Dev."},{"key":"749_CR21","doi-asserted-by":"publisher","first-page":"298","DOI":"10.21136\/CMJ.1973.101168","volume":"23","author":"M Fiedler","year":"1973","unstructured":"Fiedler, M.: Algebraic connectivity of graphs. Czechoslov. Math. J. 23, 298\u2013305 (1973)","journal-title":"Czechoslov. Math. J."},{"key":"749_CR22","unstructured":"Naumov, M., Moon, T.: Parallel spectral graph partitioning. Technical Report NVR-2016-001, NVIDIA (March 2016)"},{"issue":"4","key":"749_CR23","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1007\/s11222-007-9033-z","volume":"17","author":"U Luxburg","year":"2007","unstructured":"Luxburg, U.: A tutorial on spectral clustering. Stat. Comput. 17(4), 395\u2013416 (2007)","journal-title":"Stat. Comput."},{"key":"749_CR24","doi-asserted-by":"crossref","unstructured":"Rota\u00a0Bul\u00f2, S., Pelillo, M.: New Bounds on the Clique Number of Graphs Based on Spectral Hypergraph Theory, pp. 45\u201358. Springer, Berlin, Heidelberg (2009)","DOI":"10.1007\/978-3-642-11169-3_4"},{"key":"749_CR25","doi-asserted-by":"publisher","first-page":"A2508","DOI":"10.1137\/16M1094828","volume":"39","author":"Y Chen","year":"2017","unstructured":"Chen, Y., Qi, L., Zhang, X.: The fiedler vector of a Laplacian tensor for hypergraph partitioning. SIAM J. Sci. Comput. 39, A2508 (2017)","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"749_CR26","doi-asserted-by":"publisher","first-page":"897","DOI":"10.1007\/s11075-023-01593-y","volume":"95","author":"X Zhang","year":"2023","unstructured":"Zhang, X., Chang, J., Ge, Z., Sheng, Z.: A family of gradient methods using householder transformation with application to hypergraph partitioning. Numer. Algorithms 95(2), 897\u2013927 (2023)","journal-title":"Numer. Algorithms"},{"issue":"2","key":"749_CR27","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1007\/s10107-014-0817-6","volume":"151","author":"ER Dam","year":"2015","unstructured":"Dam, E.R., Sotirov, R.: Semidefinite programming and eigenvalue bounds for the graph partition problem. Math. Program. 151(2), 379\u2013404 (2015)","journal-title":"Math. Program."},{"key":"749_CR28","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1007\/s12532-012-0040-5","volume":"4","author":"M Armbruster","year":"2012","unstructured":"Armbruster, M., F\u00fcgenschuh, M., Helmberg, C., Martin, A.: Lp and sdp branch-and-cut algorithms for the minimum graph bisection problem: a computational comparison. Math. Program. Comput. 4, 275\u2013306 (2012)","journal-title":"Math. Program. Comput."},{"issue":"1","key":"749_CR29","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1007\/s10589-022-00355-1","volume":"82","author":"A Wiegele","year":"2022","unstructured":"Wiegele, A., Zhao, S.: Sdp-based bounds for graph partition via extended admm. Comput. Optim. Appl. 82(1), 251\u2013291 (2022)","journal-title":"Comput. Optim. Appl."},{"issue":"9","key":"749_CR30","doi-asserted-by":"publisher","first-page":"2987","DOI":"10.1080\/02331934.2023.2234925","volume":"73","author":"Z Liu","year":"2024","unstructured":"Liu, Z., Liu, H., Wang, T.: New gradient methods with adaptive stepsizes by approximate models. Optimization 73(9), 2987\u20133014 (2024)","journal-title":"Optimization"},{"issue":"1","key":"749_CR31","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1007\/s10589-019-00143-4","volume":"75","author":"Z Liu","year":"2020","unstructured":"Liu, Z., Liu, H., Dai, Y.: An improved dai-kou conjugate gradient algorithm for unconstrained optimization. Comput. Optim. Appl. 75(1), 145\u2013167 (2020)","journal-title":"Comput. Optim. Appl."},{"issue":"3","key":"749_CR32","doi-asserted-by":"publisher","first-page":"811","DOI":"10.1007\/s10957-021-01897-w","volume":"190","author":"W Sun","year":"2021","unstructured":"Sun, W., Liu, H., Liu, Z.: A class of accelerated subspace minimization conjugate gradient methods. J. Optim. Theory Appl. 190(3), 811\u2013840 (2021)","journal-title":"J. Optim. Theory Appl."},{"key":"749_CR33","doi-asserted-by":"publisher","first-page":"863","DOI":"10.1007\/s10898-024-01366-4","volume":"89","author":"H Liu","year":"2024","unstructured":"Liu, H., Wang, T., Liu, Z.: A nonmonotone accelerated proximal gradient method with variable stepsize strategy for nonsmooth and nonconvex minimization problems. J. Global Optim. 89, 863\u2013897 (2024)","journal-title":"J. Global Optim."},{"issue":"1","key":"749_CR34","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1007\/s11075-023-01569-y","volume":"95","author":"T Wang","year":"2024","unstructured":"Wang, T., Liu, H.: A class of modified accelerated proximal gradient methods for nonsmooth and nonconvex minimization problems. Numer. Algorithms 95(1), 207\u2013241 (2024)","journal-title":"Numer. Algorithms"},{"issue":"2","key":"749_CR35","doi-asserted-by":"publisher","first-page":"438","DOI":"10.1287\/moor.1100.0449","volume":"35","author":"H Attouch","year":"2010","unstructured":"Attouch, H., Bolte, J., Redont, P., Soubeyran, A.: Proximal alternating minimization and projection methods for nonconvex problems: An approach based on the kurdyka-\u0142ojasiewicz inequality. Math. Oper. Res. 35(2), 438\u2013457 (2010)","journal-title":"Math. Oper. Res."},{"issue":"7","key":"749_CR36","doi-asserted-by":"publisher","first-page":"673","DOI":"10.1109\/71.780863","volume":"10","author":"UV Catalyurek","year":"1999","unstructured":"Catalyurek, U.V., Aykanat, C.: Hypergraph-partitioning-based decomposition for parallel sparse-matrix vector multiplication. IEEE Trans. Parallel Distrib. Syst. 10(7), 673\u2013693 (1999)","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"749_CR37","doi-asserted-by":"publisher","first-page":"449","DOI":"10.4153\/CJM-1965-045-4","volume":"17","author":"J Edmonds","year":"1965","unstructured":"Edmonds, J.: Paths, trees, and flowers. Can. J. Math. 17, 449\u2013467 (1965)","journal-title":"Can. J. Math."},{"key":"749_CR38","doi-asserted-by":"crossref","unstructured":"Alpert, C.J.: The ispd98 circuit benchmark suite. In: Proceedings of the 1998 International Symposium on Physical Design, pp. 80\u201385 (1998)","DOI":"10.1145\/274535.274546"},{"key":"749_CR39","doi-asserted-by":"crossref","unstructured":"Murray, K.E., Whitty, S., Liu, S., Luu, J., Betz, V.: Titan: Enabling large and complex benchmarks in academic cad. In: 2013 23rd International Conference on Field Programmable Logic and Applications, pp. 1\u20138 (2013)","DOI":"10.1109\/FPL.2013.6645503"},{"key":"749_CR40","doi-asserted-by":"crossref","unstructured":"Gottesb\u00fcren, L., Heuer, T., Sanders, P., Schlag, S.: Scalable shared-memory hypergraph partitioning. In: 2021 Proceedings of the Symposium on Algorithm Engineering and Experiments, pp. 16\u201330 (2021)","DOI":"10.1137\/1.9781611976472.2"},{"key":"749_CR41","unstructured":"Gottesb\u00fcren, L., Heuer, T., Sanders, P.: Parallel flow-based hypergraph partitioning. In: 20th International Symposium on Experimental Algorithms. Leibniz International Proceedings in Informatics, vol. 233, pp. 1\u201321. Schloss Dagstuhl-Leibniz-Zentrum f\u00fcr Informatik, Dagstuhl, Germany (2022)"},{"issue":"2","key":"749_CR42","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/s101070100263","volume":"91","author":"ED Dolan","year":"2002","unstructured":"Dolan, E.D., Mor\u00e9, J.J.: Benchmarking optimization software with performance profiles. Math. Program. 91(2), 201\u2013213 (2002)","journal-title":"Math. Program."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-025-00749-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10589-025-00749-x","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-025-00749-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T11:17:49Z","timestamp":1773227869000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10589-025-00749-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,20]]},"references-count":42,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2026,4]]}},"alternative-id":["749"],"URL":"https:\/\/doi.org\/10.1007\/s10589-025-00749-x","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,20]]},"assertion":[{"value":"24 December 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 November 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 November 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}