{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,27]],"date-time":"2025-12-27T07:31:08Z","timestamp":1766820668755,"version":"3.41.0"},"reference-count":55,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2025,5,28]],"date-time":"2025-05-28T00:00:00Z","timestamp":1748390400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,5,28]],"date-time":"2025-05-28T00:00:00Z","timestamp":1748390400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Supercomput"],"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Many computing workloads in big data and machine learning applications are structured as directed acyclic graphs (DAG) and deployed on PC clusters for parallel execution using multiple physical or virtual machines. The scheduling of such workloads is critical to the application performance such as execution time and a plethora of techniques have been developed, taking into account various aspects such as data locality, network bandwidth, and server capability. We formulate DAG-structured workload scheduling as a nonlinear integer programming (NIP) problem and prove it to be NP-complete. Our empirical study reveals a positive correlation between scheduling plan distance (<jats:italic>SPD<\/jats:italic>) and finish time gap (<jats:italic>FTG<\/jats:italic>), and based on this finding, we propose a running time gap strategy (RTGS) to tackle this scheduling problem in multiprocessor environments. RTGS follows the main optimization strategy in the family of whale optimization algorithm (WOA). We derive a new function and use a greedy algorithm to generate an effective scheduling plan in RTGS. Extensive experiments with real production traces from Alibaba on simulation environments and realistic Hadoop environments show that our approach significantly improves the stability of WOA when applied to the scheduling problem of DAG-structured workloads, and also reduces the workload completion time by up to <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$93\\%$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mn>93<\/mml:mn>\n                    <mml:mo>%<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> in comparison with seven state-of-the-art baseline algorithms.<\/jats:p>","DOI":"10.1007\/s11227-025-07415-3","type":"journal-article","created":{"date-parts":[[2025,5,28]],"date-time":"2025-05-28T13:50:54Z","timestamp":1748440254000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Scheduling DAG-structured workloads based on whale optimization algorithm"],"prefix":"10.1007","volume":"81","author":[{"given":"Nana","family":"Du","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yudong","family":"Ji","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chase","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aiqin","family":"Hou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weike","family":"Nie","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,5,28]]},"reference":[{"key":"7415_CR1","doi-asserted-by":"crossref","unstructured":"Garefalakis P, Karanasos K, Pietzuch P, Suresh A, Rao S (2018) Medea: scheduling of long running applications in shared production clusters. In: Proceedings of the Thirteenth EuroSys Conference, pp 1\u201313","DOI":"10.1145\/3190508.3190549"},{"key":"7415_CR2","doi-asserted-by":"crossref","unstructured":"Vavilapalli VK, Murthy AC, Douglas C, Agarwal S, Konar M, Evans R, Graves T, Lowe J, Shah H, Seth S et al (2013) Apache hadoop yarn: yet another resource negotiator. In: Proceedings of the 4th Annual Symposium on Cloud Computing, pp 1\u201316","DOI":"10.1145\/2523616.2523633"},{"key":"7415_CR3","unstructured":"Google CNCF (2017) What is kubernetes, Website. https:\/\/kubernetes.io\/docs\/concepts\/overview\/what-is-kubernetes\/"},{"key":"7415_CR4","unstructured":"Hindman B, Konwinski A, Zaharia M, Ghodsi A, Joseph AD, Katz R, Shenker S, Stoica I (2011) Mesos: a platform for fine-grained resource sharing in the data center. In: 8th USENIX Symposium on Networked Systems Design and Implementation (NSDI 11)"},{"key":"7415_CR5","doi-asserted-by":"crossref","unstructured":"Sun P, Guo Z, Wang J, Li J, Lan J, Hu Y (2021) Deepweave: accelerating job completion time with deep reinforcement learning-based coflow scheduling. In: Proceedings of the Twenty-Ninth International Conference on International Joint Conferences on Artificial Intelligence (IJCAI 29), pp 3314\u20133320","DOI":"10.24963\/ijcai.2020\/458"},{"key":"7415_CR6","doi-asserted-by":"crossref","unstructured":"Mao H, Schwarzkopf M, Venkatakrishnan SB, Meng Z, Alizadeh M (2019) Learning scheduling algorithms for data processing clusters. In: Proceedings of the ACM Special Interest Group on Data Communication (SIGCOMM 2019), pp 270\u2013288","DOI":"10.1145\/3341302.3342080"},{"key":"7415_CR7","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/j.advengsoft.2016.01.008","volume":"95","author":"S Mirjalili","year":"2016","unstructured":"Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51\u201367","journal-title":"Adv Eng Softw"},{"key":"7415_CR8","doi-asserted-by":"crossref","unstructured":"Shivahare BD, Singh M, Gupta A, Ranjan S, Pareta D, Sahu BM (2021) Survey paper: whale optimization algorithm and its variant applications. In: 2021 International Conference on Innovative Practices in Technology and Management (ICIPTM), IEEE, pp 77\u201382","DOI":"10.1109\/ICIPTM52218.2021.9388344"},{"issue":"1","key":"7415_CR9","first-page":"8718571","volume":"2019","author":"HM Mohammed","year":"2019","unstructured":"Mohammed HM, Umar SU, Rashid TA (2019) A systematic and meta-analysis survey of whale optimization algorithm. Comput Intell Neurosci 2019(1):8718571","journal-title":"Comput Intell Neurosci"},{"key":"7415_CR10","unstructured":"Banerjee S, Jha S, Kalbarczyk Z, Iyer R (2020) Inductive-bias-driven reinforcement learning for efficient schedules in heterogeneous clusters. In: International Conference on Machine Learning, pp 629\u2013641"},{"key":"7415_CR11","first-page":"9000","volume":"35","author":"SS Mondal","year":"2021","unstructured":"Mondal SS, Sheoran N, Mitra S (2021) Scheduling of time-varying workloads using reinforcement learning. Proc AAAI Conf Artif Intell 35:9000\u20139008","journal-title":"Proc AAAI Conf Artif Intell"},{"key":"7415_CR12","doi-asserted-by":"crossref","unstructured":"Marcus R, Papaemmanouil O (2016) Wisedb: a learning-based workload management advisor for cloud databases, arXiv preprint arXiv:1601.08221","DOI":"10.14778\/2977797.2977804"},{"key":"7415_CR13","doi-asserted-by":"crossref","unstructured":"Chen Y, Brock B, Porumbescu S, Bulu\u00e7 A, Yelick K, Owens JD (2022) Scalable irregular parallelism with GPUs: getting CPUs out of the way. In: SC22: International Conference for High Performance Computing, Networking, Storage and Analysis. IEEE, pp 1\u201316","DOI":"10.1109\/SC41404.2022.00055"},{"issue":"8","key":"7415_CR14","doi-asserted-by":"publisher","first-page":"1341","DOI":"10.1109\/TC.2017.2669964","volume":"66","author":"D Cheng","year":"2017","unstructured":"Cheng D, Zhou X, Lama P, Wu J, Jiang C (2017) Cross-platform resource scheduling for spark and MapReduce on yarn. IEEE Trans Comput 66(8):1341\u20131353","journal-title":"IEEE Trans Comput"},{"key":"7415_CR15","doi-asserted-by":"crossref","unstructured":"Yoo D, Sim KM (2011) A comparative review of job scheduling for MapReduce. In: 2011 IEEE International Conference on Cloud Computing and Intelligence Systems. IEEE, pp 353\u2013358","DOI":"10.1109\/CCIS.2011.6045089"},{"key":"7415_CR16","doi-asserted-by":"crossref","unstructured":"Patil A, Bagban T, Pande A (2015) Recent job scheduling algorithms in hadoop cluster environments: a survey. Int J Adv Res Comput Commun Eng 4(2)","DOI":"10.17148\/IJARCCE.2015.4226"},{"key":"7415_CR17","volume-title":"Operating systems: three easy pieces","author":"RH Arpaci-Dusseau","year":"2018","unstructured":"Arpaci-Dusseau RH, Arpaci-Dusseau AC (2018) Operating systems: three easy pieces. Arpaci-Dusseau Books, LLC"},{"key":"7415_CR18","unstructured":"Alibaba web services. https:\/\/www.alibaba.com\/"},{"key":"7415_CR19","unstructured":"Google cloud platform. https:\/\/cloud.google.com\/"},{"key":"7415_CR20","doi-asserted-by":"crossref","unstructured":"Du J, Wei J, Jiang J, Cheng S, Huang D, Chen Z, Lu Y (2024) Liger: interleaving intra-and inter-operator parallelism for distributed large model inference. In: Proceedings of the 29th ACM SIGPLAN Annual Symposium on Principles and Practice of Parallel Programming, pp 42\u201354","DOI":"10.1145\/3627535.3638466"},{"key":"7415_CR21","doi-asserted-by":"crossref","unstructured":"Wang C, Sun D, Bai Y (2023) Pipad: pipelined and parallel dynamic GNN training on GPUs. In: Proceedings of the 28th ACM SIGPLAN Annual Symposium on Principles and Practice of Parallel Programming, pp 405\u2013418","DOI":"10.1145\/3572848.3577487"},{"key":"7415_CR22","doi-asserted-by":"crossref","unstructured":"Osama M, Porumbescu SD, Owens JD (2023) A programming model for GPU load balancing. In: Proceedings of the 28th ACM SIGPLAN Annual Symposium on Principles and Practice of Parallel Programming, pp 79\u201391","DOI":"10.1145\/3572848.3577434"},{"key":"7415_CR23","doi-asserted-by":"crossref","unstructured":"Stec R, Novak A, Sucha P, Hanzalek Z (2019) Scheduling jobs with stochastic processing time on parallel identical machines. In: IJCAI, pp 5628\u20135634","DOI":"10.24963\/ijcai.2019\/781"},{"key":"7415_CR24","doi-asserted-by":"crossref","unstructured":"Angelopoulos S, Jin S (2019) Earliest-completion scheduling of contract algorithms with end guarantees. In: IJCAI, pp 5493\u20135499","DOI":"10.24963\/ijcai.2019\/763"},{"key":"7415_CR25","doi-asserted-by":"crossref","unstructured":"Dong H, Wang B, Qiao B, Xing W, Luo C, Qin S, Lin Q, Zhang D, Virdi G, Moscibroda T (2021) Predictive job scheduling under uncertain constraints in cloud computing. In: IJCAI, pp 3627\u20133634","DOI":"10.24963\/ijcai.2021\/499"},{"issue":"13","key":"7415_CR26","doi-asserted-by":"publisher","first-page":"24334","DOI":"10.1109\/JIOT.2024.3391024","volume":"11","author":"A Ali","year":"2024","unstructured":"Ali A, Shah SAA, Al Shloul T, Assam M, Ghadi YY, Lim S, Zia A (2024) Multiobjective Harris Hawks optimization-based task scheduling in cloud-fog computing. IEEE Internet Things J 11(13):24334\u201324352","journal-title":"IEEE Internet Things J"},{"issue":"24","key":"7415_CR27","doi-asserted-by":"publisher","first-page":"18035","DOI":"10.1007\/s00521-023-08682-y","volume":"35","author":"M Mollajafari","year":"2023","unstructured":"Mollajafari M (2023) An efficient lightweight algorithm for scheduling tasks onto dynamically reconfigurable hardware using graph-oriented simulated annealing. Neural Comput Appl 35(24):18035\u201318057","journal-title":"Neural Comput Appl"},{"key":"7415_CR28","doi-asserted-by":"crossref","unstructured":"Schardl TB, Lee I-TA (2023) Opencilk: a modular and extensible software infrastructure for fast task-parallel code. In: Proceedings of the 28th ACM SIGPLAN Annual Symposium on Principles and Practice of Parallel Programming, pp 189\u2013203","DOI":"10.1145\/3572848.3577509"},{"key":"7415_CR29","first-page":"1512","volume":"34","author":"A Godet","year":"2020","unstructured":"Godet A, Lorca X, Hebrard E, Simonin G (2020) Using approximation within constraint programming to solve the parallel machine scheduling problem with additional unit resources. Proc AAAI Conf Artif Intell 34:1512\u20131519","journal-title":"Proc AAAI Conf Artif Intell"},{"issue":"6","key":"7415_CR30","doi-asserted-by":"publisher","first-page":"1785","DOI":"10.1109\/TNET.2012.2233213","volume":"21","author":"C Joe-Wong","year":"2013","unstructured":"Joe-Wong C, Sen S, Lan T, Chiang M (2013) Multiresource allocation: fairness-efficiency tradeoffs in a unifying framework. IEEE\/ACM Trans Netw 21(6):1785\u20131798","journal-title":"IEEE\/ACM Trans Netw"},{"issue":"4","key":"7415_CR31","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1145\/2740070.2626334","volume":"44","author":"R Grandl","year":"2014","unstructured":"Grandl R, Ananthanarayanan G, Kandula S, Rao S, Akella A (2014) Multi-resource packing for cluster schedulers. ACM SIGCOMM Comput Commun Rev 44(4):455\u2013466","journal-title":"ACM SIGCOMM Comput Commun Rev"},{"issue":"4","key":"7415_CR32","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1145\/2644865.2541941","volume":"49","author":"C Delimitrou","year":"2014","unstructured":"Delimitrou C, Kozyrakis C (2014) Quasar: resource-efficient and qos-aware cluster management. ACM SIGPLAN Notices 49(4):127\u2013144","journal-title":"ACM SIGPLAN Notices"},{"issue":"4","key":"7415_CR33","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1145\/2499368.2451125","volume":"48","author":"C Delimitrou","year":"2013","unstructured":"Delimitrou C (2013) Paragon: Qos-aware scheduling for heterogeneous datacenters. ACM SIGPLAN Notices 48(4):77\u201388","journal-title":"ACM SIGPLAN Notices"},{"issue":"2","key":"7415_CR34","doi-asserted-by":"publisher","first-page":"1421","DOI":"10.1007\/s10586-023-04021-x","volume":"27","author":"R Ghafari","year":"2024","unstructured":"Ghafari R, Mansouri N (2024) Improved Harris Hawks optimizer with chaotic maps and opposition-based learning for task scheduling in cloud environment. Clust Comput 27(2):1421\u20131469","journal-title":"Clust Comput"},{"key":"7415_CR35","unstructured":"Boutin E, Ekanayake J, Lin W, Shi B, Zhou J, Qian Z, Wu M, Zhou L (2014) Apollo: scalable and coordinated scheduling for cloud-scale computing. In: 11th USENIX Symposium on Operating Systems Design and Implementation (OSDI 14), pp 285\u2013300"},{"key":"7415_CR36","unstructured":"Gog I, Schwarzkopf M, Gleave A, Watson RN, Hand S (2016) Firmament: fast, centralized cluster scheduling at scale. In: 12th USENIX Symposium on Operating Systems Design and Implementation (OSDI 16), pp 99\u2013115"},{"key":"7415_CR37","doi-asserted-by":"crossref","unstructured":"Fu Y, Liu L, Wang H, Cheng Y, Chen S (2022) SFS: smart OS scheduling for serverless functions. In: SC22: International Conference for High Performance Computing, Networking, Storage and Analysis. IEEE, pp 1\u201316","DOI":"10.1109\/SC41404.2022.00047"},{"issue":"9","key":"7415_CR38","doi-asserted-by":"publisher","first-page":"3469","DOI":"10.1007\/s12652-018-1071-1","volume":"10","author":"HR Boveiri","year":"2019","unstructured":"Boveiri HR, Khayami R, Elhoseny M, Gunasekaran M (2019) An efficient swarm-intelligence approach for task scheduling in cloud-based internet of things applications. J Amb Intell Hum Comput 10(9):3469\u20133479","journal-title":"J Amb Intell Hum Comput"},{"issue":"1","key":"7415_CR39","doi-asserted-by":"publisher","first-page":"e12536","DOI":"10.1111\/exsy.12536","volume":"38","author":"HR Boveiri","year":"2021","unstructured":"Boveiri HR, Javidan R, Khayami R (2021) An intelligent hybrid approach for task scheduling in cluster computing environments as an infrastructure for biomedical applications. Expert Syst 38(1):e12536","journal-title":"Expert Syst"},{"issue":"13","key":"7415_CR40","doi-asserted-by":"publisher","first-page":"10075","DOI":"10.1007\/s00500-019-04520-3","volume":"24","author":"HR Boveiri","year":"2020","unstructured":"Boveiri HR (2020) An enhanced cuckoo optimization algorithm for task graph scheduling in cluster-computing systems. Soft Comput 24(13):10075\u201310093","journal-title":"Soft Comput"},{"key":"7415_CR41","unstructured":"Ibm ilog cplex optimization. https:\/\/www.ibm.com\/docs\/en\/icos"},{"key":"7415_CR42","doi-asserted-by":"crossref","unstructured":"Karp RM (1972) Reducibility among combinatorial problems. In: Complexity of Computer Computations. Springer, pp 85\u2013103","DOI":"10.1007\/978-1-4684-2001-2_9"},{"key":"7415_CR43","unstructured":"Cormen TH, Leiserson CE, Rivest RL, Stein C (2001) Topological sort. In: Introduction to Algorithms, 2nd ed. MIT Press, Ch. 22.4, pp 549\u2013552"},{"key":"7415_CR44","unstructured":"Cormen TH, Leiserson CE, Rivest RL, Stein C (2001) Single-source shortest paths in directed acyclic graphs. In: Introduction to Algorithms, 2nd ed. MIT Press, Ch. 24.2, pp 592\u2013595"},{"key":"7415_CR45","first-page":"246","volume":"15","author":"F Galton","year":"1886","unstructured":"Galton F (1886) Regression towards mediocrity in hereditary stature. J Anthropol Inst G B Irel 15:246\u2013263","journal-title":"J Anthropol Inst G B Irel"},{"issue":"1","key":"7415_CR46","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1177\/011542650802300176","volume":"23","author":"BR Overholser","year":"2008","unstructured":"Overholser BR, Sowinski KM (2008) Biostatistics primer: part 2. Nutr Clin Pract 23(1):76\u201384","journal-title":"Nutr Clin Pract"},{"issue":"2","key":"7415_CR47","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1525\/bio.2013.63.2.5","volume":"63","author":"JA Goldbogen","year":"2013","unstructured":"Goldbogen JA, Friedlaender AS, Calambokidis J, McKenna MF, Simon M, Nowacek DP (2013) Integrative approaches to the study of baleen whale diving behavior, feeding performance, and foraging ecology. BioScience 63(2):90\u2013100","journal-title":"BioScience"},{"issue":"1","key":"7415_CR48","doi-asserted-by":"publisher","first-page":"155","DOI":"10.2307\/1379766","volume":"60","author":"WA Watkins","year":"1979","unstructured":"Watkins WA, Schevill WE (1979) Aerial observation of feeding behavior in four baleen whales: Eubalaena glacialis, Balaenoptera borealis, Megaptera novaeangliae, and Balaenoptera physalus. J Mammal 60(1):155\u2013163","journal-title":"J Mammal"},{"issue":"3","key":"7415_CR49","doi-asserted-by":"publisher","first-page":"3117","DOI":"10.1109\/JSYST.2019.2960088","volume":"14","author":"X Chen","year":"2020","unstructured":"Chen X, Cheng L, Liu C, Liu Q, Liu J, Mao Y, Murphy J (2020) A WOA-based optimization approach for task scheduling in cloud computing systems. IEEE Syst J 14(3):3117\u20133128","journal-title":"IEEE Syst J"},{"key":"7415_CR50","doi-asserted-by":"crossref","unstructured":"Dorigo M, Di\u00a0Caro G (1999) Ant colony optimization: a new meta-heuristic. In: Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406), vol\u00a02. IEEE, pp 1470\u20131477","DOI":"10.1109\/CEC.1999.782657"},{"key":"7415_CR51","doi-asserted-by":"crossref","unstructured":"Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN\u201995-International Conference on Neural Networks, vol\u00a04. IEEE, pp 1942\u20131948","DOI":"10.1109\/ICNN.1995.488968"},{"key":"7415_CR52","doi-asserted-by":"crossref","unstructured":"Gen M, Cheng R (1999) Genetic algorithms and engineering optimization, vol\u00a07. Wiley","DOI":"10.1002\/9780470172261"},{"issue":"2","key":"7415_CR53","doi-asserted-by":"publisher","first-page":"238","DOI":"10.1137\/0717021","volume":"17","author":"FN Fritsch","year":"1980","unstructured":"Fritsch FN, Carlson RE (1980) Monotone piecewise cubic interpolation. SIAM J Numer Anal 17(2):238\u2013246","journal-title":"SIAM J Numer Anal"},{"issue":"200","key":"7415_CR54","doi-asserted-by":"publisher","first-page":"675","DOI":"10.1080\/01621459.1937.10503522","volume":"32","author":"M Friedman","year":"1937","unstructured":"Friedman M (1937) The use of ranks to avoid the assumption of normality implicit in the analysis of variance. J Am Stat Assoc 32(200):675\u2013701","journal-title":"J Am Stat Assoc"},{"key":"7415_CR55","volume-title":"Distribution-free multiple comparisons","author":"PB Nemenyi","year":"1963","unstructured":"Nemenyi PB (1963) Distribution-free multiple comparisons. Princeton University"}],"container-title":["The Journal of Supercomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-025-07415-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11227-025-07415-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-025-07415-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,28]],"date-time":"2025-05-28T13:51:03Z","timestamp":1748440263000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11227-025-07415-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,28]]},"references-count":55,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2025,6]]}},"alternative-id":["7415"],"URL":"https:\/\/doi.org\/10.1007\/s11227-025-07415-3","relation":{},"ISSN":["1573-0484"],"issn-type":[{"value":"1573-0484","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,5,28]]},"assertion":[{"value":"6 May 2025","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 May 2025","order":2,"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 that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"911"}}