{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T21:17:14Z","timestamp":1763414234539,"version":"3.45.0"},"publisher-location":"Cham","reference-count":38,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032111265","type":"print"},{"value":"9783032111272","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T00:00:00Z","timestamp":1763424000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T00:00:00Z","timestamp":1763424000000},"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\/978-3-032-11127-2_10","type":"book-chapter","created":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T20:03:52Z","timestamp":1763409832000},"page":"93-110","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Centroid Approximation with\u00a0Multidimensional Approximate Agreement Protocols"],"prefix":"10.1007","author":[{"given":"M\u00e9lanie","family":"Cambus","sequence":"first","affiliation":[]},{"given":"Darya","family":"Melnyk","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,11,18]]},"reference":[{"key":"10_CR1","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2021.110046","volume":"136","author":"W Abbas","year":"2022","unstructured":"Abbas, W., Shabbir, M., Li, J., Koutsoukos, X.: Resilient distributed vector consensus using centerpoint. Automatica 136, 110046 (2022)","journal-title":"Automatica"},{"key":"10_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1007\/11516798_17","volume-title":"Principles of Distributed Systems","author":"I Abraham","year":"2005","unstructured":"Abraham, I., Amit, Y., Dolev, D.: Optimal resilience asynchronous approximate agreement. In: Higashino, T. (ed.) OPODIS 2004. LNCS, vol. 3544, pp. 229\u2013239. Springer, Heidelberg (2005). https:\/\/doi.org\/10.1007\/11516798_17"},{"key":"10_CR3","doi-asserted-by":"publisher","unstructured":"Abraham, I., Devadas, S., Nayak, K., Ren, L.: Brief announcement: practical synchronous byzantine consensus. In: 31st International Symposium on Distributed Computing (DISC 2017) (2017). https:\/\/doi.org\/10.4230\/LIPIcs.DISC.2017.41","DOI":"10.4230\/LIPIcs.DISC.2017.41"},{"key":"10_CR4","doi-asserted-by":"crossref","unstructured":"Ai, L., Yu, J., Wu, Z., He, Y., Guan, T.: Optimized residual vector quantization for efficient approximate nearest neighbor search. Multimedia Syst. 23 (2017)","DOI":"10.1007\/s00530-015-0470-9"},{"key":"10_CR5","unstructured":"Allouah, Y., Guerraoui, R., Hoang, L., Villemaud, O.: Robust sparse voting. CoRR arxiv:2202.08656 (2022)"},{"key":"10_CR6","unstructured":"Attiya, H., Ellen, F.: The step complexity of multidimensional approximate agreement. In: 26th International Conference on Principles of Distributed Systems (OPODIS 2022) (2023)"},{"key":"10_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"380","DOI":"10.1007\/BFb0040405","volume-title":"VLSI Algorithms and Architectures","author":"A Bar-Noy","year":"1988","unstructured":"Bar-Noy, A., Dolev, D.: Families of consensus algorithms. In: Reif, J.H. (ed.) AWOC 1988. LNCS, vol. 319, pp. 380\u2013390. Springer, New York (1988). https:\/\/doi.org\/10.1007\/BFb0040405"},{"key":"10_CR8","doi-asserted-by":"publisher","unstructured":"Berman, P., Garay, J., Perry, K.: Towards optimal distributed consensus. In: 30th Annual Symposium on Foundations of Computer Science (1989). https:\/\/doi.org\/10.1109\/SFCS.1989.63511","DOI":"10.1109\/SFCS.1989.63511"},{"issue":"2","key":"10_CR9","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1016\/0890-5401(87)90054-X","volume":"75","author":"G Bracha","year":"1987","unstructured":"Bracha, G.: Asynchronous byzantine agreement protocols. Inf. Comput. 75(2), 130\u2013143 (1987)","journal-title":"Inf. Comput."},{"key":"10_CR10","doi-asserted-by":"publisher","unstructured":"Bracha, G., Toueg, S.: Resilient consensus protocols. In: Proceedings of the Second Annual ACM Symposium on Principles of Distributed Computing, PODC \u201983 (1983). https:\/\/doi.org\/10.1145\/800221.806706","DOI":"10.1145\/800221.806706"},{"key":"10_CR11","volume-title":"Introduction to Reliable and Secure Distributed Programming","author":"C Cachin","year":"2014","unstructured":"Cachin, C., Guerraoui, R., Rodrigues, L.: Introduction to Reliable and Secure Distributed Programming, 2nd edn. Springer, Heidelberg (2014)","edition":"2"},{"key":"10_CR12","unstructured":"Cambus, M., Melnyk, D.: Centroid approximation with multidimensional approximate agreement protocols (2025). https:\/\/arxiv.org\/abs\/2306.12741"},{"key":"10_CR13","doi-asserted-by":"crossref","unstructured":"Civit, P., et al.: Byzantine consensus is $$\\theta $$ (n$$^2$$): the Dolev-Reischuk bound is tight even in partial synchrony! In: 36th International Symposium on Distributed Computing (DISC 2022). Schloss Dagstuhl-Leibniz-Zentrum f\u00fcr Informatik (2022)","DOI":"10.1007\/s00446-023-00458-w"},{"key":"10_CR14","doi-asserted-by":"crossref","unstructured":"Civit, P., Gilbert, S., Gramoli, V.: Polygraph: accountable byzantine agreement. In: 2021 IEEE 41st International Conference on Distributed Computing Systems (ICDCS), pp. 403\u2013413. IEEE (2021)","DOI":"10.1109\/ICDCS51616.2021.00046"},{"key":"10_CR15","doi-asserted-by":"publisher","unstructured":"Civit, P., Gilbert, S., Guerraoui, R., Komatovic, J., Vidigueira, M.: On the validity of consensus. In: Proceedings of the 2023 ACM Symposium on Principles of Distributed Computing, PODC \u201923, pp. 332\u2013343 (2023). https:\/\/doi.org\/10.1145\/3583668.3594567","DOI":"10.1145\/3583668.3594567"},{"key":"10_CR16","doi-asserted-by":"publisher","unstructured":"Crain, T., Gramoli, V., Larrea, M., Raynal, M.: DBFT: efficient leaderless byzantine consensus and its application to blockchains. In: 2018 IEEE 17th International Symposium on Network Computing and Applications (NCA) (2018). https:\/\/doi.org\/10.1109\/NCA.2018.8548057","DOI":"10.1109\/NCA.2018.8548057"},{"key":"10_CR17","doi-asserted-by":"publisher","unstructured":"De\u00a0Prisco, R., Malkhi, D., Reiter, M.K.: On k-set consensus problems in asynchronous systems. In: Proceedings of the Eighteenth Annual ACM Symposium on Principles of Distributed Computing, PODC \u201999 (1999). https:\/\/doi.org\/10.1145\/301308.301368","DOI":"10.1145\/301308.301368"},{"issue":"3","key":"10_CR18","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1145\/5925.5931","volume":"33","author":"D Dolev","year":"1986","unstructured":"Dolev, D., Lynch, N.A., Pinter, S.S., Stark, E.W., Weihl, W.E.: Reaching approximate agreement in the presence of faults. J. ACM 33(3), 499\u2013516 (1986)","journal-title":"J. ACM"},{"key":"10_CR19","doi-asserted-by":"publisher","unstructured":"Dotan, M., Stern, G., Zohar, A.: Validated byzantine asynchronous multidimensional approximate agreement. CoRR arxiv:2211.02126 (2022). https:\/\/doi.org\/10.48550\/ARXIV.2211.02126","DOI":"10.48550\/ARXIV.2211.02126"},{"key":"10_CR20","unstructured":"El-Mhamdi, E.M., Farhadkhani, S., Guerraoui, R., Guirguis, A., Hoang, L.N., Rouault, S.: Collaborative learning in the jungle (decentralized, byzantine, heterogeneous, asynchronous and nonconvex learning). In: Advances in Neural Information Processing Systems, vol.\u00a034. Curran Associates, Inc. (2021)"},{"issue":"1","key":"10_CR21","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1007\/BF01783662","volume":"4","author":"AD Fekete","year":"1990","unstructured":"Fekete, A.D.: Asymptotically optimal algorithms for approximate agreement. Distrib. Comput. 4(1), 9\u201329 (1990)","journal-title":"Distrib. Comput."},{"issue":"2","key":"10_CR22","doi-asserted-by":"publisher","first-page":"575","DOI":"10.2307\/1954111","volume":"72","author":"MP Fiorina","year":"1978","unstructured":"Fiorina, M.P., Plott, C.R.: Committee decisions under majority rule: an experimental study. Am. Polit. Sci. Rev. 72(2), 575\u2013598 (1978)","journal-title":"Am. Polit. Sci. Rev."},{"issue":"4","key":"10_CR23","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1016\/0020-0190(82)90033-3","volume":"14","author":"MJ Fischer","year":"1982","unstructured":"Fischer, M.J., Lynch, N.A.: A lower bound for the time to assure interactive consistency. Inf. Process. Lett. 14(4), 183\u2013186 (1982)","journal-title":"Inf. Process. Lett."},{"key":"10_CR24","doi-asserted-by":"crossref","unstructured":"F\u00fcgger, M., Nowak, T.: Fast multidimensional asymptotic and approximate consensus. In: 32nd International Symposium on Distributed Computing (DISC 2018) (2018)","DOI":"10.1145\/3212734.3212762"},{"key":"10_CR25","unstructured":"Li, B., Kamuhanda, D., He, K.: Centroid-based multiple local community detection. IEEE Trans. Comput. Soc. Syst. (2022)"},{"issue":"2","key":"10_CR26","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1109\/TIT.1982.1056489","volume":"28","author":"S Lloyd","year":"1982","unstructured":"Lloyd, S.: Least squares quantization in PCM. IEEE Trans. Inf. Theory 28(2), 129\u2013137 (1982)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"10_CR27","doi-asserted-by":"crossref","unstructured":"Melnyk, D., Wang, Y., Wattenhofer, R.: Byzantine preferential voting. In: Web and Internet Economics (WINE), pp. 327\u2013340 (2018)","DOI":"10.1007\/978-3-030-04612-5_22"},{"key":"10_CR28","doi-asserted-by":"crossref","unstructured":"Melnyk, D., Wattenhofer, R.: Byzantine agreement with interval validity. In: 2018 IEEE 37th Symposium on Reliable Distributed Systems (SRDS) (2018)","DOI":"10.1109\/SRDS.2018.00036"},{"key":"10_CR29","doi-asserted-by":"crossref","unstructured":"Mendes, H., Herlihy, M.: Multidimensional approximate agreement in byzantine asynchronous systems. In: Proceedings of the Forty-Fifth Annual ACM Symposium on Theory of Computing, STOC (2013)","DOI":"10.1145\/2488608.2488657"},{"issue":"6","key":"10_CR30","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1007\/s00446-014-0240-5","volume":"28","author":"H Mendes","year":"2015","unstructured":"Mendes, H., Herlihy, M., Vaidya, N., Garg, V.K.: Multidimensional agreement in byzantine systems. Distrib. Comput. 28(6), 423\u2013441 (2015)","journal-title":"Distrib. Comput."},{"key":"10_CR31","doi-asserted-by":"crossref","unstructured":"Naz, A., Piranda, B., Goldstein, S.C., Bourgeois, J.: Approximate-centroid election in large-scale distributed embedded systems. In: 2016 IEEE 30th International Conference on Advanced Information Networking and Applications (AINA), pp. 548\u2013556 (2016)","DOI":"10.1109\/AINA.2016.109"},{"issue":"3","key":"10_CR32","doi-asserted-by":"publisher","first-page":"565","DOI":"10.1109\/TRO.2017.2658604","volume":"33","author":"H Park","year":"2017","unstructured":"Park, H., Hutchinson, S.A.: Fault-tolerant rendezvous of multirobot systems. IEEE Trans. Rob. 33(3), 565\u2013582 (2017). https:\/\/doi.org\/10.1109\/TRO.2017.2658604","journal-title":"IEEE Trans. Rob."},{"key":"10_CR33","unstructured":"Stolz, D., Wattenhofer, R.: Byzantine agreement with median validity. In: 19th International Conference on Priniciples of Distributed Systems. OPODIS (2015)"},{"key":"10_CR34","doi-asserted-by":"publisher","unstructured":"Tverberg, H.: A generalization of radon\u2019s theorem. J. Lond. Math. Soc. s1-41(1), 123\u2013128 (1966). https:\/\/doi.org\/10.1112\/jlms\/s1-41.1.123","DOI":"10.1112\/jlms\/s1-41.1.123"},{"key":"10_CR35","doi-asserted-by":"crossref","unstructured":"Vaidya, N.H., Garg, V.K.: Byzantine vector consensus in complete graphs. In: Proceedings of the 2013 ACM Symposium on Principles of Distributed Computing, PODC (2013)","DOI":"10.1145\/2484239.2484256"},{"issue":"3","key":"10_CR36","doi-asserted-by":"publisher","first-page":"269","DOI":"10.3934\/naco.2019018","volume":"9","author":"X Wang","year":"2019","unstructured":"Wang, X., Mou, S., Sundaram, S.: A resilient convex combination for consensus-based distributed algorithms. Numer. Algebra Control Optim. 9(3), 269\u2013281 (2019)","journal-title":"Numer. Algebra Control Optim."},{"key":"10_CR37","unstructured":"Xiang, Z., Vaidya, N.H.: Relaxed byzantine vector consensus. In: 20th International Conference on Principles of Distributed Systems (OPODIS 2016) (2017)"},{"key":"10_CR38","doi-asserted-by":"crossref","unstructured":"Yin, M., Malkhi, D., Reiter, M.K., Gueta, G.G., Abraham, I.: Hotstuff: BFT consensus with linearity and responsiveness. In: Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing, pp. 347\u2013356 (2019)","DOI":"10.1145\/3293611.3331591"}],"container-title":["Lecture Notes in Computer Science","Stabilization, Safety, and Security of Distributed Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-11127-2_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T20:03:55Z","timestamp":1763409835000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-11127-2_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,18]]},"ISBN":["9783032111265","9783032111272"],"references-count":38,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-11127-2_10","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,18]]},"assertion":[{"value":"18 November 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"SSS","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Symposium on Stabilizing, Safety, and Security of Distributed Systems","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Kathmandu","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Nepal","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":"9 October 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"11 October 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"27","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"sss2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}