{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T20:07:45Z","timestamp":1757621265518,"version":"3.44.0"},"publisher-location":"Singapore","reference-count":45,"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_23","type":"book-chapter","created":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T21:09:30Z","timestamp":1754168970000},"page":"313-326","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Revisit the\u00a0Partial Coloring Method: Prefix Spencer and\u00a0Sampling"],"prefix":"10.1007","author":[{"given":"Dongrun","family":"Cai","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0966-5151","authenticated-orcid":false,"given":"Xue","family":"Chen","sequence":"additional","affiliation":[]},{"given":"Wenxuan","family":"Shu","sequence":"additional","affiliation":[]},{"given":"Haoyu","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Guangyi","family":"Zou","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,8,3]]},"reference":[{"key":"23_CR1","doi-asserted-by":"crossref","unstructured":"Alweiss, R., Liu, Y.P., Sawhney, M.: Discrepancy minimization via a self-balancing walk. In: STOC 2021: 53rd Annual ACM SIGACT Symposium on Theory of Computing, pp. 14\u201320. ACM (2021)","DOI":"10.1145\/3406325.3450994"},{"key":"23_CR2","doi-asserted-by":"crossref","unstructured":"Banaszczyk, W.: Balancing vectors and gaussian measures of n-dimensional convex bodies. Random Struct. Algorithms 12(4), 351\u2013360 (1998)","DOI":"10.1002\/(SICI)1098-2418(199807)12:4<351::AID-RSA3>3.0.CO;2-S"},{"issue":"3","key":"23_CR3","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1002\/rsa.20373","volume":"40","author":"W Banaszczyk","year":"2012","unstructured":"Banaszczyk, W.: On series of signed vectors and their rearrangements. Random Struct. Algorithms 40(3), 301\u2013316 (2012)","journal-title":"Random Struct. Algorithms"},{"key":"23_CR4","doi-asserted-by":"crossref","unstructured":"Bansal, N.: Constructive algorithms for discrepancy minimization. In: 51th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2010, pp. 3\u201310. IEEE Computer Society (2010)","DOI":"10.1109\/FOCS.2010.7"},{"issue":"2","key":"23_CR5","doi-asserted-by":"publisher","first-page":"534","DOI":"10.1137\/17M1126795","volume":"48","author":"N Bansal","year":"2019","unstructured":"Bansal, N., Dadush, D., Garg, S.: An algorithm for Koml\u00f3s conjecture matching Banaszczyk\u2019s bound. SIAM J. Comput. 48(2), 534\u2013553 (2019)","journal-title":"SIAM J. Comput."},{"key":"23_CR6","first-page":"1","volume":"15","author":"N Bansal","year":"2019","unstructured":"Bansal, N., Dadush, D., Garg, S., Lovett, S.: The gram-Schmidt walk: a cure for the Banaszczyk blues. Theory Comput. 15, 1\u201327 (2019)","journal-title":"Theory Comput."},{"key":"23_CR7","doi-asserted-by":"crossref","unstructured":"Bansal, N., Garg, S.: Algorithmic discrepancy beyond partial coloring. In: Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017, pp. 914\u2013926. ACM (2017)","DOI":"10.1145\/3055399.3055490"},{"key":"23_CR8","doi-asserted-by":"crossref","unstructured":"Bansal, N., Jiang, H., Meka, R.: Resolving matrix spencer conjecture up to poly-logarithmic rank. In: Proceedings of the 55th Annual ACM Symposium on Theory of Computing, STOC 2023, pp. 1814\u20131819. ACM (2023)","DOI":"10.1145\/3564246.3585103"},{"key":"23_CR9","unstructured":"Bansal, N., Laddha, A., Vempala, S.S.: A unified approach to discrepancy minimization. In: APPROX\/RANDOM 2022. LIPIcs, vol.\u00a0245, pp. 1:1\u20131:22. Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik (2022)"},{"key":"23_CR10","doi-asserted-by":"crossref","unstructured":"Bansal, N., Rohwedder, L., Svensson, O.: Flow time scheduling and prefix Beck-Fiala. In: Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing, pp. 331\u2013342 (2022)","DOI":"10.1145\/3519935.3520077"},{"key":"23_CR11","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1007\/BF02579452","volume":"1","author":"J Beck","year":"1981","unstructured":"Beck, J.: Roth\u2019s estimate of the discrepancy of integer sequences is nearly sharp. Combinatorica 1, 319\u2013325 (1981)","journal-title":"Combinatorica"},{"key":"23_CR12","doi-asserted-by":"crossref","unstructured":"Beck, J., Fiala, T.: \u201cinteger-making\u201d theorems. Discrete Appl. Math. 3(1), 1\u20138 (1981)","DOI":"10.1016\/0166-218X(81)90022-6"},{"key":"23_CR13","doi-asserted-by":"crossref","unstructured":"Bozzai, R., Reis, V., Rothvoss, T.: The vector balancing constant for zonotopes. In: 64th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2023, pp. 1292\u20131300. IEEE (2023)","DOI":"10.1109\/FOCS57990.2023.00077"},{"key":"23_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0024-3795(81)90085-9","volume":"41","author":"I B\u00e1r\u00e1ny","year":"1981","unstructured":"B\u00e1r\u00e1ny, I., Grinberg, V.: On some combinatorial questions in finite-dimensional spaces. Linear Algebra Appl. 41, 1\u20139 (1981)","journal-title":"Linear Algebra Appl."},{"key":"23_CR15","unstructured":"Chazelle, B.: The Discrepancy Method (Randomness and Complexity). Cambridge University Press (2002)"},{"key":"23_CR16","unstructured":"Chen, X., Price, E.: Active regression via linear-sample sparsification. In: Conference on Learning Theory, COLT 2019, 25\u201328 June 2019. Proceedings of Machine Learning Research, vol.\u00a099, pp. 663\u2013695. PMLR (2019)"},{"issue":"2","key":"23_CR17","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1090\/S0002-9947-1948-0026274-0","volume":"64","author":"KL Chung","year":"1948","unstructured":"Chung, K.L.: On the maximum partial sums of sequences of independent random variables. Trans. Am. Math. Soc. 64(2), 205\u2013233 (1948)","journal-title":"Trans. Am. Math. Soc."},{"key":"23_CR18","doi-asserted-by":"crossref","unstructured":"Dadush, D., Jiang, H., Reis, V.: A new framework for matrix discrepancy: partial coloring bounds via mirror descent. In: STOC 2022: 54th Annual ACM SIGACT Symposium on Theory of Computing, pp. 649\u2013658. ACM (2022)","DOI":"10.1145\/3519935.3519967"},{"key":"23_CR19","first-page":"503","volume":"33","author":"RA Fisher","year":"1926","unstructured":"Fisher, R.A.: The arrangement of field experiments. J. Minist. Agric. 33, 503\u2013515 (1926)","journal-title":"J. Minist. Agric."},{"key":"23_CR20","unstructured":"Fisher, R.: Statistical Methods for Research Workers. Biological monographs and manuals, Oliver and Boyd (1925)"},{"key":"23_CR21","doi-asserted-by":"crossref","unstructured":"Gluskin, E.D.: Extremal properties of orthogonal parallelepipeds and their applications to the geometry of banach spaces. Sbornik Math. 64(1), 85\u201396 (1989)","DOI":"10.1070\/SM1989v064n01ABEH003295"},{"key":"23_CR22","unstructured":"Harshaw, C., S\u00e4vje, F., Spielman, D.A., Zhang, P.: Balancing covariates in randomized experiments with the gram\u2013schmidt walk design. J. Am. Stat. Assoc. 0(0), 1\u201313 (2024)"},{"key":"23_CR23","doi-asserted-by":"crossref","unstructured":"Khatri, C.G.: On certain inequalities for normal distributions and their applications to simultaneous confidence bounds. Ann. Math. Stat., 1853\u20131867 (1967)","DOI":"10.1214\/aoms\/1177698618"},{"key":"23_CR24","doi-asserted-by":"crossref","unstructured":"Kulkarni, J., Reis, V., Rothvoss, T.: Optimal online discrepancy minimization. In: Proceedings of the 56th Annual ACM Symposium on Theory of Computing, STOC 2024, pp. 1832\u20131840. ACM (2024)","DOI":"10.1145\/3618260.3649720"},{"key":"23_CR25","doi-asserted-by":"crossref","unstructured":"Levy, A., Ramadas, H., Rothvoss, T.: Deterministic discrepancy minimization via the multiplicative weight update method. In: IPCO 2017, Proceedings, vol. 10328, pp. 380\u2013391. Springer (2017)","DOI":"10.1007\/978-3-319-59250-3_31"},{"key":"23_CR26","volume-title":"Th\u00e9orie de l\u2019addition des variables al\u00e9atoires","author":"P L\u00e9vy","year":"1938","unstructured":"L\u00e9vy, P.: Th\u00e9orie de l\u2019addition des variables al\u00e9atoires. Gauthier-Villars, Paris (1938)"},{"key":"23_CR27","unstructured":"Liu, Y.P., Sah, A., Sawhney, M.: A gaussian fixed point random walk. In: 13th Innovations in Theoretical Computer Science Conference, ITCS 2022. LIPIcs, vol.\u00a0215, pp. 101:1\u2013101:10 (2022)"},{"key":"23_CR28","doi-asserted-by":"crossref","unstructured":"Lovett, S., Meka, R.: Constructive discrepancy minimization by walking on the edges. In: 53rd Annual Symposium on Foundations of Computer Science, FOCS 2012, pp. 61\u201367. IEEE (2012)","DOI":"10.1109\/FOCS.2012.23"},{"issue":"1","key":"23_CR29","doi-asserted-by":"publisher","first-page":"327","DOI":"10.4007\/annals.2015.182.1.8","volume":"182","author":"AW Marcus","year":"2015","unstructured":"Marcus, A.W., Spielman, D.A., Srivastava, N.: Interlacing families II: mixed characteristic polynomials and the Kadison\u2013Singer problem. Ann. Math. 182(1), 327\u2013350 (2015)","journal-title":"Ann. Math."},{"key":"23_CR30","unstructured":"Matousek, J.: Geometric Discrepancy: An Illustrated Guide. Springer Science (2009)"},{"issue":"10","key":"23_CR31","first-page":"751","volume":"2020","author":"J Matousek","year":"2020","unstructured":"Matousek, J., Nikolov, A., Talwar, K.: Factorization norms and hereditary discrepancy. Int. Math. Res. Not. 2020(10), 751\u2013780 (2020)","journal-title":"Int. Math. Res. Not."},{"key":"23_CR32","doi-asserted-by":"crossref","unstructured":"Newman, A., Neiman, O., Nikolov, A.: Beck\u2019s three permutations conjecture: a counterexample and some consequences. In: 53rd Annual IEEE Symposium on Foundations of Computer Science, FOCS 2012, pp. 253\u2013262. IEEE (2012)","DOI":"10.1109\/FOCS.2012.84"},{"key":"23_CR33","doi-asserted-by":"crossref","unstructured":"Pesenti, L., Vladu, A.: Discrepancy minimization via regularization. In: Bansal, N., Nagarajan, V. (eds.) Proceedings of the 2023 ACM-SIAM Symposium on Discrete Algorithms, SODA 2023, pp. 1734\u20131758. SIAM (2023)","DOI":"10.1137\/1.9781611977554.ch66"},{"key":"23_CR34","unstructured":"Reis, V.: Vector Balancing and Integer Programming. University of Washington (2023)"},{"key":"23_CR35","doi-asserted-by":"crossref","unstructured":"Reis, V., Rothvoss, T.: Linear size sparsifier and the geometry of the operator norm ball. In: Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms, SODA 2020, pp. 2337\u20132348. SIAM (2020)","DOI":"10.1137\/1.9781611975994.143"},{"issue":"3","key":"23_CR36","doi-asserted-by":"publisher","first-page":"667","DOI":"10.1002\/rsa.21113","volume":"62","author":"V Reis","year":"2023","unstructured":"Reis, V., Rothvoss, T.: Vector balancing in lebesgue spaces. Random Struct. Algorithms 62(3), 667\u2013688 (2023)","journal-title":"Random Struct. Algorithms"},{"issue":"1","key":"23_CR37","doi-asserted-by":"publisher","first-page":"224","DOI":"10.1137\/141000282","volume":"46","author":"T Rothvoss","year":"2017","unstructured":"Rothvoss, T.: Constructive discrepancy minimization for convex sets. SIAM J. Comput. 46(1), 224\u2013234 (2017)","journal-title":"SIAM J. Comput."},{"issue":"2","key":"23_CR38","first-page":"139","volume":"48","author":"T Royen","year":"2014","unstructured":"Royen, T.: A simple proof of the gaussian correlation conjecture extended to multivariate gamma distributions. Far East J. Theoret. Stat. 48(2), 139\u2013145 (2014)","journal-title":"Far East J. Theoret. Stat."},{"key":"23_CR39","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1007\/BF01066719","volume":"6","author":"QM Shao","year":"1993","unstructured":"Shao, Q.M.: A note on small ball probability of a gaussian process with stationary increments. J. Theor. Probab. 6, 595\u2013602 (1993)","journal-title":"J. Theor. Probab."},{"issue":"318","key":"23_CR40","first-page":"626","volume":"62","author":"Z \u0160id\u00e1k","year":"1967","unstructured":"\u0160id\u00e1k, Z.: Rectangular confidence regions for the means of multivariate normal distributions. J. Am. Stat. Assoc. 62(318), 626\u2013633 (1967)","journal-title":"J. Am. Stat. Assoc."},{"issue":"2","key":"23_CR41","doi-asserted-by":"publisher","first-page":"679","DOI":"10.1090\/S0002-9947-1985-0784009-0","volume":"289","author":"J Spencer","year":"1985","unstructured":"Spencer, J.: Six standard deviations suffice. Trans. Am. Math. Soc. 289(2), 679\u2013706 (1985)","journal-title":"Trans. Am. Math. Soc."},{"key":"23_CR42","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1007\/BF02579409","volume":"6","author":"J Spencer","year":"1986","unstructured":"Spencer, J.: Balancing vectors in the max norm. Combinatorica 6, 55\u201365 (1986)","journal-title":"Combinatorica"},{"key":"23_CR43","unstructured":"Spencer, J.H., Srinivasan, A., Tetali, P.: The discrepancy of permutation families. Unpublished manuscript (2001)"},{"key":"23_CR44","doi-asserted-by":"crossref","unstructured":"Student: Comparison between balanced and random arrangements of field plots. Biometrika 29(3\/4), 363\u2013378 (1938)","DOI":"10.2307\/2332011"},{"issue":"2","key":"23_CR45","first-page":"363","volume":"108","author":"M Talagrand","year":"1990","unstructured":"Talagrand, M.: Embedding subspaces of l1 into ln 1. Proc. Am. Math. Soc. 108(2), 363\u2013369 (1990)","journal-title":"Proc. Am. Math. Soc."}],"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_23","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T12:42:19Z","timestamp":1757335339000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-981-95-0218-9_23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,3]]},"ISBN":["9789819502172","9789819502189"],"references-count":45,"URL":"https:\/\/doi.org\/10.1007\/978-981-95-0218-9_23","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"}}]}}