{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T09:05:18Z","timestamp":1777539918064,"version":"3.51.4"},"reference-count":15,"publisher":"Springer Science and Business Media LLC","issue":"12","license":[{"start":{"date-parts":[[2018,1,2]],"date-time":"2018-01-02T00:00:00Z","timestamp":1514851200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100007052","name":"Universit\u00e0 degli Studi di Verona","doi-asserted-by":"publisher","award":["Ph.D. Grant \u201cComputational Mathematics and Biology\u201d"],"award-info":[{"award-number":["Ph.D. Grant \u201cComputational Mathematics and Biology\u201d"]}],"id":[{"id":"10.13039\/501100007052","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Algorithmica"],"published-print":{"date-parts":[[2018,12]]},"DOI":"10.1007\/s00453-017-0402-5","type":"journal-article","created":{"date-parts":[[2018,1,2]],"date-time":"2018-01-02T13:40:47Z","timestamp":1514900447000},"page":"3525-3562","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["An Improved Upper Bound on Maximal Clique Listing via Rectangular Fast Matrix Multiplication"],"prefix":"10.1007","volume":"80","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5748-2029","authenticated-orcid":false,"given":"Carlo","family":"Comin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Romeo","family":"Rizzi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,1,2]]},"reference":[{"key":"402_CR1","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/0166-218X(95)00026-N","volume":"65","author":"D Avis","year":"1993","unstructured":"Avis, D., Fukuda, K.: Reverse search for enumeration. Discrete Appl. Math. 65, 21\u201346 (1993)","journal-title":"Discrete Appl. Math."},{"issue":"9","key":"402_CR2","doi-asserted-by":"publisher","first-page":"575","DOI":"10.1145\/362342.362367","volume":"16","author":"C Bron","year":"1973","unstructured":"Bron, C., Kerbosch, J.: Finding all cliques of an undirected graph (algorithm 457). Commun. ACM 16(9), 575\u2013576 (1973). https:\/\/doi.org\/10.1145\/362342.362367","journal-title":"Commun. ACM"},{"issue":"1","key":"402_CR3","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1007\/s00453-012-9632-8","volume":"66","author":"L Chang","year":"2013","unstructured":"Chang, L., Yu, J.X., Qin, L.: Fast maximal cliques enumeration in sparse graphs. Algorithmica 66(1), 173\u2013186 (2013). https:\/\/doi.org\/10.1007\/s00453-012-9632-8","journal-title":"Algorithmica"},{"issue":"1","key":"402_CR4","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1137\/0214017","volume":"14","author":"N Chiba","year":"1985","unstructured":"Chiba, N., Nishizeki, T.: Arboricity and subgraph listing algorithms. SIAM J. Comput. 14(1), 210\u2013223 (1985)","journal-title":"SIAM J. Comput."},{"key":"402_CR5","unstructured":"Conte, A., Grossi, R., Marino, A., Versari, L.: Sublinear-space bounded-delay enumeration for massive network analytics: maximal cliques. In: 43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016, Rome, Italy, 11\u201315 July 2016, pp. 148:1\u2013148:15 (2016). https:\/\/doi.org\/10.4230\/LIPIcs.ICALP.2016.148"},{"key":"402_CR6","doi-asserted-by":"publisher","first-page":"3.1:3.1","DOI":"10.1145\/2543629","volume":"18","author":"D Eppstein","year":"2013","unstructured":"Eppstein, D., L\u00f6ffler, M., Strash, D.: Listing all maximal cliques in large sparse real-world graphs. J. Exp. Algorithm. 18, 3.1:3.1\u20133.1:3.21 (2013). https:\/\/doi.org\/10.1145\/2543629","journal-title":"J. Exp. Algorithm."},{"key":"402_CR7","doi-asserted-by":"crossref","unstructured":"Gall, F.L.: Faster algorithms for rectangular matrix multiplication. In: 53rd Annual IEEE Symposium on Foundations of Computer Science, FOCS 2012, New Brunswick, NJ, USA, 20\u201323 Oct 2012, pp. 514\u2013523 (2012)","DOI":"10.1109\/FOCS.2012.80"},{"key":"402_CR8","doi-asserted-by":"crossref","unstructured":"Gall, F.L.: Powers of tensors and fast matrix multiplication. In: International Symposium on Symbolic and Algebraic Computation, ISSAC \u201914, Kobe, Japan, 23\u201325 July 2014, pp. 296\u2013303 (2014)","DOI":"10.1145\/2608628.2608664"},{"issue":"2","key":"402_CR9","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1006\/jcom.1998.0476","volume":"14","author":"X Huang","year":"1998","unstructured":"Huang, X., Pan, V.Y.: Fast rectangular matrix multiplication and applications. J. Complex. 14(2), 257\u2013299 (1998)","journal-title":"J. Complex."},{"key":"402_CR10","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/0020-0190(88)90065-8","volume":"27","author":"D Johnson","year":"1988","unstructured":"Johnson, D., Yanakakis, M., Papadimitriou, C.: On generating all maximal independent sets. Inf. Proc. Lett. 27, 119\u2013123 (1988)","journal-title":"Inf. Proc. Lett."},{"key":"402_CR11","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1007\/978-3-540-27810-8_23","volume-title":"Algorithm Theory: SWAT 2004. Lecture Notes in Computer Science","author":"K Makino","year":"2004","unstructured":"Makino, K., Uno, T.: New algorithms for enumerating all maximal cliques. In: Hagerup, T., Katajainen, J. (eds.) Algorithm Theory: SWAT 2004. Lecture Notes in Computer Science, vol. 3111, pp. 260\u2013272. Springer, Berlin (2004)"},{"key":"402_CR12","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/BF02760024","volume":"3","author":"J Moon","year":"1965","unstructured":"Moon, J., Moser, L.: On cliques in graphs. Isr. J. Math. 3, 23\u201328 (1965)","journal-title":"Isr. J. Math."},{"key":"402_CR13","unstructured":"Takeaki, U.: Two general methods to reduce delay and change of enumeration algorithms. Technical Report E4, National Institute of Informatics, Japan (2003)"},{"issue":"1","key":"402_CR14","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1016\/j.tcs.2006.06.015","volume":"363","author":"E Tomita","year":"2006","unstructured":"Tomita, E., Tanaka, A., Takahashi, H.: The worst-case time complexity for generating all maximal cliques and computational experiments. Theor. Comput. Sci. 363(1), 28\u201342 (2006). https:\/\/doi.org\/10.1016\/j.tcs.2006.06.015","journal-title":"Theor. Comput. Sci."},{"issue":"3","key":"402_CR15","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1137\/0206036","volume":"6","author":"S Tsukiyama","year":"1977","unstructured":"Tsukiyama, S., Ide, M., Ariyoshi, H., Shirakawa, I.: A new algorithm for generating all the maximal independent sets. SIAM J. Comput. 6(3), 505\u2013517 (1977)","journal-title":"SIAM J. Comput."}],"container-title":["Algorithmica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00453-017-0402-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00453-017-0402-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00453-017-0402-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,29]],"date-time":"2025-06-29T09:59:02Z","timestamp":1751191142000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00453-017-0402-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,2]]},"references-count":15,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2018,12]]}},"alternative-id":["402"],"URL":"https:\/\/doi.org\/10.1007\/s00453-017-0402-5","relation":{},"ISSN":["0178-4617","1432-0541"],"issn-type":[{"value":"0178-4617","type":"print"},{"value":"1432-0541","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1,2]]}}}