{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T11:57:09Z","timestamp":1725537429774},"publisher-location":"Berlin, Heidelberg","reference-count":22,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642041273"},{"type":"electronic","value":"9783642041280"}],"license":[{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009]]},"DOI":"10.1007\/978-3-642-04128-0_37","type":"book-chapter","created":{"date-parts":[[2009,9,14]],"date-time":"2009-09-14T18:16:36Z","timestamp":1252952196000},"page":"408-419","source":"Crossref","is-referenced-by-count":10,"title":["A Fast Output-Sensitive Algorithm for Boolean Matrix Multiplication"],"prefix":"10.1007","author":[{"given":"Andrzej","family":"Lingas","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"issue":"2","key":"37_CR1","doi-asserted-by":"publisher","first-page":"781","DOI":"10.4007\/annals.2004.160.781","volume":"160","author":"M. Agrawal","year":"2004","unstructured":"Agrawal, M., Kayal, N., Saxena, N.: PRIMES is in P. Annals of Mathematics\u00a0160(2), 781\u2013793 (2004)","journal-title":"Annals of Mathematics"},{"key":"37_CR2","doi-asserted-by":"crossref","unstructured":"Amossen, R.R., Pagh, R.: Faster Join-Projects and Sparse Matrix Multiplication. To appear in proc. ACM International Conference on Database Theory (ICDT 2009), St. Petersburg (March 2009)","DOI":"10.1145\/1514894.1514909"},{"key":"37_CR3","first-page":"1209","volume":"11","author":"V.L. Arlazow","year":"1970","unstructured":"Arlazow, V.L., Dinic, E.A., Kronrod, M.A., Faradzev, I.A.: On economical construction of the transitive closure of an oriented graph. Soviet Math. Dokl.\u00a011, 1209\u20131210 (1970)","journal-title":"Soviet Math. Dokl."},{"key":"37_CR4","doi-asserted-by":"publisher","first-page":"434","DOI":"10.1007\/BF01940874","volume":"16","author":"N. Alon","year":"1996","unstructured":"Alon, N., Naor, M.: Derandomization, Witnesses for Boolean Matrix Multiplication and Construction of Perfect hash functions. Algorithmica\u00a016, 434\u2013449 (1996)","journal-title":"Algorithmica"},{"key":"37_CR5","unstructured":"Bash, J., Khanna, S., Motwani, R.: On Diameter Verification and Boolean Matrix Multiplication. Technical Report, Stanford University CS department (1995)"},{"key":"37_CR6","doi-asserted-by":"publisher","first-page":"630","DOI":"10.1006\/jcss.1999.1690","volume":"60","author":"A.Z. Broder","year":"2000","unstructured":"Broder, A.Z., Charikar, M., Frieze, A.M., Mitzenmacher, M.: Min-Wise Independent Permutations. Journal of Computer and System Sciences\u00a060, 630\u2013659 (2000)","journal-title":"Journal of Computer and System Sciences"},{"key":"37_CR7","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1023\/A:1009716300509","volume":"2","author":"E. Cohen","year":"1999","unstructured":"Cohen, E.: Structure Prediction and Computation of Sparse Matrix Products. Journal of Combinatorial Optimization\u00a02, 307\u2013332 (1999)","journal-title":"Journal of Combinatorial Optimization"},{"key":"37_CR8","first-page":"42","volume":"13","author":"D. Coppersmith","year":"1997","unstructured":"Coppersmith, D.: Rectangular matrix multiplication revisited. Journal of Symbolic Computation\u00a013, 42\u201349 (1997)","journal-title":"Journal of Symbolic Computation"},{"key":"37_CR9","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1016\/S0747-7171(08)80013-2","volume":"9","author":"D. Coppersmith","year":"1990","unstructured":"Coppersmith, D., Winograd, S.: Matrix Multiplication via Arithmetic Progressions. J. of Symbolic Computation\u00a09, 251\u2013280 (1990)","journal-title":"J. of Symbolic Computation"},{"key":"37_CR10","doi-asserted-by":"crossref","unstructured":"Czumaj, A., Kowaluk, M., Lingas, A.: Faster algorithms for finding lowest common ancestors in directed acyclic graphs. The special ICALP 2005 issue of Theoretical Computer Science\u00a0380(1-2), 37\u201346 (2005)","DOI":"10.1016\/j.tcs.2007.02.053"},{"key":"37_CR11","doi-asserted-by":"crossref","unstructured":"Galil, Z., Margalit, O.: Witnesses for Boolean Matrix Multiplication and Shortest Paths. Journal of Complexity, 417\u2013426 (1993)","DOI":"10.1006\/jcom.1993.1014"},{"key":"37_CR12","series-title":"The IMA Volumes in Mathematics and its Applications","volume-title":"Graph Theory and Sparse Matrix Computation","year":"1993","unstructured":"George, A., Gilbert, J., Liu, J.W.H. (eds.): Graph Theory and Sparse Matrix Computation. The IMA Volumes in Mathematics and its Applications, vol.\u00a056. Springer, Heidelberg (1993)"},{"volume-title":"Matrix Computations","year":"1989","key":"37_CR13","unstructured":"Golub, G., Van Loan, C. (eds.): Matrix Computations. The Johns Hopkins U. Press, Baltimore (1989)"},{"key":"37_CR14","doi-asserted-by":"publisher","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 multiplications and applications. Journal of Complexity\u00a014, 257\u2013299 (1998)","journal-title":"Journal of Complexity"},{"key":"37_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1007\/11523468_20","volume-title":"Automata, Languages and Programming","author":"M. Kowaluk","year":"2005","unstructured":"Kowaluk, M., Lingas, A.: LCA queries in directed acyclic graphs. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol.\u00a03580, pp. 241\u2013248. Springer, Heidelberg (2005)"},{"key":"37_CR16","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511814075","volume-title":"Randomized Algorithms","author":"R. Motwani","year":"1995","unstructured":"Motwani, R., Raghavan, P.: Randomized Algorithms. Cambridge University Press, Cambridge (1995)"},{"issue":"2","key":"37_CR17","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1016\/0020-0190(71)90006-8","volume":"1","author":"J.I. Munro","year":"1971","unstructured":"Munro, J.I.: Efficient determination of the transitive closure of a directed graph. Information Processing Letters\u00a01(2), 56\u201358 (1971)","journal-title":"Information Processing Letters"},{"issue":"1-3","key":"37_CR18","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1016\/S0019-9958(85)80024-3","volume":"67","author":"W. Rytter","year":"1985","unstructured":"Rytter, W.: Fast recognition of pushdown automaton and context-free languages. Information and Control\u00a067(1-3), 12\u201322 (1985)","journal-title":"Information and Control"},{"key":"37_CR19","unstructured":"Shapira, A., Yuster, R., Zwick, U.: All-pairs bottleneck paths in vertex weighted graphs. In: Proc. SODA 2007, pp. 978\u2013985 (2007)"},{"key":"37_CR20","doi-asserted-by":"crossref","unstructured":"Seidel, R.: On the All-Pairs-Shortest-Path Problem. In: Proc. 24th annual ACM Symposium on Theory of Computing, pp. 745\u2013749 (1992)","DOI":"10.1145\/129712.129784"},{"key":"37_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"218","DOI":"10.1007\/3-540-49543-6_18","volume-title":"Randomization and Approximation Techniques in Computer Science","author":"C.P. Schnorr","year":"1998","unstructured":"Schnorr, C.P., Subramanian, C.R.: Almost Optimal (on the average) Combinatorial Algorithms for Boolean Matrix Product Witnesses, Computing the Diameter. In: Rolim, J.D.P., Serna, M., Luby, M. (eds.) RANDOM 1998. LNCS, vol.\u00a01518, pp. 218\u2013231. Springer, Heidelberg (1998)"},{"key":"37_CR22","doi-asserted-by":"crossref","unstructured":"Yuster, R., Zwick, U.: Fast sparse matrix multiplication. ACM Transactions on Algorithms (TALG)\u00a01(1), 2\u201313 (2004) (Preliminary version in proc. ESA 2004)","DOI":"10.1145\/1077464.1077466"}],"container-title":["Lecture Notes in Computer Science","Algorithms - ESA 2009"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-04128-0_37","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,26]],"date-time":"2023-05-26T19:09:27Z","timestamp":1685128167000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-04128-0_37"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"ISBN":["9783642041273","9783642041280"],"references-count":22,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-04128-0_37","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2009]]}}}