{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T08:25:41Z","timestamp":1742977541347,"version":"3.40.3"},"publisher-location":"Berlin, Heidelberg","reference-count":24,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540646822"},{"type":"electronic","value":"9783540691068"}],"license":[{"start":{"date-parts":[[1998,1,1]],"date-time":"1998-01-01T00:00:00Z","timestamp":883612800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1998]]},"DOI":"10.1007\/bfb0054375","type":"book-chapter","created":{"date-parts":[[2006,6,7]],"date-time":"2006-06-07T07:43:28Z","timestamp":1149666208000},"page":"276-287","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Determinant: Old algorithms, new insights"],"prefix":"10.1007","author":[{"given":"Meena","family":"Mahajan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"V.","family":"Vinay","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2006,5,26]]},"reference":[{"key":"26_CR1","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/0020-0190(84)90018-8","volume":"18","author":"S. J. Berkowitz","year":"1984","unstructured":"S. J. Berkowitz. On computing the determinant in small parallel time using a small number of processors. Information Processing Letters, 18:147\u2013150, 1984.","journal-title":"Information Processing Letters"},{"key":"26_CR2","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1137\/0603033","volume":"3","author":"S. Chaiken","year":"1982","unstructured":"S. Chaiken. A combinatorial proof of the all minors matrix theorem. SIAM J. Algebraic Discrete Methods, 3:319\u2013329, 1982.","journal-title":"SIAM J. Algebraic Discrete Methods"},{"key":"26_CR3","doi-asserted-by":"crossref","unstructured":"A. L. Chistov. Fast parallel calculation of the rank of matrices over a field of arbitrary characteristic. In Proc Int. Conf. Foundations of Computation Theory, LNCS 199, pages 63\u201369. Springer, 1985.","DOI":"10.1007\/BFb0028792"},{"key":"26_CR4","doi-asserted-by":"crossref","first-page":"818","DOI":"10.1137\/0205040","volume":"5","author":"L. Csanky","year":"1976","unstructured":"L. Csanky. Fast parallel inversion algorithm. SIAM J of Computing, 5:818\u2013823, 1976.","journal-title":"SIAM J of Computing"},{"key":"26_CR5","unstructured":"C. Damm. DET=L(#L). Technical Report Informatik-Preprint 8, Fachbereich Informatik der Humboldt-Universit\u00c4t zu Berlin, 1991."},{"key":"26_CR6","volume-title":"Computational Methods in Linear Algebra","author":"D. Fadeev","year":"1963","unstructured":"D. Fadeev and V. Fadeeva. Computational Methods in Linear Algebra. Freeman, San Francisco, 1963."},{"key":"26_CR7","first-page":"81","volume":"14","author":"D. Foata","year":"1965","unstructured":"D. Foata. Etude alg\u00e9brique de certains probl\u00e8mes d'analyse combinatoire et du calcul des probabilit\u00e9s. Publ. Inst. Statist. Univ. Paris, 14:81\u2013241, 1965.","journal-title":"Publ. Inst. Statist. Univ. Paris"},{"key":"26_CR8","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1016\/S0167-5060(08)70699-X","volume":"6","author":"D. Foata","year":"1980","unstructured":"D. Foata. A combinatorial proof of Jacobi's identity. Ann. Discrete Math., 6:125\u2013135, 1980.","journal-title":"Ann. Discrete Math."},{"key":"26_CR9","unstructured":"A. Garsia and \u00f6. Egecioglu. Combinatorial foundations of computer science. unpublished collection."},{"key":"26_CR10","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1002\/jgt.3190030315","volume":"3","author":"I. Gessel","year":"1979","unstructured":"I. Gessel. Tournaments and Vandermonde's determinant. J Graph Theory, 3:305\u2013307, 1979.","journal-title":"J Graph Theory"},{"key":"26_CR11","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4400-4","volume-title":"The Design and Analysis of Algorithms","author":"D. Kozen","year":"1992","unstructured":"D. Kozen. The Design and Analysis of Algorithms. Springer-Verlag, New York, 1992."},{"key":"26_CR12","volume-title":"Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes","author":"T. F. Leighton","year":"1992","unstructured":"T. F. Leighton. Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes. Morgan Kaufmann Publishers Inc., San Mateo, 1992."},{"key":"26_CR13","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1016\/S0012-365X(96)00015-5","volume":"171","author":"M. Minoux","year":"1997","unstructured":"M. Minoux. Bideterminants, arborescences and extension of the matrix-tree theorem to semirings. Discrete Mathematics, 171:191\u2013200, 1997.","journal-title":"Discrete Mathematics"},{"key":"26_CR14","first-page":"5","volume":"1997","author":"M. Mahajan","year":"1997","unstructured":"M. Mahajan and V Vinay. Determinant: combinatorics, algorithms, complexity. Chicago Journal of Theoretical Computer Science http:\/\/cs-www.uchicago.edu\/publications\/cjtcs, 1997:5, 1997. A preliminary version appeared as \u201cA combinatorial algorithm for the determinant\u201d in Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms SODA97.","journal-title":"Chicago Journal of Theoretical Computer Science"},{"key":"26_CR15","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1016\/0095-8956(78)90038-2","volume":"25","author":"J. B. Orlin","year":"1978","unstructured":"J. B. Orlin. Line-digraphs, arborescences, and theorems of Tutte and Knuth. J. Combin. Theory Ser. B, 25:187\u2013198, 1978.","journal-title":"J. Combin. Theory Ser. B"},{"key":"26_CR16","doi-asserted-by":"crossref","first-page":"424","DOI":"10.1214\/aoms\/1177731540","volume":"13","author":"P. A. Samuelson","year":"1942","unstructured":"P. A. Samuelson. A method of determining explicitly the coefficients of the characteristic polynomial. Ann. Math. Stat., 13:424\u2013429, 1942.","journal-title":"Ann. Math. Stat."},{"key":"26_CR17","first-page":"182","volume":"264","author":"V. Strassen","year":"1973","unstructured":"V. Strassen. Vermeidung von divisionen. Journal of Reine U. Angew Math, 264:182\u2013202, 1973.","journal-title":"Journal of Reine U. Angew Math"},{"key":"26_CR18","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1016\/0012-365X(83)90164-4","volume":"43","author":"H. Straubing","year":"1983","unstructured":"H. Straubing. A combinatorial proof of the Cayley-Hamilton theorem. Discrete Maths., 43:273\u2013279, 1983.","journal-title":"Discrete Maths."},{"key":"26_CR19","doi-asserted-by":"crossref","unstructured":"D. Stanton and D. White. Constructive Combinatorics. Springer-Verlag, 1986.","DOI":"10.1007\/978-1-4612-4968-9"},{"key":"26_CR20","volume-title":"Graph Theory and Applications","author":"H. N. V. Tempereley","year":"1981","unstructured":"H. N. V. Tempereley. Graph Theory and Applications. Ellis Horwood, Chichester, 1981."},{"key":"26_CR21","unstructured":"S. Toda. Counting problems computationally equivalent to the determinant. manuscript, 1991."},{"key":"26_CR22","doi-asserted-by":"crossref","unstructured":"L. G. Valiant. Why is boolean complexity theory difficult? In M. S. Paterson, editor, Boolean Function Complexity. Cambridge University Press, 1992. London Mathematical Society Lecture Notes Series 169.","DOI":"10.1017\/CBO9780511526633.008"},{"key":"26_CR23","doi-asserted-by":"crossref","unstructured":"V Vinay. Counting auxiliary pushdown automata and semi-unbounded arithmetic circuits. In Proc. 6th Structure in Complexity Theory Conference, pages 270\u2013284, 1991.","DOI":"10.1109\/SCT.1991.160269"},{"key":"26_CR24","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/0012-365X(85)90192-X","volume":"56","author":"D. Zeilberger","year":"1985","unstructured":"D. Zeilberger. A combinatorial approach to matrix algebra. Discrete Mathematics, 56:61\u201372, 1985.","journal-title":"Discrete Mathematics"}],"container-title":["Lecture Notes in Computer Science","Algorithm Theory \u2014 SWAT'98"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/BFb0054375","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,9]],"date-time":"2025-01-09T07:20:35Z","timestamp":1736407235000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/BFb0054375"}},"subtitle":["Extended abstract"],"short-title":[],"issued":{"date-parts":[[1998]]},"ISBN":["9783540646822","9783540691068"],"references-count":24,"URL":"https:\/\/doi.org\/10.1007\/bfb0054375","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[1998]]},"assertion":[{"value":"26 May 2006","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}