{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T08:25:43Z","timestamp":1759134343564},"publisher-location":"Berlin\/Heidelberg","reference-count":18,"publisher":"Springer-Verlag","isbn-type":[{"type":"print","value":"354055422X"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/bfb0038664","type":"book-chapter","created":{"date-parts":[[2006,1,25]],"date-time":"2006-01-25T14:11:55Z","timestamp":1138198315000},"page":"169-185","source":"Crossref","is-referenced-by-count":7,"title":["Recognizing and parallelizing bounded recurrences"],"prefix":"10.1007","author":[{"given":"D.","family":"Callahan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"11_CR1","doi-asserted-by":"crossref","unstructured":"J. R. Allen, D. Callahan, and K. Kennedy. Automatic decomposition of scientific programs for parallel execution. In Conference Record of the Fourteenth ACM Symposium on the Principles of Programming Languages, Munich, West Germany, January 1987.","DOI":"10.1145\/41625.41631"},{"issue":"4","key":"11_CR2","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1145\/29873.29875","volume":"9","author":"J. R. Allen","year":"1987","unstructured":"J. R. Allen and K. Kennedy. Automatic translation of FORTRAN programs to vector form. ACM Transactions on Programming Languages and Systems, 9(4):491\u2013542, October 1987.","journal-title":"ACM Transactions on Programming Languages and Systems"},{"key":"11_CR3","doi-asserted-by":"crossref","unstructured":"J. R. Allen, K. Kennedy, C. Porterfield, and J. Warren. Conversion of control dependence to data dependence. In Conference Record of the Tenth ACM Symposium on the Principles of Programming Languages, Austin, Tx., January 1983.","DOI":"10.1145\/567067.567085"},{"key":"11_CR4","doi-asserted-by":"crossref","unstructured":"R. Alverson, D. Callahan, D. Cummings, B. Koblenz, A. Porterfield, and B. Smith. The Tera computer system. In Proceedings of the International Conference on Supercomputing, Amsterdam, 1990.","DOI":"10.1145\/77726.255132"},{"issue":"9","key":"11_CR5","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1109\/TC.1979.1675434","volume":"C-28","author":"U. Banerjee","year":"1979","unstructured":"U. Banerjee, S. C. Chen, D. Kuck, and R. Towle. Time and parallel processor bounds for Fortran-like loops. IEEE Transactions on Computers, C-28(9):660\u2013670, September 1979.","journal-title":"IEEE Transactions on Computers"},{"issue":"3","key":"11_CR6","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1145\/24039.24041","volume":"9","author":"J. Ferrante","year":"1987","unstructured":"J. Ferrante, K. J. Ottenstein, and J. D. Warren. The program dependence graph and its use in optimization. ACM Transactions on Programming Languages and Systems, 9(3):319\u2013349, July 1987.","journal-title":"ACM Transactions on Programming Languages and Systems"},{"issue":"4","key":"11_CR7","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1137\/0713042","volume":"13","author":"D. Heller","year":"1976","unstructured":"D. Heller. Some aspects of cyclic reduction algorithm for block tridiagonal systems. SIAM Journal of Numerical Analysis, 13(4):484\u2013496, 1976.","journal-title":"SIAM Journal of Numerical Analysis"},{"issue":"8","key":"11_CR8","doi-asserted-by":"crossref","first-page":"786","DOI":"10.1109\/TC.1973.5009159","volume":"C-22","author":"P. M. Kogge","year":"1973","unstructured":"P. M. Kogge and H. S. Stone. A parallel algorithm for the efficient solution of a general class of recurrence equations. IEEE Transactions on Computers, C-22(8):786\u2013792, August 1973.","journal-title":"IEEE Transactions on Computers"},{"key":"11_CR9","doi-asserted-by":"crossref","unstructured":"C. Kruskal, L. Rudolph, and M. Snir. The power of parallel prefix. In Proceedings of the 1985 International Conference on Parallel Processing, pages 180\u2013183, August 1985.","DOI":"10.1109\/TC.1985.6312202"},{"key":"11_CR10","unstructured":"D. J. Kuck, R. H. Kuhn, B. Leasure, D. A. Padua, and M. Wolfe. Compiler transformation of dependence graphs. In Conference Record of the Tenth ACM Symposium on the Principles of Programming Languages, Williamsburg, Va, January 1983."},{"issue":"4","key":"11_CR11","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1145\/322217.322232","volume":"27","author":"R. E. Ladner","year":"1980","unstructured":"R. E. Ladner and M. J. Fisher. Parallel prefix computation. Journal of the ACM, 27(4):831\u2013839, October 1980.","journal-title":"Journal of the ACM"},{"key":"11_CR12","unstructured":"F. H. McMahon. The Livermore Fortran kernels: A computer test of the numerical performance range. Technical Report UCRL-53745, Lawrence Livermore National Laboratory, December 1986."},{"key":"11_CR13","doi-asserted-by":"crossref","unstructured":"A. Nicolau and H. Wang. Optimal schedules for parallel prefix computation with bounded resources. In Third ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, April 1991.","DOI":"10.1145\/109625.109627"},{"key":"11_CR14","doi-asserted-by":"crossref","unstructured":"S. S. Pinter and R. Y. Pinter. Program optimization and parallelization using idioms. In Conference Record of the Eighteenth ACM Symposium on the Principles of Programming Languages, January 1991.","DOI":"10.1145\/99583.99597"},{"key":"11_CR15","unstructured":"G. Rodrigue, editor. Parallel Computations. Academic Press, !982."},{"issue":"6","key":"11_CR16","doi-asserted-by":"crossref","first-page":"1101","DOI":"10.1137\/0714076","volume":"14","author":"A. Sameh","year":"1977","unstructured":"A. Sameh and R. Brent. Solving triangular systems of equations. SIAM Journal of Numerical Analysis, 14(6):1101\u20131113, 1977.","journal-title":"SIAM Journal of Numerical Analysis"},{"key":"11_CR17","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/0196-6774(86)90003-9","volume":"7","author":"M. Snir","year":"1986","unstructured":"M. Snir. Depth-size trade-offs for parallel prefix computation. Journal of Algorithms, 7:185\u2013201, 1986.","journal-title":"Journal of Algorithms"},{"issue":"1","key":"11_CR18","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/BF00162343","volume":"4","author":"Y. Tanaka","year":"1990","unstructured":"Y. Tanaka, K. Iwasawa, Y. Umetani, and S. Gotou. Compiling techniques for first-order linear recurrences on a vector computer. The Journal of Supercomputing, 4(1):63\u201382, March 1990.","journal-title":"The Journal of Supercomputing"}],"container-title":["Lecture Notes in Computer Science","Languages and Compilers for Parallel Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BFb0038664.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,9]],"date-time":"2020-12-09T22:23:32Z","timestamp":1607552612000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BFb0038664"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["354055422X"],"references-count":18,"URL":"https:\/\/doi.org\/10.1007\/bfb0038664","relation":{},"subject":[]}}