{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,22]],"date-time":"2025-05-22T04:06:48Z","timestamp":1747886808806,"version":"3.41.0"},"publisher-location":"Cham","reference-count":20,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319151465"},{"type":"electronic","value":"9783319151472"}],"license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"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":[[2015]]},"DOI":"10.1007\/978-3-319-15147-2_26","type":"book-chapter","created":{"date-parts":[[2015,3,19]],"date-time":"2015-03-19T14:46:02Z","timestamp":1426776362000},"page":"309-320","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Perfectly Nested Loop Tiling Transformations Based on the Transitive Closure of the Program Dependence Graph"],"prefix":"10.1007","author":[{"given":"Wlodzimierz","family":"Bielecki","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marek","family":"Palkowski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,3,20]]},"reference":[{"key":"26_CR1","doi-asserted-by":"crossref","unstructured":"Bastoul, C.: Code generation in the polyhedral model is easier than you think. In: IEEE International Conference on Parallel Architecture and Compilation Techniques PACT\u201913, Juan-les-Pins, pp. 7\u201316 September 2004","DOI":"10.1109\/PACT.2004.1342537"},{"key":"26_CR2","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1016\/j.parco.2010.12.005","volume":"37","author":"A Beletska","year":"2011","unstructured":"Beletska, A., Bielecki, W., Cohen, A., Palkowski, M., Siedlecki, K.: Coarse-grained loop parallelization: iteration space slicing vs affine transformations. Parallel Comput. 37, 479\u2013497 (2011)","journal-title":"Parallel Comput."},{"key":"26_CR3","doi-asserted-by":"crossref","unstructured":"Benabderrahmane, M.W., Pouchet, L.N., Cohen, A., Bastoul, C.: The polyhedral model is more widely applicable than you think. In: Proceedings of the 19th Joint European Conference on Theory and Practice of Software. International Conference on Compiler Construction, CC\u201910\/ETAPS\u201910, pp. 283\u2013303. Springer, Berlin (2010). http:\/\/dx.doi.org\/10.1007\/978-3-642-11970-5_16","DOI":"10.1007\/978-3-642-11970-5_16"},{"key":"26_CR4","unstructured":"Bielecki, W., Palkowski, M.: A parallelizing and optimizing compiler\u2014traco.\u00a0http:\/\/traco.sourceforge.net (2013)"},{"issue":"9","key":"26_CR5","doi-asserted-by":"publisher","first-page":"518","DOI":"10.1016\/j.parco.2012.06.001","volume":"38","author":"W Bielecki","year":"2012","unstructured":"Bielecki, W., Palkowski, M., Klimek, T.: Free scheduling for statement instances of parameterized arbitrarily nested affine loops. Parallel Comput. 38(9), 518\u2013532 (2012)","journal-title":"Parallel Comput."},{"issue":"6","key":"26_CR6","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1145\/1379022.1375595","volume":"43","author":"U Bondhugula","year":"2008","unstructured":"Bondhugula, U., Hartono, A., Ramanujam, J., Sadayappan, P.: A practical automatic polyhedral parallelizer and locality optimizer. SIGPLAN Not. 43(6), 101\u2013113 (2008)","journal-title":"SIGPLAN Not."},{"key":"26_CR7","unstructured":"Griebl, M.: Automatic parallelization of loop programs for distributed memory architectures (2004)"},{"key":"26_CR8","doi-asserted-by":"crossref","unstructured":"Irigoin, F., Triolet, R.: Supernode partitioning. In: Proceedings of the 15th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL\u201988, pp. 319\u2013329. ACM, New York (1988)","DOI":"10.1145\/73560.73588"},{"key":"26_CR9","unstructured":"Kelly, W., Maslov, V., Pugh, W., Rosser, E., Shpeisman, T., Wonnacott, D.: The Omega project. http:\/\/www.cs.umd.edu\/projects\/omega\/release-1.0.html"},{"issue":"6","key":"26_CR10","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1007\/BF03356760","volume":"24","author":"W Kelly","year":"1996","unstructured":"Kelly, W., Pugh, W., Rosser, E., Shpeisman, T.: Transitive closure of infinite graphs and its applications. Int. J. Parallel Program. 24(6), 579\u2013598 (1996)","journal-title":"Int. J. Parallel Program."},{"key":"26_CR11","doi-asserted-by":"crossref","unstructured":"Lim, A., Cheong, G.I., Lam, M.S.: An affine partitioning algorithm to maximize parallelism and minimize communication. In: Proceedings of the 13th ACM SIGARCH International Conference on Supercomputing, pp. 228\u2013237. ACM Press (1999)","DOI":"10.1145\/305138.305197"},{"key":"26_CR12","unstructured":"NAS benchmarks suite. http:\/\/www.nas.nasa.gov (2013)"},{"key":"26_CR13","unstructured":"The Polyhedral Benchmark suite.\u00a0http:\/\/www.cse.ohio-state.edu\/pouchet\/software\/polybench\/ (2012)"},{"key":"26_CR14","doi-asserted-by":"crossref","unstructured":"Pugh, W., Rosser, E.: Iteration space slicing and its application to communication optimization. In: International Conference on Supercomputing, pp. 221\u2013228 (1997)","DOI":"10.1145\/263580.263637"},{"key":"26_CR15","unstructured":"Verdoolaege, S.: Integer set library\u2014manual. Technical Report\u00a0http:\/\/www.kotnet.org\/skimo\/\/isl\/manual.pdf (2011)"},{"key":"26_CR16","unstructured":"Verdoolaege, S.: Barvinok: User guide. Version: barvinok-0.36.\u00a0http:\/\/garage.kotnet.org\/skimo\/barvinok\/barvinok.pdf (2012)"},{"key":"26_CR17","doi-asserted-by":"crossref","unstructured":"Verdoolaege, S., Cohen, A., Beletska, A.: Transitive closures of affine integer tuple relations and their overapproximations. In: Proceedings of the 18th International Conference on Static Analysis, SAS\u201911, pp. 216\u2013232. Springer, Berlin (2011).\u00a0http:\/\/dl.acm.org\/citation.cfm?id=2041552.2041570","DOI":"10.1007\/978-3-642-23702-7_18"},{"issue":"4","key":"26_CR18","doi-asserted-by":"publisher","first-page":"452","DOI":"10.1109\/71.97902","volume":"2","author":"ME Wolf","year":"1991","unstructured":"Wolf, M.E., Lam, M.S.: A loop transformation theory and an algorithm to maximize parallelism. IEEE Trans. Parallel Distrib. Syst. 2(4), 452\u2013471 (1991)","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"26_CR19","unstructured":"Wonnacott, D.G., Strout, M.M.: On the scalability of loop tiling techniques. In: Proceedings of the 3rd International Workshop on Polyhedral Compilation Techniques (IMPACT) (January 2013)"},{"issue":"4","key":"26_CR20","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1142\/S0129626497000401","volume":"7","author":"J Xue","year":"1997","unstructured":"Xue, J.: On tiling as a loop transformation. Parallel Process. Lett. 7(4), 409\u2013424 (1997)","journal-title":"Parallel Process. Lett."}],"container-title":["Advances in Intelligent Systems and Computing","Soft Computing in Computer and Information Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-15147-2_26","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,21]],"date-time":"2025-05-21T04:13:09Z","timestamp":1747800789000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-15147-2_26"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783319151465","9783319151472"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-15147-2_26","relation":{},"ISSN":["2194-5357","2194-5365"],"issn-type":[{"type":"print","value":"2194-5357"},{"type":"electronic","value":"2194-5365"}],"subject":[],"published":{"date-parts":[[2015]]},"assertion":[{"value":"20 March 2015","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}