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For scientific applications, reordering computation by certain space-filling curves can significantly improve data reuse because of the locality properties of these curves. However, when space-filling curves are used in programs for reordering data, traversal or indexing of the curves must be efficient. To address this problem, we present the table-driven framework SFCGen to efficiently generate multi-dimensional space-filling curves on the fly. The framework is general and easy enough to be used in any application that can be partitioned recursively in multiple dimensions. We describe a movement specification table, a universal turtle algorithm to enumerate points along a space-filling curve, a table-based indexing algorithm to transform coordinates of a point into its position along the curve and an algorithm to pregenerate the table automatically. As examples, we show how high-dimensional Hilbert, Morton, and Peano curves and a two-dimensional Sierpi\u0144ski curve can be generated with our algorithms. We present performance results for Hilbert, Morton, and Peano curves and compare the efficiency of our curve generation algorithm with the most recent work on generating Hilbert curves. Our experimental results on three modern microprocessor-based platforms show that SFCGen performs up to 63% faster than the most recent recursive algorithm on 2D curve generation and up to a factor of 132 faster than two previous byte-oriented non-recursive implementations. On curve indexing, SFCGen performs as much as a factor of three faster than the byte-oriented implementation. Our results on 4D space-filling curves also show that SFCGen scales very well with curve level for higher dimensional spaces.<\/jats:p>","DOI":"10.1145\/1055531.1055537","type":"journal-article","created":{"date-parts":[[2005,8,3]],"date-time":"2005-08-03T08:30:55Z","timestamp":1123057855000},"page":"120-148","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":38,"title":["SFCGen: A framework for efficient generation of multi-dimensional space-filling curves by recursion"],"prefix":"10.1145","volume":"31","author":[{"given":"Guohua","family":"Jin","sequence":"first","affiliation":[{"name":"Rice University, Houston, TX"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"John","family":"Mellor-Crummey","sequence":"additional","affiliation":[{"name":"Rice University, Houston, TX"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2005,3]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1080\/02693799008941526","article-title":"A comparative analysis of some two-dimensional orderings","volume":"4","author":"Abel D. 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Space-filling curves: Their generation and their application to bandwidth reduction . IEEE Trans. Info. Theory IT-15 , 6 ( Nov. ), 658 -- 664 . Bially, T. 1969. Space-filling curves: Their generation and their application to bandwidth reduction. IEEE Trans. Info. Theory IT-15, 6 (Nov.), 658--664.","journal-title":"IEEE Trans. Info. Theory IT-15"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/502807.502809"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/290200.290219"},{"volume-title":"Proceedings of 2000 ACM\/IEEE Conference on Supercomputing","author":"Browne S.","key":"e_1_2_1_8_1","unstructured":"Browne , S. , Dongarra , J. , Garner , N. , London , K. , and Mucci , P . 2000. A scalable cross-platform infrastructure for application performance tuning using hardware counters . In Proceedings of 2000 ACM\/IEEE Conference on Supercomputing . Dallas, TX. Browne, S., Dongarra, J., Garner, N., London, K., and Mucci, P. 2000. A scalable cross-platform infrastructure for application performance tuning using hardware counters. In Proceedings of 2000 ACM\/IEEE Conference on Supercomputing. Dallas, TX."},{"key":"e_1_2_1_9_1","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1016\/S0019-9958(68)90367-7","article-title":"Space filling curves and mathematical programming","volume":"12","author":"Butz A. R.","year":"1968","unstructured":"Butz , A. R. 1968 . Space filling curves and mathematical programming . Information and Control 12 , 314 -- 330 . Butz, A. R. 1968. Space filling curves and mathematical programming. Information and Control 12, 314--330.","journal-title":"Information and Control"},{"key":"e_1_2_1_10_1","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1016\/S0022-0000(69)80010-3","article-title":"Convergence with Hilbert's space filling curve","volume":"3","author":"Butz A. R.","year":"1969","unstructured":"Butz , A. R. 1969 . Convergence with Hilbert's space filling curve . J. 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C., Cox, A., and Zwaenepoel, W. 2000. Improving fine-grained irregular shared-memory benchmarks by data reordering. In Proceedings of the 2000 ACM\/IEEE Conference on Supercomputing. Dallas, TX."},{"key":"e_1_2_1_19_1","volume-title":"Proceedings of the 1990 ACM SIGMOD Conference. 332--342","author":"Jagadish H. V.","year":"1990","unstructured":"Jagadish , H. V. 1990 . Linear clustering of objects with multiple attributes . In Proceedings of the 1990 ACM SIGMOD Conference. 332--342 . 10.1145\/93597.98742 Jagadish, H. V. 1990. Linear clustering of objects with multiple attributes. In Proceedings of the 1990 ACM SIGMOD Conference. 332--342. 10.1145\/93597.98742"},{"key":"e_1_2_1_20_1","volume-title":"Proceedings of the 2001 ACM\/IEEE Conference on Supercomputing","author":"Jin G.","year":"2034","unstructured":"Jin , G. , Mellor-Crummey , J. , and Fowler , R . 2001. Increasing temporal locality with skewing and recursive blocking . 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H.","year":"1996","unstructured":"Lamarque , C. H. and Robert , F. 1996 . Image analysis using space-filling curves and 1D wavelet bases . Pattern Recognition 29 , 8, 1309 -- 1322 . Lamarque, C. H. and Robert, F. 1996. Image analysis using space-filling curves and 1D wavelet bases. Pattern Recognition 29, 8, 1309--1322.","journal-title":"Pattern Recognition"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/373626.373678"},{"key":"e_1_2_1_25_1","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1016\/0022-5193(68)90079-9","article-title":"Mathematical models for cellular interaction in development, parts I and II","volume":"18","author":"Lindenmayer A.","year":"1968","unstructured":"Lindenmayer , A. 1968 . Mathematical models for cellular interaction in development, parts I and II . J. Theore. Biol. 18 , 280 -- 315 . Lindenmayer, A. 1968. Mathematical models for cellular interaction in development, parts I and II. J. Theore. Biol. 18, 280--315.","journal-title":"J. Theore. Biol."},{"key":"e_1_2_1_26_1","doi-asserted-by":"crossref","unstructured":"Matias Y. and Shamir A. 1987. A video scrambling technique based on space filling curve. In Advances in Cryptology---CRYPTO'89. 398--416.   Matias Y. and Shamir A. 1987. A video scrambling technique based on space filling curve. In Advances in Cryptology---CRYPTO'89. 398--416.","DOI":"10.1007\/3-540-48184-2_35"},{"volume-title":"Proceedings of the 13th ACM International Conference on Supercomputing","author":"Mellor-Crummey J.","key":"e_1_2_1_27_1","unstructured":"Mellor-Crummey , J. , Whalley , D. , and Kennedy , K . 1999. Improving memory hierarchy performance for irregular applications . In Proceedings of the 13th ACM International Conference on Supercomputing . Rhodes, Greece, 425--433. 10.1145\/305138.305228 Mellor-Crummey, J., Whalley, D., and Kennedy, K. 1999. Improving memory hierarchy performance for irregular applications. In Proceedings of the 13th ACM International Conference on Supercomputing. Rhodes, Greece, 425--433. 10.1145\/305138.305228"},{"volume-title":"Proceedings of the SPIE. 414--421","author":"Moghaddam B.","key":"e_1_2_1_28_1","unstructured":"Moghaddam , B. , Hintz , K. J. , and Stewart , C. V . 1991. Space-filling curves for image compression . In Proceedings of the SPIE. 414--421 . Moghaddam, B., Hintz, K. J., and Stewart, C. V. 1991. Space-filling curves for image compression. In Proceedings of the SPIE. 414--421."},{"volume-title":"Proceedings of the Tenth International Conference on Information and Knowledge Management. 512--519","author":"Mokbel M. F.","key":"e_1_2_1_29_1","unstructured":"Mokbel , M. F. and Aref , W. G . 2001. Multimedia information processing: Irregularity in multi-dimensional space-filling curves with applications in multimedia database . In Proceedings of the Tenth International Conference on Information and Knowledge Management. 512--519 . 10.1145\/502585.502671 Mokbel, M. F. and Aref, W. G. 2001. Multimedia information processing: Irregularity in multi-dimensional space-filling curves with applications in multimedia database. In Proceedings of the Tenth International Conference on Information and Knowledge Management. 512--519. 10.1145\/502585.502671"},{"key":"e_1_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1025196714293"},{"key":"e_1_2_1_31_1","unstructured":"Moore D. 2000. http:\/\/www.caam.rice.edu\/~dougm\/twiddle\/Hilbert.  Moore D. 2000. http:\/\/www.caam.rice.edu\/~dougm\/twiddle\/Hilbert."},{"key":"e_1_2_1_32_1","unstructured":"Morton G. M. 1966. A computer oriented geodetic data base and a new technique in file sequencing. Technique Report IBM Canada.  Morton G. M. 1966. A computer oriented geodetic data base and a new technique in file sequencing. Technique Report IBM Canada."},{"volume-title":"Academic","author":"Musgrave K.","key":"e_1_2_1_33_1","unstructured":"Musgrave , K. 1991. A Peano curve generation algorithm . In Graphics Gems II, J. Arvo, Ed. Academic Press , San Diego, CA , 25. Musgrave, K. 1991. A Peano curve generation algorithm. In Graphics Gems II, J. Arvo, Ed. Academic Press, San Diego, CA, 25."},{"key":"e_1_2_1_34_1","first-page":"161","article-title":"A catalog of symmetric self-similar space-filling curves","volume":"23","author":"Ohno Y.","year":"1991","unstructured":"Ohno , Y. and Ohyama , K. 1991 . A catalog of symmetric self-similar space-filling curves . J. Recreational Math. 23 , 161 -- 173 . Ohno, Y. and Ohyama, K. 1991. A catalog of symmetric self-similar space-filling curves. J. Recreational Math. 23, 161--173.","journal-title":"J. Recreational Math."},{"key":"e_1_2_1_35_1","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/BF01199438","article-title":"Sur une courbe qui remplit toute une aire plane","volume":"36","author":"Peano G.","year":"1890","unstructured":"Peano , G. 1890 . Sur une courbe qui remplit toute une aire plane . Mathematishe Annalen 36 , 157 -- 160 . Peano, G. 1890. Sur une courbe qui remplit toute une aire plane. Mathematishe Annalen 36, 157--160.","journal-title":"Mathematishe Annalen"},{"key":"e_1_2_1_36_1","doi-asserted-by":"publisher","DOI":"10.1145\/76359.76361"},{"key":"e_1_2_1_37_1","unstructured":"Prusinkiewicz P. Lindenmayer A. and Fracchia F. D. 1991. Synthesis of space-filling curves on the square grid. In Fractals in the Fundamental and Applied Sciences H. O. Peitgen J. M. Henriques and L. F. Penedo Eds. Elsevier Science Publisher BV Amsterdam The Netherlands 341--366.  Prusinkiewicz P. Lindenmayer A. and Fracchia F. D. 1991. Synthesis of space-filling curves on the square grid. In Fractals in the Fundamental and Applied Sciences H. O. Peitgen J. M. Henriques and L. F. Penedo Eds. Elsevier Science Publisher BV Amsterdam The Netherlands 341--366."},{"key":"e_1_2_1_38_1","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1080\/0020739920230309","article-title":"On the geometrization of the Peano curve and the arithmetization of the Hilbert curve","volume":"23","author":"Sagan H.","year":"1992","unstructured":"Sagan , H. 1992 . On the geometrization of the Peano curve and the arithmetization of the Hilbert curve . Int. J. Math. Educ. Sci. Tech. 23 , 403 -- 411 . Sagan, H. 1992. On the geometrization of the Peano curve and the arithmetization of the Hilbert curve. Int. J. Math. Educ. Sci. Tech. 23, 403--411.","journal-title":"Int. J. Math. Educ. Sci. Tech."},{"key":"e_1_2_1_39_1","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1080\/0020739930240405","article-title":"A three-dimensional Hilbert curve","volume":"24","author":"Sagan H.","year":"1993","unstructured":"Sagan , H. 1993 . A three-dimensional Hilbert curve . Int. J. Math. Educ. Sci. Tech. 24 , 541 -- 545 . Sagan, H. 1993. A three-dimensional Hilbert curve. Int. J. Math. Educ. Sci. Tech. 24, 541--545.","journal-title":"Int. J. Math. Educ. Sci. Tech."},{"key":"e_1_2_1_40_1","doi-asserted-by":"crossref","unstructured":"Sagan H. 1994. Space-Filling Curves. Springer-Verlag New York NY.  Sagan H. 1994. Space-Filling Curves. Springer-Verlag New York NY.","DOI":"10.1007\/978-1-4612-0871-6"},{"key":"e_1_2_1_41_1","unstructured":"Sierpi\u0144ski W. 1912. Sur une nouvelle courbe countinue qui remplit toute une aire plane. Bull. Acad. Sci. de Cracovie (Sci. math. et nat. S\u00e9rie A) 462--478.  Sierpi\u0144ski W. 1912. Sur une nouvelle courbe countinue qui remplit toute une aire plane. Bull. Acad. Sci. de Cracovie (Sci. math. et nat. S\u00e9rie A) 462--478."},{"key":"e_1_2_1_42_1","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1109\/TPAMI.1983.4767431","article-title":"Manipulation and presentation of multidimensional image data using the Peano scan","volume":"5","author":"Stevens R. J.","year":"1983","unstructured":"Stevens , R. J. , Lehar , A. F. , and Preston , F. H. 1983 . Manipulation and presentation of multidimensional image data using the Peano scan . IEEE Trans. Pattern Anal. Mach. Intell. 5 , 520 -- 526 . Stevens, R. J., Lehar, A. F., and Preston, F. H. 1983. Manipulation and presentation of multidimensional image data using the Peano scan. IEEE Trans. Pattern Anal. Mach. Intell. 5, 520--526.","journal-title":"IEEE Trans. Pattern Anal. Mach. 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