
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
Masood Ahmed, Shahid Bokhari, "Mapping with Space Filling Surfaces," IEEE Transactions on Parallel and Distributed Systems, vol. 18, no. 9, pp. 12581269, September, 2007.  
BibTex  x  
@article{ 10.1109/TPDS.2007.1049, author = {Masood Ahmed and Shahid Bokhari}, title = {Mapping with Space Filling Surfaces}, journal ={IEEE Transactions on Parallel and Distributed Systems}, volume = {18}, number = {9}, issn = {10459219}, year = {2007}, pages = {12581269}, doi = {http://doi.ieeecomputersociety.org/10.1109/TPDS.2007.1049}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Parallel and Distributed Systems TI  Mapping with Space Filling Surfaces IS  9 SN  10459219 SP1258 EP1269 EPD  12581269 A1  Masood Ahmed, A1  Shahid Bokhari, PY  2007 KW  Fractals KW  Hilbert curve KW  parallel computing KW  Peano curve KW  Sierpinski carpet KW  space filling curves KW  space filling surfaces VL  18 JA  IEEE Transactions on Parallel and Distributed Systems ER   
[1] G. Cantor, “Über Unendliche, Lineare Punktmannigfaltigkeiten V,” Mathematische Annalen, vol. 21, pp. 545591, 1883.
[2] G. Peano, “Sur une Courbe, Qui Remplit Toute une Aire Plane,” Mathematische Annalen, vol. 36, pp. 157160, 1890.
[3] D. Hilbert, “Über die Stetige Abbildung Einer Linie auf Ein Flächenstück,” Mathematische Annalen, vol. 38, pp. 459460, 1891.
[4] W. Sierpiński, “Sur une Courbe Cantorienne Qui Contient une Image Biunivoque et Continue de Toute Courbe Donnée,” Comptes Rendus de l'Academie des Sciences, Paris, vol. 162, pp. 629632, 1916.
[5] B.B. Mandelbrot, The Fractal Geometry of Nature. W.H. Freeman and Co., 1977.
[6] M. Schroeder, Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise. W.H. Freeman and Co., 1991.
[7] S.H. Bokhari, T.W. Crockett, and D.M. Nicol, “Parametric Binary Dissection,” Technical Report 9339, Inst. for Computer Applications in Science and Eng., 1993.
[8] C.W. Ou, M. Gunwani, and S. Ranka, “ArchitectureIndependent LocalityImproving Transformations of Computational Graphs Embedded in kDimensions,” Proc. Ninth ACM Int'l Conf. Supercomputing, pp. 289297, July 1995.
[9] J.R. Pilkington and S.B. Baden, “Dynamic Partitioning of NonUniform Structured Workloads with Spacefilling Curves,” IEEE Trans. Parallel and Distributed Systems, vol. 7, no. 3, pp. 288300, Mar. 1996.
[10] S. Aluru and F. Sevilgen, “Parallel Domain Decomposition and Load Balancing Using SpaceFilling Curves,” Proc. Fourth IEEE Int'l Conf. High Performance Computing, pp. 230235, 1997.
[11] S. Chatterjee, A. Lebeck, P. Patnala, and M. Thottethodi, “Recursive Array Layouts and Fast Parallel Matrix Multiplication,” Proc. Ann. ACM Symp. Parallel Algorithms and Architectures (SPAA), pp. 222231, 1999.
[12] Y. Zhu and Y. Hu, “Efficient, ProximityAware Load Balancing for DHTBased P2P Systems,” IEEE Trans. Parallel and Distributed Systems, vol. 16, no. 4, pp. 349361, Apr. 2005.
[13] J.K. Lawder, “Calculation of Mappings between One and nDimensional Values Using the Hilbert SpaceFilling Curve,” www.dcs.bbk.ac.uk/TriStarp/pubsJL1_00.ps.Z , Aug. 2000.
[14] J.J. Bartholdi III and P. Goldsman, “VertexLabeling Algorithms for the Hilbert Spacefilling Curve,” Software—Practice and Experience, vol. 31, no. 5, pp. 395408, 2001.
[15] M.F. Mokbel, W.G. Aref, and I. Kamel, “Performance of MultiDimensional SpaceFilling Curves,” Proc. 10th ACM Int'l Symp. Advances in Geographical Infomation Systems, pp. 149154, 2002.
[16] R. Niedermeier, K. Reinhardt, and P. Sanders, “Towards Optimal Locality in MeshIndexings,” Discrete Applied Mathematics, vol. 117, no. 13, pp. 211237, 2002.
[17] H.V. Jagadish, “Analysis of the Hilbert Curve for Representing TwoDimensional Space,” Information Processing Letters, vol. 62, pp. 1722, 1997.
[18] B. Moon, H.V. Jagadish, C. Faloutsos, and J.H. Saltz, “Analysis ofthe Clustering Properties of the Hilbert SpaceFilling Curve,” IEEE Trans. Knowledge and Data Eng., vol. 13, no. 1, pp. 124141, Jan.Feb. 2001.
[19] T. Kurç, Ü. Çatalyürek, C. Chang, A. Sussman, and J. Saltz, “Visualization of Large Data Sets with the Active Data Repository,” IEEE Computer Graphics and Applications, vol. 21, pp. 2433, July/Aug. 2001.
[20] A. Alhosni and S.Y. Berkovich, “Application of Lebesgue Space Filling Curve in Progressive Image Transmission,” Proc. Third IASTED Int'l Conf. Visualization, Imaging, and Image Processing, Sept. 2003.
[21] M. Quweider and E. Salari, “Use of Space Filling Curves in Fast Encoding of VQ Images,” Proc. Int'l Conf. Image Processing, vol. 3, p.3101, 1995.
[22] S. Patil, S.R. Das, and A. Nasipuri, “Serial Data Fusion Using SpaceFilling Curves in Wireless Sensor Networks,” Proc. IEEE Comm. Soc. Conf. Sensors and Ad Hoc Comm. and Networks, vol. 1, pp. 182190, Oct. 2004.
[23] M.J. Aftosmis, M.J. Berger, and S. Murman, “Applications of Space Filling Curves to Cartesian Methods for CFD,” Proc. 42nd AIAA Aerospace Sciences Meeting, 2004.
[24] D.J. Mavriplis, M.J. Aftosmis, and M. Berger, “High Resolution Aerospace Applications Using the NASA Columbia Supercomputer,” Proc. Conf. HighPerformance Networking and Computing (SC '05), Nov. 2005.
[25] J.M. Dennis, “Partitioning with SpaceFilling Curves on the CubedSphere,” Proc. 17th Int'l Parallel and Distributed Processing Symp. (IPDPS '03), p. 269, Apr.2226, 2003.
[26] G. Jin and J. MellorCrummey, “Sfcgen: A Framework for Efficient Generation of MultiDimensional SpaceFilling Curves by Recursion,” ACM Trans. Mathematical Software, vol. 31, pp. 120148, Mar. 2005.
[27] E. SkubalskaRafajlowicz and A. Krzyzak, “Fast kNN Classification Rule Using Metric on SpaceFilling Curves,” Proc. 13th Int'l Conf. Pattern Recognition, vol. 2, pp. 121125, 1996.
[28] H.L. Chen and Y.I. Chang, “NeighborFinding Based on SpaceFilling Curves,” Infomation Systems, vol. 30, pp. 205226, May 2005.
[29] S.H. Bokhari, “On the Mapping Problem,” IEEE Trans. Computers, vol. C30, pp. 207214, Mar. 1981.
[30] K. Falconer, Fractal Geometry: Mathematical Foundations and Applications. John Wiley & Sons, 1990.
[31] H. Sagan, SpaceFilling Curves. SpringerVerlag, 1994.
[32] “Chaotic Dynamics and Fractals,” Notes and Reports in Mathematics in Science and Engineering, M.F. Barnsley and S.G. Demko, eds., vol. 2, 1986.
[33] M.F. Barnsley, Fractals Everywhere, second ed. Academic Press, 1993.
[34] H. von Koch, “Sur Une Courbe Continue Sans Tangente, Obtenue Par une Construction Géométrique Élémentaire,” Arkiv för Matematik, vol. 1, pp. 681704, 1904.
[35] K. Menger, “Allgemeine Räume und Cartesische Räume,” Proc. Koniklijke Akademie van Wetenschappen te Amsterdam, vol. 29, pp.11251128, 1926.
[36] S.H. Bokhari, T.W. Crockett, and D.M. Nicol, “Binary Dissection: Variants and Applications,” Technical Report 9729, Inst. for Computer Applications in Science and Eng., www.compsci.wm. edu/~tom9729.pdf, 1997.
[37] C. Gotsman and M. Lindenbaum, “On the Metric Properties ofDiscrete SpaceFilling Curves,” www.cs.technion.ac.il/~gotsman/AmendedPubl/ OnTheMetricOnTheMetric.pdf, July 1996.
[38] G. Chochia and M. Cole, “Recursive 3D Mesh Indexing with Improved Locality,” Proc. Int'l Conf. and Exhibition HighPerformance Computing and Networking (HPCN Europe), pp. 10141015, 1997.
[39] A.J. Cole, “Compaction Techniques for Raster Scan Graphics Using SpaceFilling Curves,” Computer J., vol. 30, no. 1, pp.8792, 1987.