ISSN 2456-0235

International Journal of Modern Science and Technology

INDEXED IN 

​​International Journal of Modern Science and Technology, 1(8), 2016, Pages 264-268. 


Survey Report on Space Filling Curves 

R. Prethee, A. R. Rishivarman
Department of Mathematics, Theivanai Ammal College for Women (Autonomous), Villupuram - 605 401. Tamilnadu, India.

Abstract
Space-filling Curves have been extensively used as a mapping from the multi-dimensional space into the one-dimensional space. Space filling curve represent one of the oldest areas of fractal geometry. Mapping the multi-dimensional space into one-dimensional domain plays an important role in every application that involves multidimensional data. We describe the notion of space filling curves and describe some of the popularly used curves. There are numerous kinds of space filling curves. The difference between such curves is in their way of mapping to the one dimensional space. Selecting the appropriate curve for any application requires knowledge of the mapping scheme provided by each space filling curve. Space filling curves are the basis for scheduling has numerous advantages like scalability in terms of the number of scheduling parameters, ease of code development and maintenance. The present paper report on various space filling curves, classifications, and its applications. It elaborates the space filling curves and their applicability in scheduling, especially in transaction.

​​Keywords: Space filling curve, Holder Continuity, Bi-Measure-Preserving Property, Transaction Scheduling. 

​References

  1. Parker F. Space-Filling Curves. Math635:2008.
  2. Cole AJ. A note on space filling curves, Journal of Software: Practice and Experience. 1983;13:1181-1189.
  3. Apostal TM. Mathematical Analysis. Addison-Wesley Publishing Company; 1974.
  4. Sagan H. Space-filling curves. University Text Series; Springer-Verlag: 1994.
  5. Michael B. Peano curve, Space-Filling Curves. Texts in Computational Science and Engineering. Springer: 2012;19:25–27.
  6. Butz AR. Alternative algorithm for Hilbert's space filling curve. IEEE Transactions on Computers. 1971;3:424-426.
  7. Bially T. Space filling curves: Their generation and their application to bandwidth reduction. IEEE Transactions on Information Theory. 1969;15(6):658-664.
  8. Ahmed M, Bokhar S. Mapping with Space Filling Surfaces. IEEE Transactions on Parallel and distributed Systems. 2007;18:1258-1269.
  9. Ali MA, Ladhak SA. Overview of space-filling curves and their applications in scheduling. International Journal of Advances in Engineering and Technology. 2009;1:148-154.
  10. Abbott R, Garcia-Molina. Scheduling Real-Time Transactions with Disk Resident Data. Proceedings of 15th International Conference. 1989;87:385-396.
  11. Bamnote GR, Ali MS. Resource Scheduling in Real-time Database Systems. 2009.
  12. Mokbel MF, Aref WG. Irregularity in Multi-Dimensional Space-Filling Curves with Applications in Multimedia Databases. Proceedings of the Conference on Information and Knowledge Management. November 5-10, 2001:512-518.
  13. Mokbel MF, Aref WG. Analysis of multi-dimensional space-filling curves. GeoInformatica. 2003;7(3):179-209.
  14. Butz AR. Space filling curves and mathematical programming. Information and Control. 1968;12(4):314-330.
  15. Albert J, Niedermeier R. On multidimensional curves with Hilbert property. Theory of Computing Systems. New York; Springer-Verlag:2000.