Abstract
We define external memory (or I/O) models which capture space complexity and develop a general technique for deriving I/O-space trade-offs in these models from internal memory model time-space tradeoffs. Using this technique we show strong I/O-space product lower bounds for Sorting and Element Distinctness. We also develop new space efficient external memory Sorting algorithms.
Supported in part by National Science Foundation ESS grant EIA-9870734, RI grant EIA-997287, and CAREER grant EIA-9984099. E-mail: large@cs.duke.edu.
Partially supported by the IST Programme of the EU under contract number IST-1999-14186 (ALCOM-FT). Parts of this work was done while the author was visiting Duke University and while visiting University of Toronto. E-mail: pagter@brics. dk.
Basic Research in Computer Science. Centre of the Danish National Research Foundation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Adler. New coding techniques for improved bandwidth utilization. In Proc. 37th Annual Symposium on Foundations of Computer Science, pages 173–182, 1996.
A. Aggarwal and J. S. Vitter. The Input/Output Complexity of Sorting and Related Problems. Communications of the ACM, 31(9):1116–1127, 1988.
M. Ajtai. Determinism versus Non-Determinism for Linear Time RAMs with Memory Restrictions. In Proc. Thirty-First ACM Symposium on Theory of Computing, 1999.
L. Arge. The Buffer Tree: A New Technique for Optimal I/O-Algorithms. In Proc. Workshop on Algorithms and Data Structures, LNCS 955, pages 334–345, 1995. A complete version appears as BRICS technical report RS-96-28, University of Aarhus.
L. Arge. Efficient External-Memory Data Structures and Applications. PhD thesis, University of Aarhus, 1996.
L. Arge, M. Knudsen, and K. Larsen. A General Lower Bound on the I/O-Complexity of Comparison-based Algorithms. In Proc. of the Workshop on Algorithms and Datastructures, LNCS 709, pages 83–94, 1993.
L. Arge and P. B. Miltersen. On showing lower bounds for external-memory computational geometry problems. In J. Abello and J. S. Vitter, editors, External Memory Algorithms and Visualization. AMS Press, 1999.
L. Arge and J. Pagter. I/O-Space Trade-Offs. Technical Report BRICS-RS-00-7, BRICS, University of Aarhus, Denmark, April 2000. Available via http://www.brics.dk.
P. Beame. A General Sequential Time-Space Tradeoff for Finding Unique Elements. SIAM Journal on Computing, 20:270–277, 1991.
A. Borodin and S. Cook. A Time-Space Tradeoff for Sorting on a General Sequential Model of Computation. SIAM Journal on Computing, 11(2):287–297, 1982.
A. Borodin, F. E. Fich, F. Meyer auf der Heide, E. Upfal, and A. Wigderson. A Time-Space Tradeoff for Element Distinctness. SIAM Journal on Computing, 16:97–99, 1987.
A. Borodin, M. J. Fischer, D. G. Kirkpatrick, N. A. Lynch, and M. Tompa. A Time-Space Tradeoff for Sorting on Non-Oblivious Machines. Journal of Computer and System Sciences, 22:351–364, 1981.
G. N. Frederickson. Upper Bounds for Time-Space Trade-offs in Sorting and Selection. Journal of Computer and Systems Sciences, 34:19–26, 1987.
J. W. Hong and H. T. Kung. I/O complexity: The red-blue pebble game. In Proc. ACM Symp. on Theory of Computation, pages 326–333, 1981.
M. Karchmer. Two Time-Space Tradeoffs for Element Distinctness. Theoretical Computer Science, 47:237–246, 1986.
D. E. Knuth. Sorting and Searching, volume 3 of The Art of Computer Programming. Addison-Wesley, 2nd edition, 1998.
Y. Mansour, N. Nisan, and P. Tiwari. The Computational Complexity of Universal Hashing. Theoretical Computer Science, (107):121–133, 1993.
K. Munagala and A. Ranade. I/O-complexity of graph algorithm. In Proc. Eleventh Annual ACM-SIAM Symposium on Discrete Algorithms, pages 687–694, 1999.
J. I. Munro and M. S. Paterson. Selection and Sorting with Limited Storage. Theoretical Computer Science, 12:315–323, 1980.
J. Pagter and T. Rauhe. Optimal Time-Space Trade-Offs for Sorting. In proc. 39th Annual Symposium on Foundations of Computer Science, pages 264–268, 1998.
J. E. Savage. Models of Computation. Addison-Wesley, 1998.
M. Tompa. Time-Space Tradeoffs for Straight-Line and Branching Programs. Technical Report 122/78, Department of Computer Science, University of Toronto, July 1978. Ph.D. Thesis.
J. S. Vitter. External memory algorithms and data structures. In J. Abello and J. S. Vitter, editors, External Memory Algorithms and Visualization. AMS Press, 1999.
A. C.-C. Yao. Near-optimal Time-Space Tradeoff for Element Distinctness. SIAM Journal on Computing, 23:966–975, 1994.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Arge, L., Pagter, J. (2000). I/O-Space Trade-Offs. In: Algorithm Theory - SWAT 2000. SWAT 2000. Lecture Notes in Computer Science, vol 1851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44985-X_38
Download citation
DOI: https://doi.org/10.1007/3-540-44985-X_38
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67690-4
Online ISBN: 978-3-540-44985-0
eBook Packages: Springer Book Archive