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Scanning and Traversing: Maintaining Data for Traversals in a Memory Hierarchy

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Algorithms — ESA 2002 (ESA 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2461))

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Abstract

We study the problem of maintaining a dynamic ordered set subject to insertions, deletions, and traversals of k consecutive elements. This problem is trivially solved on a RAM and on a simple two-level memory hierarchy. We explore this traversal problem on more realistic memory models: the cache-oblivious model, which applies to unknown and multi-level memory hierarchies, and sequential-access models, where sequential block transfers are less expensive than random block transfers.

Supported in part by HRL Laboratories, NSF Grant EIA-0112849, and Sandia National Laboratories.

Supported in part by NSF Grants CCR-9800085 and CCR-0105678.

Supported in part by NSF Grant EIA-0112849.

Supported in part by NSF Grant CCR-9820879.

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References

  1. A. Aggarwal and J. S. Vitter. The input/output complexity of sorting and related problems. CACM, 31(9):1116–1127, Sept. 1988.

    MathSciNet  Google Scholar 

  2. L. Arge, M. A. Bender, E. D. Demaine, B. Holland-Minkley, and J. I. Munro. Cache-oblivious priority queue and graph algorithm applications. In STOC, 2002.

    Google Scholar 

  3. M. A. Bender, R. Cole, E.D. Demaine, and M. Farach-Colton. Two simplified algorithms for maintaining order in a list. In ESA, 2002.

    Google Scholar 

  4. M. A. Bender, E. Demaine, and M. Farach-Colton. Cache-oblivious search trees. In FOCS, 2000.

    Google Scholar 

  5. M. A. Bender, E.D. Demaine, and M. Farach-Colton. Efficient tree layout in a multilevel memory hierarchy. In ESA, 2002.

    Google Scholar 

  6. M. A. Bender, Z. Duan, J. Iacono, and J. Wu. A locality-preserving cacheoblivious dynamic dictionary. In SODA, 2002.

    Google Scholar 

  7. G. S. Brodal, R. Fagerberg, and R. Jacob. Cache oblivious search trees via binary trees of small height (extended abstract). In SODA, 2002.

    Google Scholar 

  8. P. Dietz. Maintaining order in a linked list. In STOC, 1982.

    Google Scholar 

  9. P. Dietz, J. I. Seiferas, and J. Zhang. At ight lower bound for on-line monotonic list labeling. In SWAT, 1994.

    Google Scholar 

  10. P. Dietz and J. Zhang. Lower bounds for monotonic list labeling. In SWAT, 1990.

    Google Scholar 

  11. P. F. Dietz and D.D. Sleator. Two algorithms for maintaining order in a list00. In STOC, 1987.

    Google Scholar 

  12. M. Farach-Colton, P. Ferragina, and S. Muthukrishnan. Overcoming the memory bottleneck in suffix tree construction. In FOCS, 1998.

    Google Scholar 

  13. W.R. Franklin. Padded lists: Set operations in expected O(log logN) time. IPL, 9(4):161–166, 1979.

    Article  MathSciNet  Google Scholar 

  14. M. Frigo, C. E. Leiserson, H. Prokop, and S. Ramachandran. Cache-oblivious algorithms. In FOCS, 1999.

    Google Scholar 

  15. J. Gray and G. Graefe. The five minute rule ten years later. SIGMOD Record, 26(4), 1997.

    Google Scholar 

  16. M. Hofri and A.G. Konheim. Padded lists revisited. SICOMP, 16:1073, 1987.

    MATH  MathSciNet  Google Scholar 

  17. A. Itai, A.G. Konheim, and M. Rodeh. A sparse table implementation of priority queues. In S. Even and O. Kariv, editors, ICALP, 1981.

    Google Scholar 

  18. R. Ladner, J. Fix, and A. LaMarca. Cache performance analysis of algorithms. In SODA, 1999.

    Google Scholar 

  19. A. LaMarca and R.E. Ladner. The influence of caches on the performance of sorting. Journal of Algorithms, 31:66–104, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  20. R. Melville and D. Gries. Controlled density sorting. IPL, 10:169–172, 1980.

    Article  MATH  Google Scholar 

  21. D. Patterson and K. Keeton. Hardware technology trends and database opportunities. In SIGMOD, 1998. Keynote address.

    Google Scholar 

  22. H. Prokop. Cache-oblivious algorithms. Master’s thesis, MIT, 1999.

    Google Scholar 

  23. V. Raman. Locality preserving dictionaries: theory and application to clustering in databases. In PODS, 1999.

    Google Scholar 

  24. S. Sen and S. Chatterjee. Towards a theory of cache-efficient algorithms. In SODA, 2000.

    Google Scholar 

  25. D.D. Sleator and R. E. Tarjan. Amortized efficiency of list update and paging rules. CACM, 28(2):202–208, 1985.

    MathSciNet  Google Scholar 

  26. D.D. Sleator and R. E. Tarjan. Self-adjusting binary search trees. Journal of the ACM, 32(3):652–686, July 1985.

    Article  MATH  MathSciNet  Google Scholar 

  27. A. Tsakalidis. Maintaining order in a generalized linked list. Acta Informatica, 21(1):101–112, May 1984.

    Article  MATH  MathSciNet  Google Scholar 

  28. J. S. Vitter. External memory algorithms. LNCS, 1461, 1998.

    Google Scholar 

  29. D. E. Willard. Maintaining dense sequential files in a dynamic environment. In STOC, 1982.

    Google Scholar 

  30. D. E. Willard. Good worst-case algorithms for inserting and deleting records in dense sequential files. In SIGMOD, 1986.

    Google Scholar 

  31. D. E. Willard. Ad ensity control algorithm for doing insertions and deletions in a sequentially ordered file in good worst-case time. Information and Computation, 97(2):150–204, Apr. 1992.

    Article  MATH  MathSciNet  Google Scholar 

  32. J. Zhang. Density control and on-line labeling problems. Technical Report TR481, University of Rochester, Computer Science Department, Dec. 1993.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Google Inc., 2400 Bayshore Parkway, 94043, Mountain View, CA, USA

    4Martin Farach-Colton

  2. Department of Computer Science, Rutgers University, Piscataway, 08855, NJ, USA

    4Martin Farach-Colton

  3. Department of Computer Science, State University of New York at Stony Brook, Stony Brook, 11794-4400, NY, USA

    Michael A. Bender

  4. Courant Institute, New York University, 251 Mercer Street, 10012, New York, NY, USA

    Richard Cole

  5. MIT Laboratory for Computer Science, 200 Technology Square, Cambridge, 02139, MA, USA

    Erik D. Demaine

Authors
  1. Michael A. Bender
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  2. Richard Cole
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  3. Erik D. Demaine
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  4. 4Martin Farach-Colton
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Editor information

Editors and Affiliations

  1. Fakultät II: Mathematik und Naturwissenschaften, Technische Universität Berlin, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Rolf Möhring

  2. Department of Mathematics and Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Rajeev Raman

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© 2002 Springer-Verlag Berlin Heidelberg

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Bender, M.A., Cole, R., Demaine, E.D., Farach-Colton, 4. (2002). Scanning and Traversing: Maintaining Data for Traversals in a Memory Hierarchy. In: Möhring, R., Raman, R. (eds) Algorithms — ESA 2002. ESA 2002. Lecture Notes in Computer Science, vol 2461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45749-6_16

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  • DOI: https://doi.org/10.1007/3-540-45749-6_16

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44180-9

  • Online ISBN: 978-3-540-45749-7

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