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Cache-Oblivious Algorithms and Data Structures

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Algorithm Theory - SWAT 2004 (SWAT 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3111))

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Abstract

Frigo, Leiserson, Prokop and Ramachandran in 1999 introduced the ideal-cache model as a formal model of computation for developing algorithms in environments with multiple levels of caching, and coined the terminology of cache-oblivious algorithms. Cache-oblivious algorithms are described as standard RAM algorithms with only one memory level, i.e. without any knowledge about memory hierarchies, but are analyzed in the two-level I/O model of Aggarwal and Vitter for an arbitrary memory and block size and an optimal off-line cache replacement strategy. The result are algorithms that automatically apply to multi-level memory hierarchies. This paper gives an overview of the results achieved on cache-oblivious algorithms and data structures since the seminal paper by Frigo et al.

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References

  1. Abello, J., Buchsbaum, A.L., Westbrook, J.R.: A functional approach to external graph algorithms. Algorithmica 32(3), 437–458 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  2. Agarwal, P., Arge, L., Danner, A., Holland-Minkley, B.: Cache-oblivious data structures for orthogonal range searching. In: Proc. 19th ACM Symposium on Computational Geometry, pp. 237–245. ACM Press, New York (2003)

    Google Scholar 

  3. Aggarwal, A., Alpern, B., Chandra, A.K., Snir, M.: A model for hierarchical memory. In: Proc. 19th Annual ACM Symposium on Theory of Computing, pp. 305–314. AMC Press (1987)

    Google Scholar 

  4. Aggarwal, A., Chandra, A.: Virtual memory algorithms. In: Proc. 20th Annual ACM symposium on Theory of computing, pp. 173–185. ACM Press, New York (1988)

    Google Scholar 

  5. Aggarwal, A., Chandra, A.K., Snir, M.: Hierarchical memory with block transfer. In: Proc. 28th Annual IEEE Symposium on Foundations of Computer Science, pp. 204–216. IEEE Computer Society Press, Los Alamitos (1987)

    Google Scholar 

  6. Aggarwal, A., Vitter, J.S.: The input/output complexity of sorting and related problems. Communications of the ACM 31(9), 1116–1127 (1988)

    Article  MathSciNet  Google Scholar 

  7. Alpern, B., Carter, L., Feig, E., Selker, T.: The uniform memory hierarchy model of computation. Algorithmica 12(2–3), 72–109 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  8. Andersson, A., Lai, T.W.: Fast updating of well-balanced trees. In: Gilbert, J.R., Karlsson, R. (eds.) SWAT 1990. LNCS, vol. 447, pp. 111–121. Springer, Heidelberg (1990)

    Google Scholar 

  9. Arge, L.: External memory data structures. In: Abello, J., Pardalos, P.M., Resende, M.G.C. (eds.) Handbook of Massive Data Sets, pp. 313–358. Kluwer Academic Publishers, Dordrecht (2002)

    Google Scholar 

  10. Arge, L.: The buffer tree: A technique for designing batched external data structures. Algorithmica 37(1), 1–24 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  11. Arge, L., Bender, M.A., Demaine, E.D., Holland-Minkley, B., Munro, J.I.: Cache-oblivious priority queue and graph algorithm applications. In: Proc. 34th Annual ACM Symposium on Theory of Computing, pp. 268–276. ACM Press, New York (2002)

    Google Scholar 

  12. Arge, L., Brodal, G., Toma, L.: On external-memory MST, SSSP, and multi-way planar graph separation (Extended abstract). In: Halldórsson, M.M. (ed.) SWAT 2000. LNCS, vol. 1851, pp. 433–447. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  13. Arge, L., Brodal, G.S., Fagerberg, R.: Cache-oblivious data structures. In: Mehta, D., Sahni, S. (eds.) Handbook of Data Structures and Applications, p. 27. CRC Press, Boca Raton (2004)

    Google Scholar 

  14. Arge, L., Chase, J., Vitter, J., Wickremesinghe, R.: Efficient sorting using registers and caches. ACM Journal of Experimental Algorithmics 7(9) (2002)

    Google Scholar 

  15. Arge, L., Knudsen, M., Larsen, K.: A general lower bound on the I/Ocomplexity of comparison-based algorithms. In: Dehne, F., Sack, J.-R., Santoro, N. (eds.) WADS 1993. LNCS, vol. 709, pp. 83–94. Springer, Heidelberg (1993)

    Google Scholar 

  16. Arge, L., Chase, J., Vitter, J., Wickremesinghe, R.: Efficient sorting using registers and caches. ACM Journal of Experimental Algorithmics 7(9) (2002)

    Google Scholar 

  17. Bayer, R., McCreight, E.: Organization and maintenance of large ordered indexes. Acta Informatica 1, 173–189 (1972)

    Article  Google Scholar 

  18. Bender, M., Cole, R., Demaine, E., Farach-Colton, M.: Scanning and traversing: Maintaining data for traversals in a memory hierarchy. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 139–151. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  19. Bender, M., Cole, R., Raman, R.: Exponential structures for efficient cache-oblivious algorithms. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 195–207. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  20. Bender, M., Demaine, E., Farach-Colton, M.: Efficient tree layout in a multilevel memory hierarchy. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 165–173. Springer, Heidelberg (2002) ,Full version at http://www.cs.sunysb.edu/~bender/pub/treelayout-full.ps

  21. Bender, M.A., Brodal, G.S., Fagerberg, R., Ge, D., He, S., Hu, H., Iacono, J., López-Ortiz, A.: The cost of cache-oblivious searching. In: Proc. 44th Annual IEEE Symposium on Foundations of Computer Science, pp. 271–282. IEEE Computer Society Press, Los Alamitos (2003)

    Chapter  Google Scholar 

  22. Bender, M.A., Demaine, E., Farach-Colton, M.: Cache-oblivious B-trees. In: Proc. 41st Annual IEEE Symposium on Foundations of Computer Science, pp. 399–409. IEEE Computer Society Press, Los Alamitos (2000)

    Google Scholar 

  23. Bender, M.A., Duan, Z., Iacono, J., Wu, J.: A locality-preserving cache-oblivious dynamic dictionary. In: Proc. 13th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 29–38. ACM-SIAM (2002)

    Google Scholar 

  24. Bentley, J.L.: Multidimensional binary search trees used for associative searching. Communication of the ACM 18, 509–517 (1975)

    Article  MATH  Google Scholar 

  25. Bentley, J.L.: Decomposable searching problems. Information Processing Letters 8(5), 244–251 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  26. Bilardi, G., Peserico, E.: A characterization of temporal locality and its portability across memory hierarchies. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 128–139. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  27. Blum, M., Floyd, R.W., Pratt, V., Rivest, R.L., Tarjan, R.E.: Time bounds for selection. Journal of Computer and System Sciences 7, 448–461 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  28. Brodal, G.S., Fagerberg, R.: Cache oblivious distribution sweeping. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 426–438. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  29. Brodal, G.S., Fagerberg, R.: Funnel heap - a cache oblivious priority queue. In: Bose, P., Morin, P. (eds.) ISAAC 2002. LNCS, vol. 2518, pp. 219–228. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  30. Brodal, G.S., Fagerberg, R.: On the limits of cache-obliviousness. In: Proc. 35th ACM Symposium on Theory of Computing, pp. 307–315. ACM Press, New York (2003)

    Google Scholar 

  31. Brodal, G.S., Fagerberg, R., Jacob, R.: Cache oblivious search trees via binary trees of small height. In: Proc. 13th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 39–48. ACM-SIAM (2002)

    Google Scholar 

  32. Brodal, G.S., Fagerberg, R., Meyer, U., Zeh, N.: Cache-oblivious data structures and algorithms for undirected breadth-first search and shortest paths. In: Hagerup, T., Katajainen, J. (eds.) SWAT 2004. LNCS, vol. 3111, pp. 480–492. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  33. Brodal, G.S., Fagerberg, R., Vinther, K.: Engineering a cache-oblivious sorting algorithm. In: Proc. 6th Workshop on Algorithm Engineering and Experiments, p. 14 (2004)

    Google Scholar 

  34. Buchsbaum, A., Goldwasser, M., Venkatasubramanian, S., Westbrook, J.: On external memory graph traversal. In: Proc. 11th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 859–860. ACM Press, New York (2000)

    Google Scholar 

  35. Chatterjee, S., Jain, V.V., Lebeck, A.R., Mundhra, S., Thottethodi, M.: Nonlinear array layouts for hierarchical memory systems. In: Proc. 1999 Conference on Supercomputing, ACM SIGARCH, pp. 444–453. ACM Press, New York (1999)

    Google Scholar 

  36. Chiang, Y., Goodrich, M.T., Grove, E.F., Tamassia, R., Vengroff, D.E., Vitter, J.S.: External-memory graph algorithms. In: Proc. 6th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 139–149. ACM-SIAM (1995)

    Google Scholar 

  37. Chowdhury, R.A., Ramachandran, V.: Cache-oblivious shortest paths in graphs using buffer heap. In: Proc. 16th Annual ACM Symposium on Parallelism in Algorithms and Architectures, ACM Press, New York (2004)

    Google Scholar 

  38. Demaine, E.D.: Cache-oblivious data structures and algorithms. In: Proc. EFF summer school on massive data sets. LNCS, Springer, Heidelberg (2004)

    Google Scholar 

  39. Dietz, P.F., Zhang, J.: Lower bounds for monotonic list labeling. In: Gilbert, J.R., Karlsson, R. (eds.) SWAT 1990. LNCS, vol. 447, pp. 173–180. Springer, Heidelberg (1990)

    Google Scholar 

  40. Farzan, A., Munro, J.I.: Cache-oblivious sorting and searching in multisets (2004) (manuscript)

    Google Scholar 

  41. Franceschini, G.: Proximity mergesort: optimal in-place sorting in the cacheoblivious model. In: Proc. 15th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 291–299. ACM-SIAM (2004)

    Google Scholar 

  42. Franceschini, G., Grossi, R.: Optimal cache-oblivious implicit dictionaries. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 316–331. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  43. Franceschini, G., Grossi, R.: Optimal worst-case operations for implicit cacheoblivious search trees. In: Dehne, F., Sack, J.-R., Smid, M. (eds.) WADS 2003. LNCS, vol. 2748, pp. 114–126. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  44. Frigo, M., Leiserson, C.E., Prokop, H., Ramachandran, S.: Cache-oblivious algorithms. In: 40th Annual IEEE Symposium on Foundations of Computer Science, pp. 285–297. IEEE Computer Society Press, Los Alamitos (1999)

    Google Scholar 

  45. Goodrich, M.T., Tsay, J.-J., Vengroff, D.E., Vitter, J.S.: External-memory computational geometry. In: Proc. 34th Annual IEEE Symposium on Foundations of Computer Science, pp. 714–723. IEEE Computer Society Press, Los Alamitos (1993)

    Google Scholar 

  46. Hennessy, J.L., Patterson, D.A.: Computer Architecture: A Quantitative Approach, 3rd edn. Morgan Kaufmann, San Francisco (2002)

    MATH  Google Scholar 

  47. Hong, J.-W., Kung, H.T.: I/O complexity: The red-blue pebble game. In: Proc. 13th Annual ACM Symposium on Theory of Computation, pp. 326–333. AMC Press (1981)

    Google Scholar 

  48. Itai, A., Konheim, A.G., Rodeh, M.: A sparse table implementation of priority queues. In: Even, S., Kariv, O. (eds.) ICALP 1981. LNCS, vol. 115, pp. 417–431. Springer, Heidelberg (1981)

    Google Scholar 

  49. Kanth, K.V.R., Singh, A.K.: Optimal dynamic range searching in non-replicating index structures. In: Beeri, C., Bruneman, P. (eds.) ICDT 1999. LNCS, vol. 1540, pp. 257–276. Springer, Heidelberg (1998)

    Google Scholar 

  50. Kumar, P.: Cache oblivious algorithms. In: Meyer, U., Sanders, P., Sibeyn, J.F. (eds.) Algorithms for Memory Hierarchies. LNCS, vol. 2625, pp. 193–212. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  51. Kumar, V., Schwabe, E.J.: Improved algorithms and data structures for solving graph problems in external memory. In: Proc. 8th SPDP, pp. 169–177. IEEE Computer Society Press, Los Alamitos (1996)

    Google Scholar 

  52. Ladner, R.E., Fix, J.D., LaMarca, A.: Cache performance analysis of traversals and random accesses. In: Proc. 10th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 613–622. ACM-SIAM (1999)

    Google Scholar 

  53. Ladner, R.E., Fortna, R., Nguyen, B.-H.: A comparison of cache aware and cache oblivious static search trees using program instrumentation. In: Fleischer, R., Moret, B.M.E., Schmidt, E.M. (eds.) Experimental Algorithmics. LNCS, vol. 2547, pp. 78–92. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  54. LaMarca, A., Ladner, R.E.: The influence of caches on the performance of heaps. ACM Journal of Experimental Algorithms 1(4) (1996)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  56. LaMarca, A., Ladner, R.E.: The influence of caches on the performance of heaps. ACM Journal of Experimental Algorithms 1(4) (1996)

    Google Scholar 

  57. Meyer, U., Sanders, P., Sibeyn, J.F.: Algorithms for Memory Hierarchies. LNCS, vol. 2625. Springer, Heidelberg (2003)

    Book  MATH  Google Scholar 

  58. Munagala, K., Ranade, A.: I/O-complexity of graph algorithms. In: Proc. 10th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 687–694. ACMSIAM (1999)

    Google Scholar 

  59. Ohashi, D.: Cache oblivious data structures. Master’s thesis, Department of Computer Science, University of Waterloo, Waterloo, Canada (2000)

    Google Scholar 

  60. Prokop, H.: Cache-oblivious algorithms. Master’s thesis, Massachusetts Institute of Technology (June 1999)

    Google Scholar 

  61. Rahman, N., Cole, R., Raman, R.: Optimised predecessor data structures for internal memory. In: Brodal, G.S., Frigioni, D., Marchetti-Spaccamela, A. (eds.) WAE 2001. LNCS, vol. 2141, pp. 67–78. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  62. Savage, J.E.: Extending the Hong-Kung model to memory hierachies. In: Li, M., Du, D.-Z. (eds.) COCOON 1995. LNCS, vol. 959, pp. 270–281. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  63. Sen, S., Chatterjee, S.: Towards a theory of cache-efficient algorithms. In: Proc. 11th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 829–838. ACM-SIAM (2000)

    Google Scholar 

  64. Sleator, D.D., Tarjan, R.E.: Amortized Efficiency of List Update and Paging Rules. Communications of the ACM 28, 202–208 (1985)

    Article  MathSciNet  Google Scholar 

  65. Strassen, V.: Gaussian elimination is not optimal. Numerische Mathematik 13, 354–356 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  66. Toledo, S.: Locality of reference in LU decomposition with partial pivoting. SIAM Journal on Matrix Analysis and Applications, 18(4), 1065–1081 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  67. van Emde Boas, P.: Preserving order in a forest in less than logarithmic time and linear space. Information Processing Letters 6, 80–82 (1977)

    Article  MATH  Google Scholar 

  68. van Emde Boas, P., Kaas, R., Zijlstra, E.: Design and implementation of an efficient priority queue. Mathematical Systems Theory 10, 99–127 (1977)

    Article  MATH  Google Scholar 

  69. Vitter, J.S.: External memory algorithms and data structures: Dealing with massive data. ACM Computing Surveys 33(2), 209–271 (2001)

    Article  Google Scholar 

  70. Vitter, J.S., Shriver, E.A.M.: Algorithms for parallel memory I: Two-level memories. Algorithmica 12(2–3), 110–147 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  71. Vitter, J.S., Shriver, E.A.M.: Algorithms for parallel memory II: Hierarchical multilevel memories. Algorithmica 12(2–3), 148–169 (1994)

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  73. Xiao, L., Zhang, X., Kubricht, S.A.: Improving memory performance of sorting algorithms. ACM Journal of Experimental Algorithmics 5(3) (2000)

    Google Scholar 

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Authors and Affiliations

  1. BRICS, Department of Computer Science, University of Aarhus, IT-parken, Åbogade 34, DK-8200, Århus N, Denmark

    Gerth Stølting Brodal

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  1. Gerth Stølting Brodal
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  1. Institut für Informatik, Universität Augsburg, 86135, Augsburg, Germany

    Torben Hagerup

  2. Department of Computing, University of Copenhagen, Denmark

    Jyrki Katajainen

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Brodal, G.S. (2004). Cache-Oblivious Algorithms and Data Structures. In: Hagerup, T., Katajainen, J. (eds) Algorithm Theory - SWAT 2004. SWAT 2004. Lecture Notes in Computer Science, vol 3111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27810-8_2

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  • DOI: https://doi.org/10.1007/978-3-540-27810-8_2

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