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Fast Boolean Matrix Multiplication for Highly Clustered Data

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Algorithms and Data Structures (WADS 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2125))

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Abstract

We consider the problem of computing the product of two n×n Boolean matrices A and B. For an n ×n Boolean matrix C, let G C be the complete weighted graph on the rows of C where the weight of an edge between two rows is equal to its Hamming distance, i.e., the number of entries in the first row having values different from the corresponding entries in the second one. Next, let MWT(C) be the weight of a minimum weight spanning tree of G C. We show that the product of A with B as well as the so called witnesses of the product can be computed in time õ(n(n + minMWT(A),MWT(B t)))1.

Õ(f(n)) means O(f(b)poly-logn) and Bt stands for the transposed matrix B.

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References

  1. A.V. Aho, J.E. Hopcroft and J.D. Ullman. The Design and Analysis of Computer Algorithms (Addison-Wesley, Reading, Massachusetts, 1974).

    MATH  Google Scholar 

  2. N. Alon and M. Naor. Derandomization, Witnesses for Boolean Matrix Multiplication and Construction of Perfect hash functions. Algorithmica 16, pp. 434–449, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  3. J. Basch, S. Khanna and R. Motwani. On Diameter Verification and Boolean Matrix Multiplication. Technical Report, Standford University CS department, 1995.

    Google Scholar 

  4. P.J. Cameron. Combinatorics. Cambridge University Press 1994.

    Google Scholar 

  5. D. Coppersmith and S. Winograd. Matrix Multiplication via Arithmetic Progressions. J. of Symbolic Computation 9 (1990), pp. 251–280.

    Article  MATH  MathSciNet  Google Scholar 

  6. Z. Galil and O. Margalit. Witnesses for Boolean Matrix Multiplication and Shortest Paths. Journal of Complexity, pp. 417–426, 1993.

    Google Scholar 

  7. P. Indyk and R. Motwani. Approximate Nearest Neighbors: Towards Removing the Curse of Dimensionality. Proceedings of the 30th ACM Symposium on Theory of Computing, 1998.

    Google Scholar 

  8. P. Indyk, S.E. Schmidt, and M. Thorup. On reducing approximate mst to closest pair problems in high dimensions. Manuscript, 1999.

    Google Scholar 

  9. C.P. Schnorr and C.R. Subramanian. Almost Optimal (on the average) Combinatorial Algorithms for Boolean Matrix Product Witnesses, Computing the Diameter. Randomization and Approximation Techniques in Computer Science. Second International Workshop, RANDOM’98, Lecture Notes in Computer Science 1518, pp. 218–231.

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Lund Institute of Technology, 22100, Lund

    Andreas Björklund

  2. Department of Computer Science, Lund University, 22100, Lund

    Andrzej Lingas

Authors
  1. Andreas Björklund
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  2. Andrzej Lingas
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Editor information

Editors and Affiliations

  1. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Candada, K1S 5B6

    Frank Dehne  & Jörg-Rüdiger Sack  & 

  2. Center for Geometric Computing, Brown University, Providence, RI, 02912-1910, USA

    Roberto Tamassia

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© 2001 Springer-Verlag Berlin Heidelberg

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Björklund, A., Lingas, A. (2001). Fast Boolean Matrix Multiplication for Highly Clustered Data. In: Dehne, F., Sack, JR., Tamassia, R. (eds) Algorithms and Data Structures. WADS 2001. Lecture Notes in Computer Science, vol 2125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44634-6_24

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  • DOI: https://doi.org/10.1007/3-540-44634-6_24

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42423-9

  • Online ISBN: 978-3-540-44634-7

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