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Evaluating Non-square Sparse Bilinear Forms on Multiple Vector Pairs in the I/O-Model

  • Gero Greiner
  • Riko Jacob
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6281)

Abstract

We consider evaluating one bilinear form defined by a sparse N y ×N x matrix A having h entries on w pairs of vectors The model of computation is the semiring I/O-model with main memory size M and block size B. For a range of low densities (small h), we determine the I/O-complexity of this task for all meaningful choices of N x , N y , w, M and B, as long as M ≥ B 2 (tall cache assumption). To this end, we present asymptotically optimal algorithms and matching lower bounds. Moreover, we show that multiplying the matrix A with w vectors has the same worst-case I/O-complexity.

Keywords

Bilinear Form Sparse Matrix Internal Memory Matrix Vector Multiplication Matrix Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Gero Greiner
    • 1
  • Riko Jacob
    • 1
  1. 1.Technische Universität München 

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