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)


We consider evaluating one bilinear form defined by a sparse Ny ×Nx 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 Nx, Ny, w, M and B, as long as M ≥ B2 (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.


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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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