Holographic Algorithms: The Power of Dimensionality Resolved

  • Jin-Yi Cai
  • Pinyan Lu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4596)

Abstract

Valiant’s theory of holographic algorithms is a novel methodology to achieve exponential speed-ups in computation. A fundamental parameter in holographic algorithms is the dimension of the linear basis vectors. We completely resolve the problem of the power of higher dimensional bases. We prove that 2-dimensional bases are universal for holographic algorithms.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Jin-Yi Cai
    • 1
  • Pinyan Lu
    • 2
  1. 1.Computer Sciences Department, University of Wisconsin, Madison, WI 53706USA
  2. 2.Department of Computer Science and Technology, Tsinghua University, Beijing, 100084P.R. China

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