A theory of even functionals and their algorithmic applications

  • Jerzy W. Jaromczyk
  • Grzegorz Świcatek
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 700)


We present a theory of even functionals of degree k. Even function als are homogeneous polynomials which are invariant with respect to permutations and reflections. These are evaluated on real symmetric matrices. Important examples of even functionais include functions for enumerating embeddings of graphs with k edges into a weighted graph with arbitrary (positive or negative) weights and computing kth moments (expected values of kth powers) of a binary form. This theory provides a uniform approach for evaluating even functionais and links their evaluation with expressions with matrices as operands. In particular, we show that any even functional of degree less than 7 can be computed in time O(nω), the time required to multiply two n × n matrices.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Jerzy W. Jaromczyk
    • 1
  • Grzegorz Świcatek
    • 2
  1. 1.Department of Computer ScienceUniversity of KentuckyLexington
  2. 2.Department of MathematicsSUNY at Stony BrookStony Brook

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