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The Complexity of Computing the k-ary Composition of a Binary Associative Operator (1996)  (Make Corrections)  
Gerth Stølting Brodal, Sven Skyum



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Abstract: We show that the problem of computing all contiguous k-ary compositions of a sequence of n values under an associative and commutative operator requires 3 k\Gamma1 k+1 n \Gamma O(k) operations. For the operator max we show in contrast that in the decision tree model the complexity is i 1 + \Theta(1= p k) j n \Gamma O(k). Finally we show that the complexity of the corresponding on-line problem for the operator max is i 2 \Gamma 1 k\Gamma1 j n \Gamma O(k). This work was... (Update)

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BibTeX entry:   (Update)

@misc{ brodal-complexity,
  author = "Gerth Stølting Brodal and Sven Skyum",
  title = "The Complexity of Computing the k-ary Composition of a Binary Associative
    Operator",
  url = "citeseer.ist.psu.edu/324451.html" }
Citations (may not include all citations):
100   Volume I: Fundamental Algorithms (context) - Knuth, of - 1968
53   Volume III: Sorting and Searching (context) - Knuth, of - 1973
12   Optimal randomized algorithms for local sorting and set-maxi.. (context) - Goddard, Kenyon et al. - 1993
5   A linear time approach to the set maxima problem (context) - Bar-Noy, Motwani et al. - 1992
2   a family of boolean matrices (context) - Andreev - 1986
1   CASOP: A fast algorithm for computing the n-ary composition .. (context) - Cooper, Kitchen - 1990
1   Some remarks on boolean sums (context) - Mehlhorn - 1979

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