Computing k-ary Compositions
نویسندگان
چکیده
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−1 k+1n−O(k) operations. For the operator max we show in contrast that in the decision tree model the complexity is ( 1 + Θ(1/ √ k) ) n − O(k). Finally we show that the complexity of the corresponding on-line problem for the operator max is ( 2− 1 k−1 ) n−O(k). ∗This work was partially supported by the ESPRIT Long Term Research Program of the EU under contract #20244 (ALCOM-IT). †Supported by the Danish Natural Science Research Council (Grant No. 9400044). ‡Basic Research in Computer Science, Centre of the Danish National Research Foundation.
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