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On the average number of registers needed to evaluate a special class of backtrack trees. (English) Zbl 0809.68104
Summary: We derive a lower bound for the average number of registers \(\underline {R}_ p (h)\) needed to evaluate the family \({\mathcal F}_ p (h)\) of nonuniformly distributed binary trees introduced by P. W. Purdom. This family consists of binary trees of height less than or equal to \(h\). Based on a parameter \(p \in [0,1]\), the probability of a particular tree \(T \in {\mathcal F}_ p (h)\) is given by a recursively defined function. We show that \(\underline {R}_ p (h)\) is smaller than 2, for \(0 \leq p \leq 1/2\), and that, for \(1/2 < p < 1\), it grows up to at least \(O (\log(h))\). Near \(p=1\), \(\underline {R}_ p (h)\) jumps to \(h+1\).

68T20 Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.)
68P05 Data structures
68Q25 Analysis of algorithms and problem complexity
binary trees
Full Text: DOI EuDML
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