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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 $$h+1$$.

##### MSC:
 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
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##### References:
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