By Michael L. Fredman, Bruce Weide
Communications of the ACM,
July 1978,
Vol. 21 No. 7, Pages 540-544
10.1145/359545.359553
Comments
The decision tree complexity of computing the measure of the union of n (possibly overlapping) intervals is shown to be &OHgr;(n log n), even if comparisons between linear functions of the interval endpoints are allowed. The existence of an &OHgr;(n log n) lower bound to determine whether any two of n real numbers are within ∈ of each other is also demonstrated. These problems provide an excellent opportunity for discussing the effects of the computational model on the ease of analysis and on the results produced.
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