On the complexity of computing the measure of ∪[ai,bi]
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.