If Input Intervals are Narrow Enough, Then Interval Computations are Almost Always Easy

Abstract

In the previous chapters, we have shown that in general, interval computations are NP-hard. This means, crudely speaking, that every algorithm that solves the interval computation problems requires, in some instances, unrealistic exponential time. Thus, the worst-case computational complexity of the problem is large. A natural question is: is this problem easy “ on average” (i.e., are complex instances rare), or is this problem difficult “ on average” too?

In this chapter, we show that “ on average”, the basic problem of interval computations is easy. To be (somewhat) more precise, we show that if input intervals are narrow enough, then interval computations are almost always easy.