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

  • Vladik Kreinovich
  • Anatoly Lakeyev
  • Jiří Rohn
  • Patrick Kahl
Part of the Applied Optimization book series (APOP, volume 10)

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.

Keywords

Rational Function Lebesgue Measure Rational Number Rational Coefficient Interval Computation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Vladik Kreinovich
    • 1
  • Anatoly Lakeyev
    • 2
  • Jiří Rohn
    • 3
  • Patrick Kahl
    • 4
  1. 1.University of Texas at El PasoUSA
  2. 2.Computing CenterRussian Academy of SciencesIrkutskRussia
  3. 3.Charles University and Academy of SciencesPragueCzech Republic
  4. 4.IBMTucsonUSA

Personalised recommendations