Reliable Computing

, Volume 1, Issue 3, pp 343–359

# A bright side of NP-hardness of interval computations: interval heuristics applied to NP-problems

• Bonnie Traylor
Mathematical Research

## Abstract

It is known that interval computations are NP-hard. In other words, the solution of many important problems can be reduced to interval computations. The immediate conclusion is negative: in the general case, one cannot expect an algorithm to do all the interval computations in less than exponential running time.

We show that this result also has a bright side: since there are many heuristics, for interval computations, we can solve other problems by reducing them to interval computations and applying these heuristics.

## Keywords

Mathematical Modeling Computational Mathematic Industrial Mathematic Interval Computation Bright Side
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.

# Въічодная сторона ПР-сложности интервальных вычислений: интервалъная зврицтика в применении К ПР-задачам

## Abstract

Извецтно, что интервалъные вычиления ПР-сложны. Друтими словами, решение многх важных задач может быжтъ сведено к интервалъным вычицлениям. Первое очевидное следствие зтого Факта негативно: в обшем слмчае мы не можем поцтроитъ алгстроитм, который выполнял цы все интервалъные вычисления быстрее, чем за зксноненциалън ое время.

Нами показано, что зто свойство имеет и свою выгодную сторону: посколъку для интервалъных выцислений сушествует мното звристик, другие задачи могут бытъ вешены решены сведением их к интервалъным вычислениям с далънейшим применением зтих звристик.

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