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

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

  • Mathematical Research
  • Published:
Reliable Computing

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.

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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Authors and Affiliations

  1. M/S 301-270 Jet Propulsion Laboratory, 4800 Oak Grove Dr., 91109, Pasadena, CA, USA

    Bonnie Traylor

  2. Computer Science Department, University of Texas at El Paso, 79968, El Paso, TX, USA

    Vladik Kreinovich

Authors
  1. Bonnie Traylor
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  2. Vladik Kreinovich
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Traylor, B., Kreinovich, V. A bright side of NP-hardness of interval computations: interval heuristics applied to NP-problems. Reliable Comput 1, 343–359 (1995). https://doi.org/10.1007/BF02385263

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  • DOI: https://doi.org/10.1007/BF02385263

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