Approximate Version of Interval Computation Is Still NP-Hard

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow
Olga Kosheleva, The University of Texas at El PasoFollow

Publication Date

6-2020

Comments

Technical Report: UTEP-CS-20-56

Abstract

It is known that, in general, the problem of computing the range of a given polynomial on given intervals is NP-hard. For some NP-hard optimization problems, the approximate version -- e.g., if we want to find the value differing from the maximum by no more than a factor of 2 -- becomes feasible. Thus, a natural question is: what if instead of computing the exact range, we want to compute the enclosure which is, e.g., no more than twice wider than the actual range? In this paper, we show that this approximate version is still NP-hard, whether we want it to be twice wider or k times wider, for any k.