Linear interval equations: Computing enclosures with bounded relative or absolute overestimation is NP-hard

نویسندگان

  • Vladik Kreinovich
  • Anatoly V. Lakeyev
چکیده

"|OK|Ill|lilt), q'l'll it:lfl .'IK)('~()I'() (~ ~" 0, eCllll i'yllleCil~yer il-ll()])ll IM t" III}:IIIH4}M|III:II,III,IM BI)C:MItIIItM ll],llll|:lHellll~ "[..'II, l :ll)Kil;lll31111llll l}ellleHlll"l llflle])l~il.'lhHeH'l CIICTeMhl .'lllHel'iHl~X yp~|llHeHlll'l l' lH'll(Wlll'ellhl4llil (II;III il~CO:llOrHOfi) lllll])elllHtIcrblo, MeBhlllefl ¢~, T¢) P : NP. Pc3ydlhTiH" Cllpillle3Ullll~ TilKie 2111~I C'lyq.'Dl CIIMM~TI)IIMHblX CIICrCM,

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Exponential Enclosure Techniques for the Computation of Guaranteed State Enclosures in ValEncIA-IVP

Verified integration of initial value problems for sets of ordinary differential equations can be performed by numerous approaches. The most important ones are based on either interval or Taylor model arithmetic and enclose with certainty the sets of reachable states at a given point of time. Commonly, such tools are based on a Taylor series expansion of the solution of differential equations i...

متن کامل

Parallelizing Assignment Problem with DNA Strands

Background:Many problems of combinatorial optimization, which are solvable only in exponential time, are known to be Non-Deterministic Polynomial hard (NP-hard). With the advent of parallel machines, new opportunities have been emerged to develop the effective solutions for NP-hard problems. However, solving these problems in polynomial time needs massive parallel machines and ...

متن کامل

Use of Grothendieck Inequality in Interval Computations: Quadratic Terms are Estimated Accurately Modulo a Constant Factor∗

One of the main problems of interval computations is to compute the range of a given function f over given intervals. For a linear function, we can feasibly estimate its range, but for quadratic (and for more complex) functions, the problem of computing the exact range is NP-hard. So, if we limit ourselves to feasible algorithms, we have to compute enclosures instead of the actual ranges. It is...

متن کامل

Asymptotic algorithm for computing the sample variance of interval data

The problem of the sample variance computation for epistemic inter-val-valued data is, in general, NP-hard. Therefore, known efficient algorithms for computing variance require strong restrictions on admissible intervals like the no-subset property or heavy limitations on the number of possible intersections between intervals. A new asymptotic algorithm for computing the upper bound of the samp...

متن کامل

For Interval Computations, If Absolute-Accuracy Optimization is NP-Hard, Then So Is Relative-Accuracy Optimization

One of the basic problems of interval computations is to compute a range of a given function f(x1, . . . , xn) over a given box [x1 , x + 1 ]× . . .× [x − n , x + n ] (i.e., to compute the maximum and the minimum of the function on the box). For many classes of functions (e.g., for quadratic functions) this problem is NP-hard; it is even NP-hard if instead of computing the minimum and maximum e...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Reliable Computing

دوره 2  شماره 

صفحات  -

تاریخ انتشار 1996