# Algorithms That Still Produce a Solution (Maybe Not Optimal) Even When Interrupted: Shary's Idea Justified

Algorithms That Still Produce a Solution (Maybe Not Optimal) Even When Interrupted: Shary's Idea... Many problems of interval computations are NP-hard; this means, crudely speaking, that every algorithm that finds an exact solution will, in some cases, require exponential time, which is often unrealistic. If it turns out that an algorithm works too long, then we have to stop it. Some algorithms, when stopped, produce a reasonable approximation to the solution (for example, an enclosure for the desired interval). Some other algorithms only produce a solution at the very end, so when interrupted, they produce no solution at all. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

# Algorithms That Still Produce a Solution (Maybe Not Optimal) Even When Interrupted: Shary's Idea Justified

, Volume 4 (1) – Oct 6, 2004
15 pages

/lp/springer_journal/algorithms-that-still-produce-a-solution-maybe-not-optimal-even-when-OcW5rgP0jW
Publisher
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1009998515856
Publisher site
See Article on Publisher Site

### Abstract

Many problems of interval computations are NP-hard; this means, crudely speaking, that every algorithm that finds an exact solution will, in some cases, require exponential time, which is often unrealistic. If it turns out that an algorithm works too long, then we have to stop it. Some algorithms, when stopped, produce a reasonable approximation to the solution (for example, an enclosure for the desired interval). Some other algorithms only produce a solution at the very end, so when interrupted, they produce no solution at all.

### Journal

Reliable ComputingSpringer Journals

Published: Oct 6, 2004

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