intractable problem
Quick Summary
In computer science, an "intractable problem" refers to a problem whose solution requires an amount of computing resources (time or space) that grows exponentially with the size of the input. This means that as the problem gets larger, the time or memory needed to solve it becomes prohibitively large, making it practically impossible to solve efficiently.12
These problems are at the far end of the computational complexity spectrum. While algorithms exist to solve them, they are not efficient for real-world applications. Computer scientists often seek heuristic algorithms for intractable problems, which aim to find near-optimal solutions in a reasonable amount of time.12
A related concept is the P versus NP problem, which questions whether all problems whose solutions can be quickly verified (NP problems) can also be quickly solved (P problems). Many important problems, like the traveling salesman problem, are NP-complete and are considered intractable.3
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- NP-complete problem
Algorithms for solving hard, or intractable, problems, on the other hand, require times that are exponential functions of the problem size n. Polynomial-time algorithms are considered to be efficient, while exponential-time algorithms are considered inefficient, because the execution times of the latter grow much more rapidly as the problem size…
Read MoreAlgorithms for solving hard, or intractable, problems, on the other hand, require times that are exponential functions of the problem size n. Polynomial-time algorithms are considered to be efficient, while exponential-time algorithms are considered inefficient, because the execution times of the latter grow much more rapidly as the problem size…
Read More - P versus NP problem
…allowed the solution of formerly intractable problems.
Read More…allowed the solution of formerly intractable problems.
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