NP-Hard and NP-Complete Problems Quiz

Group-1

Ordered Search ($O( ext{log}n)$)

Group-2

<p>Traveling Sales Person ($O(n^2 2^n)$)</p> Signup and view all the answers

<p>They take vast amounts of time to execute</p> Signup and view all the answers

<p>NP stands for Nondeterministic Polynomial time. The two groups of problems based on their solution times are Group-1, which has solution times bound by a polynomial of a small degree, and Group-II, which has solution times not bound by polynomial (simply non-polynomial).</p> Signup and view all the answers

<p>An example of a problem in Group-1 with a polynomial time algorithm is Ordered Search, with a time complexity of $O(\log n)$.</p> Signup and view all the answers

<p>An example of a problem in Group-II with a non-polynomial solution time is the Traveling Sales Person problem, with a time complexity of $O(n^22^n)$.</p> Signup and view all the answers

<p>It is challenging to develop a polynomial time algorithm for any problem in Group-II because none of the problems in this group has been solved by any polynomial time algorithm. These problems are hard or intractable, making it difficult to find efficient solutions.</p> Signup and view all the answers

<p>It is important to find algorithms with computing times greater than polynomial very quickly because problems with solution times not bound by polynomial are hard or intractable. Developing efficient algorithms for these problems is crucial for practical applications and computational advancements.</p> Signup and view all the answers