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Update index.md (#19981) 

Add a few examples of other NP-complete problems
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Anika Tabassum 2018-10-26 23:28:07 -04:00 committed by Tom
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guide/english/computer-science/np-completeness/index.md
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@ -11,7 +11,7 @@ One way would be to simply enumerate all possible subsets and check if their ele
And indeed, there is no better algorithm known, which improves on the exponential time bound. That is why it is classifies as an NP-Complete problem.
There are many such known problems apart from the subset sum problem which are known to be NP-Complete. If an efficient algorithm for one is found, it implies that we can design an efficient algorithm for all problems which are NP-Complete.
There are many such known problems apart from the subset sum problem which are known to be NP-Complete, such as the vertex cover problem, hamiltonian path problem, boolean satisfiability problem, etc. If an efficient algorithm for one is found, it implies that we can design an efficient algorithm for all problems which are NP-Complete.
If you have a problem that can be proved to be NP-complete, you should stop trying to find more efficient algorithms for it and instead use heuristics to solve the problem for most test cases, or solve an approximate version of the problem. Or maybe examine the problem you're solving to see if it can't be simplified to something that isn't NP-Complete.