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How do you determine a problem L is NP-complete explain with an example?
A decision problem L is NP-complete if: 1) L is in NP (Any given solution for NP-complete problems can be verified quickly, but there is no efficient known solution). 2) Every problem in NP is reducible to L in polynomial time (Reduction is defined below).
Why do we study NP?
The class of polynomial-time solvable problems has nice closure properties (since polynomials are closed under addition, multiplication, etc.) The class of NP-complete (Non-deterministic polynomial time complete) problems is a very important and interesting class of problems in Computer Science.
What is algorithm in DAA?
An algorithm is a distinct computational procedure that takes input as a set of values and results in the output as a set of values by solving the problem. More precisely, an algorithm is correct, if, for each input instance, it gets the correct output and gets terminated.
What is the importance of NP-complete in Computer Science?
It is important to computer science because it has been proven that any problem in NP can be transformed into another problem in NP-complete. That means that a solution to any one NP-complete problem is a solution to all NP problems. Many algorithms in security depends on the fact that no known solutions exist for NP hard problems.
How do you prove that a problem is NP-complete?
From the definition of NP-complete, it appears impossible to prove that a problem L is NP-Complete. By definition, it requires us to that show every problem in NP is polynomial time reducible to L. Fortunately, there is an alternate way to prove it.
What does NP mean in programming?
“NP” stands for “nondeterministic polynomial time,” and is the name for what is called a complexity class to which problems can belong. The important thing about the NP complexity class is that problems within that class can be verified by a polynomial time algorithm. As an example, consider the problem of counting stuff.
Can an efficient algorithm be found for every NP-complete problem?
If a problem is NP and all other NP problems are polynomial-time reducible to it, the problem is NP-complete. Thus, finding an efficient algorithm for any NP-complete problem implies that an efficient algorithm can be found for all such problems, since any problem belonging to this class can be recast into any other member of the class.