Question

From the list of problems below, check all that are known to be NP-complete. You do not need to justify your answer. (Set cover) Given a graphGand an integerk, find a set of verticesUof size at mostksuch that every edge is adjacent to at least one vertex inU. (Max SAT) Given a CNF formula and an integer g, find a truth assignment that satisfies at leastgclauses. (Linear programming) Given am×nmatrixA, and vectorsb∈Rm,c∈Rn, find the solution of maxcTx s.t. Ax≤bx≥0​(MST) Given an undirected, weighted graphG=(V,E)find a minimum spanning tree ofG, or outputs FALSE if such tree does not exist.

Answer 1

Any computing issue that falls within the category of NP-complete problem has yet to find an effective solution algorithm.

Which problems are NP-complete?

• Any of a family of computer problems that have no effective solution algorithm are referred to as NP-complete issues.
• The traveling salesman problem, satisfiability issues, and graph-covering issues are only a few examples of the significant computer science issues that fall under this category.
• The difficulty of NP and NP-Complete issues is equal. If a problem is included in both NP and NP-Hard Problems, it is said to be NP-Complete.
• This statement, "This problem can change into an NP-complete problem on a non-deterministic Turing machine," is untrue for the obvious reason that while any problem in P is also a problem in NP, no problem in P is an NP-complete problem (unless P=NP, of course). If P is an NP problem and all NP problems convert into NP-complete problems, then P must also undergo this transformation.

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