# How to show that X is NP complete?

## How to show that X is NP complete?

To show that X is NP-Complete: 1. Show that X is in NP, i.e., a polynomial time verifier exists for X. 2. Pick a suitable known NP-complete problem, S (ex: SAT) 3. Show a polynomial algorithm to transform an instance of S into an instance of X SOX RESTOX mnemonic can help.

## When is a problem in NP also in NP-complete?

• A problem x that is in NP is also in NP-Complete if and only if every other problem in NP can be quickly (ie. in polynomial time) transformed into x.

Which is a subset of the NP complete set?

• P is the set of all decision problems which can be solved in polynomial time by a deterministic Turing machine. Since it can solve in polynomial time, it can also be verified in polynomial time. Therefore P is a subset of NP. 13. NP-Complete • What is NP-Complete?

What are some examples of NP hard classes?

NP Hard and NP-Complete Classes 1 Definition of NP-Completeness. Every A in NP is polynomial time reducible to B. 2 NP-Complete Problems. Following are some NP-Complete problems, for which no polynomial time algorithm is known. 3 NP-Hard Problems. The traveling salesman problem consists of a salesman and a set of cities. 4 Proof.

### Which is better, a p or a NP?

3-S AT educes to I NDEPENDENT -S ET GRAPH-3-COLOR HAM-CYCLE TSP SUBSET-SUM PLANAR-3-COLORSCHEDULING SET-COVER SECTION 8.3 8. INTRACTABILITY II ‣ P vs. NP ‣ NP-complete ‣ co-NP ‣ NP-hard 3 Decision problems Decision problem. ・Problem Xis a set of strings. ・Instance s is one string. ・Algorithm Asolves problem X: A(s) = yesiff s∈X. Def.

### Which is the best definition of NP completeness?

NP completeness. Classes P and NP are two frequently studied classes of problems in computer science. Class P is the set of all problems that can be solved by a deterministic Turing machine in polynomial time. 1.

Which is better P or NP in intractability II?

INTRACTABILITY II ‣ P vs. NP ‣ NP-complete ‣ co-NP ‣ NP-hard 3-SATpoly-time reduces to all of these problems (and many, many more) 2 Recap 3-SAT INDEPENDENT-SETDIR-HAM-CYCLE VERTEX-COVER 3-S AT educes to I NDEPENDENT -S ET GRAPH-3-COLOR HAM-CYCLE TSP SUBSET-SUM PLANAR-3-COLORSCHEDULING SET-COVER SECTION 8.3 8. INTRACTABILITY II