Np completeness-Design and Analysis of Algorithms

Np completeness-Design and Analysis of Algorithms

• 1.
  NP-Completeness DESIGN & ANALYSISOF ALGORITHMS By Muhammad Adeel
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  What is NP-Complete?  In computational complexity theory, a decision problem is NP- complete when it is both in NP and NP-hard.  The set of NP-complete problems is often denoted by NP- C or NPC.
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  NP-Complete  “NP-Complete comesfrom: Nondeterministic Polynomial  Complete means “Solve one, Solve them all”  There are more NP-Complete problems than provably intractable problems
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  Tractability  Polynomial time(p-time)= O(nk), where n is the input size and k is a constant  Problems solvable in p-time are considered tractable  NP-complete problems have no known p-time solution, considered intractable
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  NP-Complete Problem Techniques The list below contains some well-known problems that are NP-complete when expressed as decision problems.  Boolean Satisfiability Problem  Traveling Salesman Problem  Hamiltonian Path Problem  Clique Problem  Graph Coloring Problem
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  Boolean Satisfiability Problem Take a Boolean circuit with a single output node and ask whether there is an assignment of values to the circuit’s inputs so that the output is “1”  Boolean, or propositional-logic expressions are built from variables and constants using the operators AND, OR, and NOT.
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  Thank You….