Np completeness-Design and Analysis of Algorithms

1. NP-Completeness
DESIGN & ANALYSIS OF ALGORITHMS
By Muhammad Adeel

2. 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.

3. NP-Complete
 “NP-Complete comes from: Nondeterministic Polynomial
 Complete means “Solve one, Solve them all”
 There are more NP-Complete problems than provably
intractable problems

4. 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

5. 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

6. 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.

7. Thank You….