1. Approximation Algorithms.ppt - Lecture-01 Approximation Algorithms Overview \u2022 \u2022 \u2022 \u2022 \u2022 Introduction Performance ratios The vertex-cover

# 1. Approximation Algorithms.ppt - Lecture-01 Approximation...

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Lecture-01Approximation Algorithms
OverviewIntroductionPerformance ratiosThe vertex-cover problemTraveling salesman problemSet cover problemSpring 2003Approximation Algorithmes2
IntroductionThere are many important NP-Complete problemsThere is no fast solution !But we want the answer …If the input is small use backtrack.Isolate the problem into P-problems !Find the Near-Optimalsolution in polynomial time.Spring 2003Approximation Algorithmes3
Performance ratiosWe are going to find a Near-Optimal solution for a given problem.We assume two hypothesis :Each potential solution has a positive cost.The problem may be either a maximization or a minimization problem on the cost.Spring 2003Approximation Algorithmes4
Performance ratios …If for any input of size n, the cost C of the solution produced by the algorithm is within a factor of ρ(n) of the cost C* of an optimal solution:Max ( C/C* , C*/C ) ≤ ρ(n)We call this algorithm as an ρ(n)-approximation algorithm.