May 9, 2022 · The goal of the approximation algorithm is to come as close as possible to the optimal solution in polynomial time. Such algorithms are called approximation algorithms or …

In this chapter, we present some examples of polynomial-time approximation algorithms for several NP-complete problems. We have at least three ways to get around NP-completeness. …

Given an optimization problem P, an algorithm A is said to be an approximation algorithm for P, if for any given instance I, it returns an approximate solution, that is a feasible solution.

Approximation algorithms. Guaranteed to run in polynomial time. Guaranteed to find "high quality" solution, say within 1% of optimum. Obstacle: need to prove a solution’s value is close to …

An algorithm for an optimization problem is an -approximation algorithm, if it runs in polynomial time, and for any instance to the problem, it outputs a solution whose cost (or value) is within …

Linear programming is an extremely versatile technique for designing approximation algorithms, because it is one of the most general and expressive problems that we know how to solve in …

Approximation Ratio For a minimization problem (find the shortest/smallest/least/etc.) If (G) is the value of the best solution for value that your algorithm finds, then is an algorithm if for every , ⋅ …

Popular answer: approximation algorithms (one of my main research areas!) ￿Give up on correctness, but in a provable, bounded way. ￿Applies to optimization problems only (not …

Approximation Algorithms: This is an algorithm that runs in polynomial time (ideally), and produces a solution that is within a guaranteed factor of the optimum solution.

The Greedy-Cover algorithm is a polynomial time approximation algorithm for set cover with ratio 1+log , where ≤ is the maximum size of a set in the input. Proof: Without loss of generality, …