Approximation Algorithms for Combinatorial Optimization

Abstract

In combinatorial optimization, the most important challenges are presented by problems belonging to the class NP-hard. For such problems no algorithm is known that can solve all instances in polynomial time. It is also strongly believed that no polynomial algorithm is capable of doing this. Although it is very difficult to solve exactly any of the NP-hard problems, some of them are amenable to methods that return approximate solutions in polynomial time. An important alternative to exact methods are algorithms that compute not the optimum, but some approximation that may be useful in practice. The area of approximation algorithms has the objective of providing general techniques for development of algorithms for NP-hard problems with proven guarantee of approximation. In other words, for these algorithms it can be proved that the solution returned will be within a relative distance from the optimum. In this article, we present some of the most interesting techniques used in the field of approximation algorithms, as well as problems that have been approximately solved using these algorithms.