Programação matemática e imersões métricas para aproximações em problemas de corte

In this work, we present a theoretical study about NP-hard optimization problems of cuts in graphs and the state of the art in approximation algorithms that use techniques of mathematical programming and of metric spaces. Three problems of cuts in graphs were modeled by integer mathematical programs and they are relaxed to admit solutions with continuous values. The solution of these programs describes, respectively, unit vectors on the maximum cut problem, points in a (k−1)-simplex on the multiway cut problem, and a metric on the sparsest cut problem. Each presented algorithm performs a decision based on the mathematical program solution.