A Greedy Approximation Algorithm for the Uniform Labeling Problem Analyzed by a Primal-Dual Technique (original) (raw)

In this paper we present a new fast approximation algorithm for the Uniform Metric Labeling Problem. This is an important classification problem that occur in many applications which consider the assignment of objects into labels, in a way that is consistent with some observed data that includes the relationship between the objects. The known approximation algorithms are based on solutions of large linear programs and are impractical for moderated and large size instances. We present an 8 log n-approximation algorithm analyzed by a primal-dual technique which, although has factor greater than the previous algorithms, can be applied to large sized instances. We obtained experimental results on computational generated and image processing instances with the new algorithm and two others LP-based approximation algorithms. For these instances our algorithm present a considerable gain of computational time and the error ratio, when possible to compare, was less than 2% from the optimum.