Greedy in Approximation Algorithms

  • Julián Mestre
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4168)


The objective of this paper is to characterize classes of problems for which a greedy algorithm finds solutions provably close to optimum. To that end, we introduce the notion of k-extendible systems, a natural generalization of matroids, and show that a greedy algorithm is a \(\frac{1}{k}\)-factor approximation for these systems. Many seemly unrelated problems fit in our framework, e.g.: b-matching, maximum profit scheduling and maximum asymmetric TSP.

In the second half of the paper we focus on the maximum weight b-matching problem. The problem forms a 2-extendible system, so greedy gives us a \(\frac{1}{2}\)-factor solution which runs in O(m logn) time. We improve this by providing two linear time approximation algorithms for the problem: a \(\frac{1}{2}\)-factor algorithm that runs in O(bm) time, and a \(\left(\frac{2}{3} -- \epsilon\right)\)-factor algorithm which runs in expected \(O\left(b m \log \frac{1}{\epsilon}\right)\) time.


Approximation Algorithm Greedy Algorithm Maximum Weight Factor Algorithm Matched Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Julián Mestre
    • 1
  1. 1.Department of Computer ScienceUniversity of MarylandCollege ParkUSA

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