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Greedy in Approximation Algorithms

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Algorithms – ESA 2006 (ESA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4168))

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Abstract

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.

Research supported by NSF Awards CCR-01-05413 and CCF-04-30650, and the University of Maryland Dean’s Dissertation Fellowship.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Maryland, College Park, MD, 20742, USA

    Julián Mestre

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  1. Julián Mestre
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Editor information

Editors and Affiliations

  1. Microsoft Research, One Microsoft Way, Redmond, WA 98052, USA and School of Computer Science, Tel-Aviv University, 69978, Tel-Aviv, Israel

    Yossi Azar

  2. Department of Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Thomas Erlebach

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© 2006 Springer-Verlag Berlin Heidelberg

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Mestre, J. (2006). Greedy in Approximation Algorithms. In: Azar, Y., Erlebach, T. (eds) Algorithms – ESA 2006. ESA 2006. Lecture Notes in Computer Science, vol 4168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11841036_48

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  • DOI: https://doi.org/10.1007/11841036_48

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-38875-3

  • Online ISBN: 978-3-540-38876-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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