Encyclopedia of Algorithms

2008 Edition
| Editors: Ming-Yang Kao

Fractional Packing and Covering Problems

1991; Plotkin, Shmoys, Tardos1995; Plotkin, Shmoys, Tardos
  • George Karakostas
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30162-4_149

Problem Definition

This entry presents results on fast algorithms that produce approximate solutions to problems which can be formulated as Linear Programs (LP), and therefore can be solved exactly, albeit with slower running times. The general format of the family of these problems is the following: Given a set of m inequalities on n variables, and an oracle that produces the solution of an appropriate optimization problem over a convex set \( { P \in \mathbb{R}^n } \)

Keywords

Fractional Packing Polynomial Time Approximation Scheme Unrelated Parallel Machine Fully Polynomial Time Approximation Scheme Linear Program Solution 
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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Recommended Reading

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    Leighton, F.T., Makedon, F., Plotkin, S.A., Stein, C., Tardos, É., Tragoudas, S.: Fast approximation algorithms for multicommodity flow problems. J. Comp. Syst. Sci. 50(2), 228–243 (1995)Google Scholar
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    Plotkin, S.A., Shmoys, D.B., Tardos, É.: Fast approximation algorithms for fractional packing and covering problems. In: Proceedings of 32nd Annual IEEE Symposium on Foundations of Computer Science (FOCS), 1991, pp. 495–504Google Scholar
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    Plotkin, S.A., Shmoys, D.B., Tardos, É.: Fast approximation algorithms for fractional packing and covering problems. Math. Oper. Res. 20(2) 257–301 (1995). Preliminary version appeared in [6]Google Scholar
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    Shahrokhi, F., Matula, D.W.: The maximum concurrent flow problem. J. ACM 37, 318–334 (1990)MathSciNetzbMATHCrossRefGoogle Scholar
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    Young, N.E.: Sequential and parallel algorithms for mixed packing and covering. In: Proceedings of 42nd Annual IEEE Symposium on Foundations of Computer Science (FOCS), 2001, pp. 538–546Google Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • George Karakostas
    • 1
  1. 1.Department of Computing & SoftwareMcMaster UniversityHamiltonCanada