Encyclopedia of Algorithms

2008 Edition
| Editors: Ming-Yang Kao

Approximation Schemes for Planar Graph Problems

1983; Baker1994; Baker
  • Erik D. Demaine
  • MohammadTaghi Hajiaghayi
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30162-4_32

Keywords and Synonyms

Approximation algorithms in planar graphs; Baker's approach ; Lipton–Tarjan approach            

Problem Definition

Many NP-hard graph problems become easier to approximate on planar graphs and their generalizations. (A graph is planar if it can be drawn in the plane (or the sphere) without crossings. For definitions of other related graph classes, see the entry on  bidimensionality (2004; Demaine, Fomin, Hajiaghayi, Thilikos).) For example, maximum independent set asks to find a maximum subset of vertices in a graph that induce no edges. This problem is inapproximable in general graphs within a factor of \( { n^{1-\epsilon} } \)

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Recommended Reading

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Erik D. Demaine
    • 1
  • MohammadTaghi Hajiaghayi
    • 2
  1. 1.Computer Science and Artifical Intelligence LaboratoryMITCambridgeUSA
  2. 2.Department of Computer ScienceUniversity of PittsburghPittsburghUSA