Encyclopedia of Algorithms

2016 Edition
| Editors: Ming-Yang Kao

Approximation Schemes for Planar Graph Problems

  • Mohammad Taghi HajiaghayiEmail author
  • Erik D. DemaineEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_32

Years and Authors of Summarized Original Work

  • 1983; Baker

  • 1994; Baker

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, a 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 n1−ε for any ε > 0 unless NP  = ZPP (and inapproximable within \(n^{1/2-\epsilon }\)

Keywords

Approximation algorithms in planar graphs Baker’s approach Lipton-Tarjan approach 
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Recommended Reading

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of MarylandCollege ParkUSA
  2. 2.MIT Computer Science and Artificial Intelligence LaboratoryCambridgeUSA