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Approximation Schemes for Planar Graph Problems

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  • First Online:
Encyclopedia of Algorithms

  • 94 Accesses

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 \(n^{1/2-\epsilon }\) unless P  = NP), while for planar graphs, there is a 4-approximation (or simple 5-approximation) by taking the largest color class in a vertex 4-coloring (or 5-coloring). Another is minimum dominating set, where the goal is to find a minimum subset of vertices such that every vertex is either in or adjacent to the subset....

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Recommended Reading

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Author information

Authors and Affiliations

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

    Mohammad Taghi Hajiaghayi

  2. MIT Computer Science and Artificial Intelligence Laboratory, 32 Vassar St., Cambridge, MA, USA

    Erik D. Demaine

Authors
  1. Mohammad Taghi Hajiaghayi
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  2. Erik D. Demaine
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Corresponding authors

Correspondence to Mohammad Taghi Hajiaghayi or Erik D. Demaine .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Hajiaghayi, M.T., Demaine, E.D. (2016). Approximation Schemes for Planar Graph Problems. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_32

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