Linear-time recognition of map graphs with outerplanar witness

Matthias Mnich; Ignaz Rutter; Jens M. Schmidt

doi:10.1016/j.disopt.2017.12.002

Linear-time recognition of map graphs with outerplanar witness

Matthias Mnich^*, Ignaz Rutter, Jens M. Schmidt

^*Corresponding author for this work

QE Operations research

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

Map graphs generalize planar graphs and were introduced by Chen et al. (STOC 1998, J. ACM, 2002). They showed that the problem of recognizing map graphs is in NP by proving the existence of a planar witness graph W. Shortly after, Thorup (FOGS 1998) published a polynomial-time recognition algorithm for map graphs. However, the run time of this algorithm is estimated to be Omega(n(120)) for n-vertex graphs, and a full description of its details remains unpublished.

We give a new and purely combinatorial algorithm that decides whether a graph G is a map graph having an outerplanar witness W. This is a step towards a first combinatorial recognition algorithm for general map graphs. The algorithm runs in time and space O(n + m). In contrast to Thorup's approach, it computes the witness graph W in the affirmative case. (C) 2017 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	63-77
Number of pages	15
Journal	Discrete Optimization
Volume	28
DOIs	https://doi.org/10.1016/j.disopt.2017.12.002
Publication status	Published - 1 May 2018

Keywords

Planar graphs
Map graphs
Certifying algorithms
ALGORITHMS

Access to Document

10.1016/j.disopt.2017.12.002Licence: Free access - publisher

Cite this

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title = "Linear-time recognition of map graphs with outerplanar witness",

abstract = "Map graphs generalize planar graphs and were introduced by Chen et al. (STOC 1998, J. ACM, 2002). They showed that the problem of recognizing map graphs is in NP by proving the existence of a planar witness graph W. Shortly after, Thorup (FOGS 1998) published a polynomial-time recognition algorithm for map graphs. However, the run time of this algorithm is estimated to be Omega(n(120)) for n-vertex graphs, and a full description of its details remains unpublished.We give a new and purely combinatorial algorithm that decides whether a graph G is a map graph having an outerplanar witness W. This is a step towards a first combinatorial recognition algorithm for general map graphs. The algorithm runs in time and space O(n + m). In contrast to Thorup's approach, it computes the witness graph W in the affirmative case. (C) 2017 Elsevier B.V. All rights reserved.",

keywords = "Planar graphs, Map graphs, Certifying algorithms, ALGORITHMS",

author = "Matthias Mnich and Ignaz Rutter and Schmidt, {Jens M.}",

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T1 - Linear-time recognition of map graphs with outerplanar witness

AU - Mnich, Matthias

AU - Rutter, Ignaz

AU - Schmidt, Jens M.

N1 - data source: no data used

PY - 2018/5/1

Y1 - 2018/5/1

N2 - Map graphs generalize planar graphs and were introduced by Chen et al. (STOC 1998, J. ACM, 2002). They showed that the problem of recognizing map graphs is in NP by proving the existence of a planar witness graph W. Shortly after, Thorup (FOGS 1998) published a polynomial-time recognition algorithm for map graphs. However, the run time of this algorithm is estimated to be Omega(n(120)) for n-vertex graphs, and a full description of its details remains unpublished.We give a new and purely combinatorial algorithm that decides whether a graph G is a map graph having an outerplanar witness W. This is a step towards a first combinatorial recognition algorithm for general map graphs. The algorithm runs in time and space O(n + m). In contrast to Thorup's approach, it computes the witness graph W in the affirmative case. (C) 2017 Elsevier B.V. All rights reserved.

AB - Map graphs generalize planar graphs and were introduced by Chen et al. (STOC 1998, J. ACM, 2002). They showed that the problem of recognizing map graphs is in NP by proving the existence of a planar witness graph W. Shortly after, Thorup (FOGS 1998) published a polynomial-time recognition algorithm for map graphs. However, the run time of this algorithm is estimated to be Omega(n(120)) for n-vertex graphs, and a full description of its details remains unpublished.We give a new and purely combinatorial algorithm that decides whether a graph G is a map graph having an outerplanar witness W. This is a step towards a first combinatorial recognition algorithm for general map graphs. The algorithm runs in time and space O(n + m). In contrast to Thorup's approach, it computes the witness graph W in the affirmative case. (C) 2017 Elsevier B.V. All rights reserved.

KW - Planar graphs

KW - Map graphs

KW - Certifying algorithms

KW - ALGORITHMS

U2 - 10.1016/j.disopt.2017.12.002

DO - 10.1016/j.disopt.2017.12.002

M3 - Article

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JO - Discrete Optimization

JF - Discrete Optimization

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