A Note on the Practicality of Maximal Planar Subgraph Algorithms

Given a graph G, the NP-hard Maximum Planar Subgraph problem (MPS) asks for a planar subgraph of G with the maximum number of edges. There are several heuristic, approximative, and exact algorithms to tackle the problem, but—to the best of our knowledge—they have never been compared competitively in practice.

[1]  Nicholas C. Wormald,et al.  Generating Random Regular Graphs Quickly , 1999, Combinatorics, Probability and Computing.

[2]  W. Sierpinski,et al.  Sur le probléme des courbes gauches en Topologie , 2022 .

[3]  Wei-Kuan Shih,et al.  A New Planarity Test , 1999, Theor. Comput. Sci..

[4]  Giuseppe Liotta,et al.  An Experimental Comparison of Four Graph Drawing Algorithms , 1997, Comput. Geom..

[5]  T. Koch,et al.  SteinLib: An Updated Library on Steiner Tree Problems in Graphs , 2001 .

[6]  Wen-Lian Hsu,et al.  A Linear Time Algorithm for Finding a Maximal Planar Subgraph Based on PC-Trees , 2005, COCOON.

[7]  Carlo Batini,et al.  Computer aided layout of entity relationship diagrams , 1984, J. Syst. Softw..

[8]  Michael Jünger,et al.  The Open Graph Drawing Framework (OGDF) , 2013, Handbook of Graph Drawing and Visualization.

[9]  Michael Jünger,et al.  Maximum planar subgraphs and nice embeddings: Practical layout tools , 1996, Algorithmica.

[10]  Serge A. Plotkin,et al.  Routing and admission control in general topology networks with Poisson arrivals , 1995, SODA '96.

[11]  Giuseppe Liotta,et al.  Drawing Directed Acyclic Graphs: An Experimental Study , 1996, Int. J. Comput. Geom. Appl..

[12]  Karsten Weihe,et al.  Maximum s-t-flow with k crossings in O(k3n log n) time , 2007, SODA '07.

[13]  Markus Chimani,et al.  Limits of Greedy Approximation Algorithms for the Maximum Planar Subgraph Problem , 2016, IWOCA.

[14]  Markus Chimani,et al.  Advances in the Planarization Method: Effective Multiple Edge Insertions , 2011, Graph Drawing.

[15]  Markus Chimani,et al.  Efficient Extraction of Multiple Kuratowski Subdivisions , 2007, GD.

[16]  Cristina G. Fernandes,et al.  A better approximation algorithm for finding planar subgraphs , 1996, SODA '96.

[17]  Markus Chimani,et al.  Non-planar core reduction of graphs , 2005, Discret. Math..

[18]  Petr Hliněný,et al.  Inserting Multiple Edges into a Planar Graph , 2015, SoCG.