Automatic graph drawing and readability of diagrams
IEEE Transactions on Systems, Man and Cybernetics
On heuristics for determining the thickness of a graph
Information Sciences—Informatics and Computer Science: An International Journal
The sizes of maximal planar, outerplanar, and bipartite planar subgraphs
Discrete Mathematics
Journal of Algorithms
A better approximation algorithm for finding planar subgraphs
Journal of Algorithms
An analysis of some heuristics for the maximum planar subgraph problem
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Journal of the ACM (JACM)
Linear Algorithms for Isomorphism of Maximal Outerplanar Graphs
Journal of the ACM (JACM)
Efficient Algorithms for Graphic Intersection and Parity (Extended Abstract)
Proceedings of the 12th Colloquium on Automata, Languages and Programming
Node-and edge-deletion NP-complete problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Generating Random Regular Graphs Quickly
Combinatorics, Probability and Computing
Heuristics for the Maximum Outerplanar Subgraph Problem
Journal of Heuristics
A simulated annealing algorithm for determining the thickness of a graph
Information Sciences—Informatics and Computer Science: An International Journal
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The maximum planar subgraph problem (MPS) is defined as follows: given a graph G, find a largest planar subgraph of G. The problem is NP-hard and it has applications in graph drawing and resource location optimization. Calinescu et al. [J. Alg. 27, 269-302 (1998)] presented the first approximation algorithms for MPS with nontrivial performance ratios. Two algorithms were given, a simple algorithm which runs in linear time for bounded-degree graphs with a ratio 7/18 and a more complicated algorithm with a ratio 4/9. Both algorithms produce outerplanar subgraphs. In this article we present two new versions of the simpler algorithm. The first new algorithm still runs in the same time, produces outerplanar subgraphs, has at least the same performance ratio as the original algorithm, but in practice it finds larger planar subgraphs than the original algorithm. The second new algorithm has similar properties to the first algorithm, but it produces only planar subgraphs. We conjecture that the performance ratios of our algorithms are at least 4/9 for MPS. We experimentally compare the new algorithms against the original simple algorithm. We also apply the new algorithms for approximating the thickness and outerthickness of a graph. Experiments show that the new algorithms produce clearly better approximations than the original simple algorithm by Calinescu et al.