Graph minors and parameterized algorithm design
The Multivariate Algorithmic Revolution and Beyond
What's next? future directions in parameterized complexity
The Multivariate Algorithmic Revolution and Beyond
Strong backdoors to nested satisfiability
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
Faster parameterized algorithms for deletion to split graphs
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Kernel lower bounds using co-nondeterminism: finding induced hereditary subgraphs
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Obtaining planarity by contracting few edges
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Polynomial time and parameterized approximation algorithms for boxicity
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
MSOL restricted contractibility to planar graphs
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Split Vertex Deletion meets Vertex Cover: New fixed-parameter and exact exponential-time algorithms
Information Processing Letters
Obtaining planarity by contracting few edges
Theoretical Computer Science
A faster FPT algorithm for Bipartite Contraction
Information Processing Letters
Parameterized complexity of vertex deletion into perfect graph classes
Theoretical Computer Science
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In the k-Apex problem the task is to find at most k vertices whose deletion makes the given graph planar. The graphs for which there exists a solution form a minor closed class of graphs, hence by the deep results of Robertson and Seymour (J. Comb. Theory, Ser. B 63(1):65–110, 1995; J. Comb. Theory, Ser. B 92(2):325–357, 2004), there is a cubic algorithm for every fixed value of k. However, the proof is extremely complicated and the constants hidden by the big-O notation are huge. Here we give a much simpler algorithm for this problem with quadratic running time, by iteratively reducing the input graph and then applying techniques for graphs of bounded treewidth.