Linear-time computation of optimal subgraphs of decomposable graphs
Journal of Algorithms
A separator theorem for graphs with an excluded minor and its applications
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Generating hard and diverse test sets for NP-hard graph problems
Discrete Applied Mathematics
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
How to find the best approximation results
ACM SIGACT News
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Faster exact algorithms for hard problems: a parameterized point of view
Discrete Mathematics
Vertex cover: further observations and further improvements
Journal of Algorithms
Algorithms column: the vertex cover problem
ACM SIGACT News
Algorithms for Vertex Partitioning Problems on Partial k-Trees
SIAM Journal on Discrete Mathematics
Dominating sets in planar graphs: branch-width and exponential speed-up
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Treewidth: Algorithmoc Techniques and Results
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Tree Decompositions with Small Cost
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Practical Algorithms on Partial k-Trees with an Application to Domination-like Problems
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Improved Tree Decomposition Based Algorithms for Domination-like Problems
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Solving large FPT problems on coarse-grained parallel machines
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
Parameterized complexity: exponential speed-up for planar graph problems
Journal of Algorithms
Planar Branch Decompositions I: The Ratcatcher
INFORMS Journal on Computing
Parameterized Complexity: The Main Ideas and Some Research Frontiers
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Parameterized Complexity
Computing Bond Types in Molecule Graphs
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
An experimental study on generating planar graphs
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Dealing with large hidden constants: engineering a planar steiner tree PTAS
Journal of Experimental Algorithmics (JEA)
Treewidth: characterizations, applications, and computations
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Efficient exact algorithms on planar graphs: exploiting sphere cut branch decompositions
ESA'05 Proceedings of the 13th annual European conference on Algorithms
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
Parameterized complexity of generalized vertex cover problems
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Charge group partitioning in biomolecular simulation
RECOMB'12 Proceedings of the 16th Annual international conference on Research in Computational Molecular Biology
Tree decompositions of graphs: Saving memory in dynamic programming
Discrete Optimization
Graph minors and parameterized algorithm design
The Multivariate Algorithmic Revolution and Beyond
Implementation and comparison of heuristics for the vertex cover problem on huge graphs
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
A novel parameterised approximation algorithm for minimum vertex cover
Theoretical Computer Science
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Many NP-complete problems on planar graphs are ''fixed-parameter tractable:'' Recent theoretical work provided tree decomposition-based fixed-parameter algorithms exactly solving various parameterized problems on planar graphs, among others VERTEX COVER, in time O(c^kn). Here, c is some constant depending on the graph problem to be solved, n is the number of graph vertices, and k is the problem parameter (for VERTEX COVER this is the size of the vertex cover). In this paper, we present an experimental study for such tree decomposition-based algorithms focusing on VERTEX COVER. We demonstrate that the tree decomposition-based approach provides a valuable way of exactly solving VERTEX COVER on planar graphs. Doing so, we also demonstrate the impressive power of the so-called Nemhauser/Trotter theorem which provides a VERTEX COVER-specific, extremely useful data reduction through polynomial time preprocessing. Altogether, this underpins the practical importance of the underlying theory.