A bridging model for parallel computation
Communications of the ACM
SIAM Journal on Computing
Fixed-parameter tractability and completeness II: on completeness for W[1]
Theoretical Computer Science
Fixed-Parameter Tractability and Completeness I: Basic Results
SIAM Journal on Computing
On limited nondeterminism and the complexity of the V-C dimension
Journal of Computer and System Sciences
An improved fixed-parameter algorithm for vertex cover
Information Processing Letters
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the Efficiency of Parallel Backtracking
IEEE Transactions on Parallel and Distributed Systems
Parameterized Parallel Complexity
Euro-Par '98 Proceedings of the 4th International Euro-Par Conference on Parallel Processing
Upper bounds for vertex cover further improved
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Constrained minimum vertex cover in bipartite graphs: complexity and parameterized algorithms
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
Linear FPT reductions and computational lower bounds
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Experimental evaluation of a tree decomposition-based algorithm for vertex cover on planar graphs
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Tight lower bounds for certain parameterized NP-hard problems
Information and Computation
Strong computational lower bounds via parameterized complexity
Journal of Computer and System Sciences
Real-time minimum vertex cover for two-terminal series-parallel graphs
International Journal of High Performance Computing and Networking
A Stochastic Local Search Approach to Vertex Cover
KI '07 Proceedings of the 30th annual German conference on Advances in Artificial Intelligence
Linear kernelizations for restricted 3-Hitting Set problems
Information Processing Letters
Experimental evaluation of a tree decomposition-based algorithm for vertex cover on planar graphs
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Tight lower bounds for certain parameterized NP-hard problems
Information and Computation
Improved upper bounds for vertex cover
Theoretical Computer Science
Algorithms and theory of computation handbook
A new approach for solving the maximum clique problem
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
Improved parameterized upper bounds for vertex cover
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Parameterized complexity of generalized vertex cover problems
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Maximizing pagerank with new backlinks
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
A parameterized complexity tutorial
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
The impact of parameterized complexity to interdisciplinary problem solving
The Multivariate Algorithmic Revolution and Beyond
A basic parameterized complexity primer
The Multivariate Algorithmic Revolution and Beyond
Distributed memorization for the k-vertex cover problem
ISPA'07 Proceedings of the 5th international conference on Parallel and Distributed Processing and Applications
A parallel strategy for predicting the secondary structure of polycistronic microRNAs
International Journal of Bioinformatics Research and Applications
On the approximability of the link building problem
Theoretical Computer Science
Towards optimal kernel for edge-disjoint triangle packing
Information Processing Letters
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Fixed-parameter tractability (FPT) techniques have recently been successful in solving NP-complete problem instances of practical importance which were too large to be solved with previous methods. In this paper, we show how to enhance this approach through the addition of parallelism, thereby allowing even larger problem instances to be solved in practice. More precisely, we demonstrate the potential of parallelism when applied to the bounded-tree search phase of FPT algorithms. We apply our methodology to the k-VERTEX COVER problem which has important applications in, for example, the analysis of multiple sequence alignments for computational biochemistry. We have implemented our parallel FPT method for the k-VERTEX COVER problem using C and the MPI communication library, and tested it on a 32-node Beowulf cluster. This is the first experimental examination of parallel FPT techniques. As part of our experiments, we solved larger instances of k-VERTEX COVER than in any previously reported implementations. For example, our code can solve problem instances with k≥400 in less than 1.5 h.