Stereo Correspondence Through Feature Grouping and Maximal Cliques
IEEE Transactions on Pattern Analysis and Machine Intelligence
The parameterized complexity of sequence alignment and consensus
Theoretical Computer Science
On the Approximability of the Maximum Common Subgraph Problem
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
The Parameterized Complexity of Sequence Alignment and Consensus
CPM '94 Proceedings of the 5th Annual Symposium on Combinatorial Pattern Matching
Describing parameterized complexity classes
Information and Computation
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
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We introduce the maximum common subgraph problem for multiple graphs (Multi-MCS) inspired by various biological applications such as multiple alignments of gene sequences, protein structures, metabolic pathways, or protein-protein interaction networks. Multi-MCS is a generalization of the two-graph Maximum Common Subgraph problem (MCS). On the basis of the framework of parameterized complexity theory, we derive the parameterized complexity of Multi-MCS for various parameters for different classes of graphs. For example, for directed graphs with labeled vertices, we prove that the parameterized m-Multi-MCS problem is W[2]-hard, while the parameterized k-Multi-MCS problem is W[t]-hard (@?t=1), where m and k are the size of the maximum common subgraph and the number of multiple graphs, respectively. We show similar results for other parameterized versions of the Multi-MCS problem for directed graphs with vertex labels and undirected graphs with vertex and edge labels by giving linear FPT reductions of the problems from parameterized versions of the longest common subsequence problem. Likewise, for unlabeled undirected graphs, we show that a parameterized version of the Multi-MCS problem with a fixed number of input graphs is W[1]-complete by showing a linear FPT reduction to and from a parameterized version of the maximum clique problem.