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
Fixed-parameter tractability of graph modification problems for hereditary properties
Information Processing Letters
Linear-time modular decomposition and efficient transitive orientation of comparability graphs
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
A general method to speed up fixed-parameter-tractable algorithms
Information Processing Letters
Efficient and practical algorithms for sequential modular decomposition
Journal of Algorithms
Cluster graph modification problems
Discrete Applied Mathematics - Discrete mathematics & data mining (DM & DM)
Graph-Modeled Data Clustering: Exact Algorithms for Clique Generation
Theory of Computing Systems
Parameterized Complexity
Clustering with Partial Information
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
A more effective linear kernelization for cluster editing
Theoretical Computer Science
Clustering with partial information
Theoretical Computer Science
Problem kernels for NP-complete edge deletion problems: split and related graphs
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Improved algorithms for bicluster editing
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Fixed-parameter algorithms for cluster vertex deletion
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
A more effective linear kernelization for Cluster Editing
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
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A graph G is said to be a cluster graph if G is a disjoint union of cliques (complete subgraphs), and a bicluster graph if G is a disjoint union of bicliques (complete bipartite subgraphs). In this work, we study the parameterized version of the NP-hard Bicluster Graph Editing problem, which consists of obtaining a bicluster graph by making the minimum number of modifications in the edge set of an input bipartite graph. When at most k modifications are allowed in the edge set of any input graph (Bicluster(k) Graph Editing problem), this problem is FPT, solvable in O(4km) time by applying a search tree algorithm. It is shown an algorithm with O(4k + n + m) time, which uses a new strategy based on modular decomposition techniques. Furthermore, the same techniques lead to a new form of obtaining a problem kernel with O(k2) vertices for the Cluster(k) Graph Editing problem, in O(n +m) time. This problem consists of obtaining a cluster graph by modifying at most k edges in an input graph. A previous FPT algorithm for this problem was presented by Gramm et al. [11]. In their solution, a problem kernel with O(k2) vertices and O(k3) edges is built in O(n3) time.