Computing the block triangular form of a sparse matrix
ACM Transactions on Mathematical Software (TOMS)
Fixed-parameter tractability and completeness II: on completeness for W[1]
Theoretical Computer Science
Bipartite graphs and their applications
Bipartite graphs and their applications
Using Graph Decomposition for Solving Continuous CSPs
CP '98 Proceedings of the 4th International Conference on Principles and Practice of Constraint Programming
Scene Modeling Based on Constraint System Decomposition Techniques
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Constrained minimum vertex cover in bipartite graphs: complexity and parameterized algorithms
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
Graph and combinatorial algorithms for geometric constraint solving
Graph and combinatorial algorithms for geometric constraint solving
Crown Structures for Vertex Cover Kernelization
Theory of Computing Systems
Crown reductions for the Minimum Weighted Vertex Cover problem
Discrete Applied Mathematics
Linear kernels in linear time, or how to save k colors in O(n2) steps
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Parameterized Complexity
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When solving a system of equations, it can be beneficial not to solve it in its entirety at once, but rather to decompose it into smaller subsystems that can be solved in order. Based on a bisimplicial graph representation we analyze the parameterized complexity of two problems central to such a decomposition: The Free Square Block problem related to finding smallest subsystems that can be solved separately, and the Bounded Block Decomposition problem related to determining a decomposition where the largest subsystem is as small as possible. We show both problems to be W[1]-hard. Finally we relate these problems to crown structures and settle two open questions regarding them using our results.