Approximating node-deletion problems for matroidal properties
Journal of Algorithms
Vertex cover: further observations and further improvements
Journal of Algorithms
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Crown Structures for Vertex Cover Kernelization
Theory of Computing Systems
Vertex cover might be hard to approximate to within 2-ε
Journal of Computer and System Sciences
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Breakpoint distance and PQ-trees
CPM'10 Proceedings of the 21st annual conference on Combinatorial pattern matching
Parameterized Complexity
A generalization of Nemhauser and Trotter's local optimization theorem
Journal of Computer and System Sciences
On Bounded-Degree Vertex Deletion parameterized by treewidth
Discrete Applied Mathematics
Exact combinatorial algorithms and experiments for finding maximum k-plexes
Journal of Combinatorial Optimization
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Bounded-Degree Vertex Deletion is a fundamental problem in graph theory that has new applications in computational biology. In this paper, we address a special case of Bounded-Degree Vertex Deletion, the Co-Path/Cycle Packing problem, which asks to delete as few vertices as possible such that the graph of the remaining (residual) vertices is composed of disjoint paths and simple cycles. The problem falls into the well-known class of 'node-deletion problems with hereditary properties', is hence NP-complete and unlikely to admit a polynomial time approximation algorithm with approximation factor smaller than 2. In the framework of parameterized complexity, we present a kernelization algorithm that produces a kernel with at most 37k vertices, improving on the super-linear kernel of Fellows et al.'s general theorem for Bounded-Degree Vertex Deletion. Using this kernel, and the method of bounded search trees, we devise an FPT algorithm that runs in time O*(3.24k). On the negative side, we show that the problem is APX-hard and unlikely to have a kernel smaller than 2k by a reduction from Vertex Cover.