Abstract
The P 2 -packing problem is a generalized matching problem and is known to be NP-hard. A kernelization algorithm for the parameterized P 2 -packing problem is a polynomial time algorithm that on an instance ( G , k ) of the problem produces another instance ( G ′ , k ′ ) such that k ′ ⩽ k and that ( G , k ) is a yes-instance if and only if ( G ′ , k ′ ) is a yes-instance. The graph G ′ in the reduced instance is called a kernel. We provide new structural analysis and develop a new kernelization algorithm for the problem that produces a kernel of at most 7 k vertices. This improves the previous best kernelization algorithm that produces a kernel of 15 k vertices. Based on the new kernel, we present a parameterized algorithm of running time O ∗ ( 17.66 k ) for the problem, improving the previous best upper bound O ∗ ( 32 k ) .
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