An approximation algorithm for maximum packing of 3-edge paths
Information Processing Letters
On the completeness of a generalized matching problem
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
An efficient parameterized algorithm for m-set packing
Journal of Algorithms
Improved algorithms for path, matching, and packing problems
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Parametric Duality and Kernelization: Lower Bounds and Upper Bounds on Kernel Size
SIAM Journal on Computing
An approximation algorithm for maximum triangle packing
Discrete Applied Mathematics
An O*(3.523k) parameterized algorithm for 3-set packing
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
An improved parameterized algorithm for a generalized matching problem
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Greedy localization and color-coding: improved matching and packing algorithms
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
A Problem Kernelization for Graph Packing
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
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We study (vertex-disjoint) packings of paths of length two (i.e., of P2's) in graphs under a parameterized perspective. Starting from a maximal P2-packing $\mathcal {P}$ of size jwe use extremal combinatorial arguments for determining how many vertices of $\mathcal {P}$ appear in some P2-packing of size (j+ 1) (if it exists). We prove that one can 'reuse' 2.5jvertices. Based on a WIN-WIN approach, we build an algorithm which decides if a P2-packing of size at least kexists in a given graph in time ${\mathcal{O}}^*(2.482^{3k})$.