Abstract
In this paper, we study the random methods for parameterized problems. For the Parameterized P 2-Packing problem, by randomly partitioning the vertices, a randomized parameterized algorithm of running time O *(6.75 k ) is obtained, improving the current best result O *(8 k ). For the Parameterized Co-Path Packing problem, we study the kernel and randomized algorithm for the degree-bounded instance, and then by using the iterative compression technique, a randomized algorithm of running time O *(3 k ) is given for the Parameterized Co-Path Packing problem, improving the current best result O *(3.24 k ).
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