Randomized parameterized algorithms for $$P_2$$ P 2 -Packing and Co-Path Packing problems

Abstract

In this paper, we study the Parameterized $$P_2$$ P 2 -Packing problem and Parameterized Co-Path Packing problem from random perspective. For the Parameterized $$P_2$$ P 2 -Packing problem, based on the structure analysis of the problem and using random partition technique, a randomized parameterized algorithm of running time $$O^*(6.75^k)$$ O ? ( 6 . 75 k ) is obtained, improving the current best result $$O^*(8^k)$$ O ? ( 8 k ) . For the Parameterized Co-Path Packing problem, we firstly study the kernel and randomized algorithm for the degree-bounded instance, where each vertex in the instance has degree at most three. A kernel of size $$20k$$ 20 k and a randomized algorithm of running time $$O^*(2^k)$$ O ? ( 2 k ) are given for the Parameterized Co-Path Packing problem with bounded degree constraint. By applying iterative compression technique and based on the randomized algorithm for degree bounded problem, a randomized algorithm of running time $$O^*(3^k)$$ O ? ( 3 k ) is given for the Parameterized Co-Path Packing problem.