Randomized parameterized algorithms for P-Packing and Co-Path Packing problems

Qilong Feng, Jianxin Wang, Shaohua Li, Jianer Chen

Abstract: In this paper, we study the Parameterized \(P_2\)-Packing problem and Parameterized Co-Path Packing problem from random perspective. For the Parameterized \(P_2\)-Packing problem, based on the structure analysis of the problem and using random partition technique, a randomized parameterized algorithm of running time \(O^*(6.75^k)\) is obtained, improving the current best result \(O^*(8^k)\). 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 \(20k\) and a randomized algorithm of running time \(O^*(2^k)\) 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 \(O^*(3^k)\) is given for the Parameterized Co-Path Packing problem.