Kernelization and randomized Parameterized algorithms for Co-path Set problem

Qilong Feng, Qian Zhou, Jianxin Wang

Abstract: Co-path Set problem is of important applications in mapping unique DNA sequences onto chromosomes and whole genomes. Given a graph G, the parameterized version of Co-path Set problem is to find a subset F of edges with size at most k such that each connected component in \(G[E\backslash F]\) is a path. In this paper, we give a kernel of size 6k and a randomized algorithm of running time \(O^*(2.17^k)\) for the Parameterized Co-path Set problem. The randomized methods developed in the paper are of great promising to be applied to other branch-based algorithms.