Radiation Hybrid Map Construction Problem Parameterized

In this paper, we study the Radiation Hybrid Map Construction (RHMC) problem which is about reconstructing a genome from a set of gene clusters. The problem is known to be NP-complete even when all gene clusters are of size two and the corresponding problem (RHMC2) admits efficient constant-factor approximation algorithms. In this paper, for the first time, we consider the more general case when the gene clusters can have size either two or three (RHMC3). Let p-RHMC be a parameterized version of RHMC where the parameter is the size of solution. We present a linear kernel for p-RHMC3 of size 22k, together with a bounded search tree algorithm, we obtain an FPT algorithm running in O(6k+n) time. For p-RHMC2 we present a bounded search tree algorithm which runs in O∗(2.45k) time, greatly improving the previous bound using weak kernels.