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 (RHMC 2) 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 (RHMC 3). Let p−RHMC be a parameterized version of RHMC where the parameter is the size of solution. We present a linear kernel for p−RHMC 3 of size 22k, together with a bounded search tree algorithm, we obtain an FPT algorithm running in O(6 k k + n) time. For p−RHMC 2 we present a bounded search tree algorithm which runs in O *(2.45 k ) time, greatly improving the previous bound using weak kernels.
KeywordsRadiation Hybrid Linear Kernel Good Pattern Free Cluster Search Tree Algorithm
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