Radiation hybrid map construction problem parameterized

  • Authors:

  • Chihao Zhang;Haitao Jiang;Binhai Zhu

  • Affiliations:

  • Department of Computer Science, Shanghai Jiao Tong University, Shanghai, China 200240;School of Computer Science and Technology, Shandong University, Jinan, China 250100;Department of Computer Science, Montana State University, Bozeman, USA 59717-3880

  • Venue:
  • Journal of Combinatorial Optimization
  • Year:
  • 2014

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Abstract

In this paper, we study the Radiation hybrid map construction ($$\mathsf{{RHMC} }$$) problem which is about reconstructing a genome from a set of gene clusters. The problem is known to be $$\mathsf{{NP} }$$-complete even when all gene clusters are of size two and the corresponding problem ($$\mathsf{{RHMC}_2 }$$) 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 ($$\mathsf{{RHMC}_3 }$$). Let $${p\text{- }\mathsf {RHMC} }$$ be a parameterized version of $$\mathsf{{RHMC} }$$ where the parameter is the size of solution. We present a linear kernel for $${p\text{- }\mathsf {RHMC}_3 }$$ of size $$22k$$ that when combined with a bounded search-tree algorithm, gives an FPT algorithm running in $$O(6^kk+n)$$ time. For $${p\text{- }\mathsf {RHMC}_3 }$$ we present a bounded search tree algorithm which runs in $$O^*(2.45^k)$$ time, greatly improving the previous bound using weak kernels.