Journal of Combinatorial Optimization

, Volume 27, Issue 1, pp 3–13 | Cite as

Radiation hybrid map construction problem parameterized

  • Chihao Zhang
  • Haitao Jiang
  • Binhai Zhu


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.


Radiation hybrid mapping Kernel Fixed-parameter tractable 



This research is partially supported by NSF of China under Project 60928006, 60970011 and 61202014, and by the Opening Fund of Top Key Discipline of Computer Software and Theory in Zhejiang Provincial Colleges at Zhejiang Normal University.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Computer ScienceShanghai Jiao Tong UniversityShanghaiChina
  2. 2.School of Computer Science and TechnologyShandong UniversityJinanChina
  3. 3.Department of Computer ScienceMontana State UniversityBozemanUSA

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