The Radiation Hybrid Map Construction Problem Is FPT

The Radiation Hybrid Map Construction problem (RHMC) is of prime interest in the area of Bioinformatics, and is concerned with reconstructing a genome from a set of given gene clusters. The problem is \(\mbox{$\mathcal{NP}$}\)-complete, even for the special case when the cardinality of each cluster is 2. Recently, Zhang et al. considered the case when the cardinality of each cluster is at most three, and proved that RHMC in this case is fixed-parameter tractable. They asked whether RHMC is fixed-parameter tractable for any fixed upper bound on the cluster cardinality.

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