  Genetic and comparative genomic studies indicate that extant genomes are more
properly considered to be a fusion product of random mutations over generations
and genomic material transfers between individuals of different lineages. This
has motivated researchers to adopt phylogenetic networks and other general
models to study genome evolution. One important problem arising from
reconstruction and verification of phylogenetic networks is the cluster
containment problem, namely determining whether or not a cluster of taxa is
displayed in a phylogenetic network. In this work, a new upper bound for this
NP-complete problem is established through an efficient reduction to the SAT
problem. Two efficient (albeit exponential time) methods are also implemented.
It is developed on the basis of generalization of the so-called
reticulation-visible property of phylogenetic networks.
