Consistency of Sequence-Based Gene Clusters

In comparative genomics, various combinatorial models can be used to specify gene clusters-groups of genes that are co-located in a set of genomes. Several approaches have been proposed to reconstruct putative ancestral gene clusters based on the gene order of contemporary species. One prevalent and natural reconstruction criterion is consistency: For a set of reconstructed gene clusters, there should exist a gene order that comprises all given clusters. In this paper, we discuss the consistency problem for different gene cluster models on sequences with restricted gene multiplicities. Our results range from linear-time algorithms for the simple model of adjacencies to NP completeness for more complex models like common intervals.