The assignment of orthologous genes between a pair of genomes is a fundamental and challenging problem in comparative genomics, since many computational methods for solving various biological problems critically rely on bona fide orthologs as input. While it is usually done using sequence similarity search, we recently proposed a new combinatorial approach that combines sequence similarity and genome rearrangement. This paper continues the development of the approach and unites genome rearrangement events and (post-speciation) duplication events in a single framework under the parsimony principle. In this framework, orthologous genes are assumed to correspond to each other in the most parsimonious evolutionary scenario involving both genome rearrangement and (post-speciation) gene duplication. Besides several original algorithmic contributions, the enhanced method allows for the detection of inparalogs. Following this approach, we have implemented a high-throughput system for ortholog ...