Duplication-Loss Genome Alignment: Complexity and Algorithm

Recently, an Alignment approach for the comparison of two genomes, based on an evolutionary model restricted to Duplications and Losses, has been presented. An exact linear programming algorithm has been developed and successfully applied to the Transfer RNA (tRNA) repertoire in Bacteria, leading to interesting observation on tRNA shift of identity. Here, we explore a direct dynamic programming approach for the Duplication-Loss Alignment of two genomes, which proceeds in two steps: (1) (The Dynamic Programming step) Outputs a best candidate alignment between the two genomes and (2) (Minimum Label Alignment problem) Finds an evolutionary scenario of minimum duplication-loss cost that is in agreement with the alignment. We show that the Minimum Label Alignment is APX-hard, even if the number of occurrences of a gene inside a genome is bounded by 5. We then develop a heuristic which is a thousands of times faster than the linear programming algorithm and exhibits a high degree of accuracy on simulated datasets. The heuristic has been implemented in JAVA and is available on request.