RECONSTRUCTION OF EVOLUTION OF GENOME STRUCTURES WITH PARALOGS

For any weighted directed chain-cycle graphs a and b (referred to as structures) and any equal costs of operations (intermergings and duplication), we obtain an algorithm which, by successively applying these operations to a, outputs b if the first structure contains no paralogs (edges with a repeated name) and the second has no more than two paralogs for each edge. The algorithm has a multiplicative error of at most 13/9 + ε, where ε is any strictly positive number, and its runtime is of the order of no(ε–2.6), where n is the size of the initial pair of graphs. We also obtain algorithms for reconstruction of the evolution of genome structures with a condition on ancestor structures and along the phylogenetic tree.