The link between orthology relations and gene trees: a correction perspective

Abstract

We consider four variants of relation and gene tree correction problems, and provide hardness results for all of them. More specifically, we show that it is NP-Hard to edit a minimum of set of relations to make them consistent with a given species tree. We also show that the problem of finding a maximum subset of genes that share consistent relations is hard to approximate. We then demonstrate that editing a gene tree to satisfy a given set of relations in a minimum way is NP-Hard, where "minimum" refers either to the number of modified relations depicted by the gene tree or the number of clades that are lost. We also discuss some of the algorithmic perspectives given these hardness results.