Identifying duplications and lateral gene transfers simultaneously and rapidly

This paper deals with the problem of enumerating all minimum-cost LCA-reconciliations involving gene duplications and lateral gene transfers (LGTs) for a given species tree S and a given gene tree G. Previously, Tofigh et al. [20] gave a fixed-parameter algorithm for this problem that runs in O(m + 3
^k
n) time, where m is the number of vertices in S, n is the number of vertices in G, and k is the minimum cost of an LCA-reconciliation between Sand G. In this paper, by refining their algorithm, we obtain a new one for the same problem that finds and outputs the solutions in a compact form within O(mn
²
+ 3
^k
) time.