Abstract
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 [Formula: see text] and a given gene tree [Formula: see text]. Previously, [Tofigh A, Hallett M, Lagergren J, Simultaneous identification of duplications and lateral gene transfers, IEEE/ACM Trans Comput Biol Bioinf 517-535, 2011.] gave a fixed-parameter algorithm for this problem that runs in [Formula: see text] time, where [Formula: see text] is the number of vertices in [Formula: see text], [Formula: see text] is the number of vertices in [Formula: see text], and [Formula: see text] is the minimum cost of an LCA-reconciliation between [Formula: see text] and [Formula: see text]. 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 [Formula: see text] time. In the most interesting case where [Formula: see text], our algorithm is [Formula: see text] times faster.
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