Parameterized enumeration, transversals, and imperfect phylogeny reconstruction
Artikel i vetenskaplig tidskrift, 2006
We study parameterized enumeration problems where we are interested in all solutions of limited size rather than
just some solution of minimum cardinality. (Actually, we have to enumerate the inclusion-minimal solutions in
order to get FPT results.) Two novel concepts are the
notion of a full kernel that contains all small solutions and implicit enumeration of solutions in form of
compressed descriptions. In particular, we study combinatorial and computational bounds for the transversal hypergraph (vertex covers in graphs is a special case), restricted to hyperedges with at most k elements. As an
example, we apply the results and further special-purpose techniques to almost-perfect phylogeny reconstruction, a problem in in computational biology.