  At CPM 2017, Castelli et al. define and study a new variant of the Longest
Common Subsequence Problem, termed the Longest Filled Common Subsequence
Problem (LFCS). For the LFCS problem, the input consists of two strings $A$ and
$B$ and a multiset of characters $\mathcal{M}$. The goal is to insert the
characters from $\mathcal{M}$ into the string $B$, thus obtaining a new string
$B^*$, such that the Longest Common Subsequence (LCS) between $A$ and $B^*$ is
maximized. Casteli et al. show that the problem is NP-hard and provide a
3/5-approximation algorithm for the problem.
  In this paper we study the problem from the experimental point of view. We
introduce, implement and test new heuristic algorithms and compare them with
the approximation algorithm of Casteli et al. Moreover, we introduce an Integer
Linear Program (ILP) model for the problem and we use the state of the art ILP
solver, Gurobi, to obtain exact solution for moderate sized instances.
