  We consider the problem of extracting a maximum-size reflected network in a
linear program. This problem has been studied before and a state-of-the-art SGA
heuristic with two variations have been proposed.
  In this paper we apply a new approach to evaluate the quality of<EMAIL_ADDRESS>In
particular, we solve majority of the instances in the testbed to optimality
using a new fixed-parameter algorithm, i.e., an algorithm whose runtime is
polynomial in the input size but exponential in terms of an additional
parameter associated with the given problem.
  This analysis allows us to conclude that the the existing SGA heuristic, in
fact, produces solutions of a very high quality and often reaches the optimal
objective values. However, SGA contain two components which leave some space
for improvement: building of a spanning tree and searching for an independent
set in a graph. In the hope of obtaining even better heuristic, we tried to
replace both of these components with some equivalent algorithms.
  We tried to use a fixed-parameter algorithm instead of a greedy one for
searching of an independent set. But even the exact solution of this subproblem
improved the whole heuristic insignificantly. Hence, the crucial part of SGA is
building of a spanning tree. We tried three different algorithms, and it
appears that the Depth-First search is clearly superior to the other ones in
building of the spanning tree for SGA.
  Thereby, by application of fixed-parameter algorithms, we managed to check
that the existing SGA heuristic is of a high quality and selected the component
which required an improvement. This allowed us to intensify the research in a
proper direction which yielded a superior variation of SGA.
