FPT Algorithms in Analysis of Heuristics for Extracting Networks in Linear Programs

It often happens that although a problem is FPT, the practitioners prefer to use imprecise heuristic methods to solve the problem in the real-world situation simply because of the fact that the heuristic methods are faster. In this paper we argue that in this situation an FPT algorithm for the given problem may be still of a considerable practical use. In particular, the FPT algorithm can be used to evaluate the quality of approximation of heuristic approaches. To demonstrate this way of application of FPT algorithms, we consider the problem of extracting a maximum-size reflected network in a linear program. We evaluate a known heuristic SGA and its two variations, a new heuristic and an exact algorithm. The new heuristic and algorithm use fixed-parameter tractable procedures. The new heuristic turned out to be of little practical interest, but the exact algorithm is of interest when the network is close in size to the linear program especially if the exact algorithm is used in conjunction with SGA. The most important conclusion is that a variant of SGA that was disregarded before due to it being slower than the other heuristics turns out to be the best choice because in most cases it returns optimal solutions.