Experimental Study of FPT Algorithms for the Directed Feedback Vertex Set Problem

In this experimental study we evaluate the performance of a recent fixed parameter tractable (FPT) algorithm for the directed feedback node set problem (DFVS) by Chen et al. Lacking suitable real world data, all tests are performed on random graphs. To speed up the FPT algorithm we propose several new data reduction rules for DFVS, and then use various heuristics to accelerate the FPT search. Our results show that, compared to the original FPT algorithm, our new reduction rules can significantly reduce the search space, enabling us to solve DFVS on graphs several oders of magnitude larger than before. The study also shows the influence of various factors, such as number of nodes, optimum solution size, edge density, and parameter size, on the performance of the FPT algorithm. Usually, DFVS is motivated by pointing out its usefulness for deadlock recovery. We demonstrate that for deadlock recovery with mutex locks, DFVS is not more helpful than simple cycle detection. Overall, our study provides the first thorough experimental analysis on different aspects of solving DFVS.