Parallel algorithms for transitive reduction for weighted graphs

Abstract. We present a generalization of transitive reduction for weighted graphs and give scalable polynomial algorithms for computing it based on the Floyd-Warshall algorithm for finding shortest paths in graphs. We also show how the algorithms can be optimized for memory efficiency and effectively parallelized to improve the run time. As a consequence, the algorithms can be tuned for modern general purpose graphics processors. Our prototype implementations exhibit significant speedups of more than one order of magnitude compared to their sequential counterparts. Transitive reduction for weighted graphs was instigated by problems in reconstruction of genetic networks. The first experiments in that domain show also encouraging results both regarding run time and the quality of the reconstruction

Slicing AADL specifications for model checking

To combat the state-space explosion problem in model checking larger systems, abstraction techniques can be employed. Here, methods that operate on the system specification before constructing its state space are preferable to those that try to minimize the resulting transition system as they generally reduce peak memory requirements. We sketch a slicing algorithm for system specifications written in (a variant of) the Architecture Analysis and Design Language (AADL). Given a specification and a property to be verified, it automatically removes those parts of the specification that are irrelevant for model checking the property, thus reducing the size of the corresponding transition system. The applicability and effectiveness of our approach is demonstrated by analyzing the state-space reduction for an example, employing a translator from AADL to Promela, the input language of the SPIN model checker

Efficient reconstruction of biological networks via transitive reduction on general purpose graphics processors

Background Techniques for reconstruction of biological networks which are based on perturbation experiments often predict direct interactions between nodes that do not exist. Transitive reduction removes such relations if they can be explained by an indirect path of influences. The existing algorithms for transitive reduction are sequential and might suffer from too long run times for large networks. They also exhibit the anomaly that some existing direct interactions are also removed. Results We develop efficient scalable parallel algorithms for transitive reduction on general purpose graphics processing units for both standard (unweighted) and weighted graphs. Edge weights are regarded as uncertainties of interactions. A direct interaction is removed only if there exists an indirect interaction path between the same nodes which is strictly more certain than the direct one. This is a refinement of the removal condition for the unweighted graphs and avoids to a great extent the erroneous elimination of direct edges. Conclusions Parallel implementations of these algorithms can achieve speed-ups of two orders of magnitude compared to their sequential counterparts. Our experiments show that: i) taking into account the edge weights improves the reconstruction quality compared to the unweighted case; ii) it is advantageous not to distinguish between positive and negative interactions since this lowers the complexity of the algorithms from NP-complete to polynomial without loss of quality