An empirical study of dynamic graph algorithms

The contributions of this paper are both of theoretical and of experimental nature. From the experimental point of view, we conduct an empirical study on some dynamic connectivity algorithms which where developed recently. In particular, the following implementations were tested and compared with simple algorithms: simple sparsification by Eppstein et al. and the recent randomized algorithm by Henzinger and King. In our experiments, we considered both random and non-random inputs. Moreover, we present a simplified variant of the algorithm by Henzinger and King, which for random inputs was always faster than the original implementation. For non-random inputs, simple sparsification was the fastest algorithm for small sequences of updates; for medium and large sequences of updates, the original algorithm by Henzinger and King was faster. From the theoretical point of view, we analyze the average case running time of simple sparsification and prove that for dynamic random graphs its logarithmic overhead vanishes.