We present a randomized strategy for maintaining balance in dynamically changing search trees that has optimal expected behavior. In particular, in the expected case a search or an update takes logarithmic time, with the update requiring fewer than two rotations. Moreover, the update time remains logarithmic, even if the cost of a rotation is taken to be proportional to the size of the rotated subtree. Finger searches and splits and joins can be performed in optimal expected time also. We show that these results continue to hold even if very little true randomness is available, i.e. if only a logarithmic number of truely random bits are available. Our approach generalizes naturally to weighted trees, where the expected time bounds for accesses and updates again match the worst case time bounds of the best deterministic methods. We also discuss ways of implementing our randomized strategy so that no explicit balance information is maintained. Our balancing strategy and our alg...

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 graph...

this paper. Graphs can be loaded and saved in a slightly extended sgraph[Him93] file format

We present a highly polymorphic tool for the construction, synthesis, structuring, manipulation, investigation, and (symbolic) execution of graphs.