We report on initial experimental results for a practical I/O-efficient Single-Source Shortest-Paths (SSSP) algorithm on general undirected sparse graphs where the ratio between the largest and the smallest edge weight is reasonably bounded (for example integer weights in {1, . . . , 2 32 }) and the realistic assumption holds that main memory is big enough to keep one bit per vertex. While our implementation only guarantees average-case efficiency, i.e., assuming randomly chosen edge-weights,

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... turns out that its performance on real-world instances with non-random edge weights is actually even better than on the respective inputs with random weights. Furthermore, compared to the currently best implementation for external-memory BFS [6] , which in a sense constitutes a lower bound for SSSP, the running time of our approach always stayed within a factor of five, for the most difficult graph classes the difference was even less than a factor of two. We are not aware of any previous I/O-efficient implementation for the classic general SSSP in a (semi) external setting: in two recent projects [10, 23], Kumar/Schwabe-like SSSP approaches on graphs of at most 6 million vertices have been tested, forcing the authors to artificially restrict the main memory size, M , to rather unrealistic 4 to 16 MBytes in order not to leave the semi-external setting or produce huge running times for larger graphs: for random graphs of 2 20 vertices, the best previous approach needed over six hours. In contrast, for a similar ratio of input size vs. M , but on a 128 times larger and even sparser random graph, our approach was less than seven times slower, a relative gain of nearly 20. On a real-world 24 million node street graph, our implementation was over 40 times faster. Even larger gains of over 500 can be estimated for ran- Partially supported by the DFG grant SA 933/3-1. dom line graphs based on previous experimental results for Munagala/Ranade-BFS. Finally, we also report on early results of experiments in which we replace the hard disk by a solid state disk (flash memory).