Open Access

David Veith

• Computing the diameter of a graph is a fundamental part of network analysis. Even if the data fits into main memory the best known algorithm needs O(n2) [3] with high probability to compute the exact diameter. In practice this is usually too costly. Therefore, heuristics have been developed to approximate the diameter much faster. The heuristic “double sweep lower bound” (dslb) has reasonably good results and needs only two Breadth-First Searches (BFS). Hence, dslb has a complexity of O(n+m). If the data does not fit into main memory, an external-memory algorithm is needed. In this thesis the I/O model by Vitter and Shriver [4] is used. It is widely accepted and has produced suitable results in the past. The best known external-memory BFS implementation has an I/O-complexity of W(pn B + sort(n)) for sparse graphs [5]. But this is still very expensive compared to the I/O complexity of sorting with O(N/B * logM/B (N/B)). While there is no improvement for the external-memory computation of BFS yet, Meyer published a different approach called “Parallel clustering growing approach” (PAR_APPROX) that is a trade-off between the I/O complexity and the approximation guarantee [6]. In this thesis different existing approaches will be evaluated. Also, PAR_APPROX will be implemented and analyzed if it is viable in practice. One main result will be that it is difficult to choose the parameter in a way that PAR_APPROX is reasonably fast for every graph class without using the semi external-memory Single Source Shortest Path (SSSP) implementation by [1]. However, the gain is small compared to external-memory BFS using this approach. Therefore, the approach PAR_APPROX_R will be developed. Furthermore, a lower bound for the expected error of PAR_APPROX_R will be proved on a carefully chosen difficult input class. With PAR_APPROX_R the desired gain will be reached.