The input/output complexity of sorting and related problems
Communications of the ACM
Diameter determination on restricted graph families
Discrete Applied Mathematics
External-Memory Breadth-First Search with Sublinear I/O
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Asynchronous parallel disk sorting
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
External-memory exact and approximate all-pairs shortest-paths in undirected graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On Trade-Offs in External-Memory Diameter-Approximation
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Fast computation of empirically tight bounds for the diameter of massive graphs
Journal of Experimental Algorithmics (JEA)
Finding the diameter in real-world graphs experimentally turning a lower bound into an upper bound
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
External-memory network analysis algorithms for naturally sparse graphs
ESA'11 Proceedings of the 19th European conference on Algorithms
Fast and simple approximation of the diameter and radius of a graph
WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
On computing the diameter of real-world directed (weighted) graphs
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
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Computing diameters of huge graphs is a key challenge in complex network analysis. As long as the graphs fit into main memory, diameters can be efficiently approximated (and frequently even exactly determined) using heuristics that apply a limited number of BFS traversals. If the input graphs have to be kept and processed on external storage, even a single BFS run may cause an unacceptable amount of time-consuming I/O-operations. Meyer [17] proposed the first parameterized diameter approximation algorithm with fewer I/Os than that required for exact BFS traversal. In this paper we derive hierarchical extensions of this randomized approach and experimentally compare their trade-offs between actually achieved running times and approximation ratios. We show that the hierarchical approach is frequently capable of producing surprisingly good diameter approximations in shorter time than BFS. We also provide theoretical and practical insights into worst-case input classes.