Diameter determination on restricted graph families
Discrete Applied Mathematics
Exact and Approximate Distances in Graphs - A Survey
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
External-Memory Breadth-First Search with Sublinear I/O
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
The webgraph framework I: compression techniques
Proceedings of the 13th international conference on World Wide Web
Network Analysis: Methodological Foundations (Lecture Notes in Computer Science)
Network Analysis: Methodological Foundations (Lecture Notes in Computer Science)
Fast computation of empirically tight bounds for the diameter of massive graphs
Journal of Experimental Algorithmics (JEA)
Graph Mining: Patterns, Generators and Tools
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
A comparison of three algorithms for approximating the distance distribution in real-world graphs
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
On computing the diameter of real-world directed (weighted) graphs
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
I/O-efficient hierarchical diameter approximation
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Using Pregel-like Large Scale Graph Processing Frameworks for Social Network Analysis
ASONAM '12 Proceedings of the 2012 International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2012)
On computing the diameter of real-world undirected graphs
Theoretical Computer Science
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The diameter of an unweighted graph is the maximum pairwise distance among its connected vertices. It is one of the main measures in real-world graphs and complex networks. The double sweep is a simple method to find a lower bound for the diameter. It chooses a random vertex and performs two breadth-first searches (BFSes), returning the maximum length among the shortest paths thus found. We propose an algorithm called fringe, which uses few BFSes to find a matching upper bound for almost all the graphs in our dataset of 44 real-world graphs. In the few graphs it cannot, we perform an exhaustive search of the diameter using a cluster of machines for a total of 40 cores. In all cases, the diameter is surprisingly equal to the lower bound found after very few executions of the double sweep method. The lesson learned is that the latter can be used to find the diameter of real-world graphs in many more cases than expected, and our fringe algorithm can quickly validate this finding for most of them.