On computing the diameter of real-world undirected graphs

Pilu Crescenzi (1) , Roberto Grossi (2) , Michel Habib (3, 4) , Leonardo Lanzi (5) , Andrea Marino (1)

1 Department of Systems and Computer Science [Florence]
2 Dipartimento di Informatica [Pisa]
3 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
4 GANG - Networks, Graphs and Algorithms
5 DSI - Dipartimento di Sistemi e Informatica

We propose a new algorithm for the classical problem of computing the diameter of undirected unweighted graphs, namely, the maximum distance among all the pairs of nodes, where the distance of a pair of nodes is the number of edges contained in the shortest path connecting these two nodes. Although its worst-case complexity is O(nm) time, where n is the number of nodes and m is the number of edges of the graph, we experimentally show that our algorithm works in O(m) time in practice, requiring few breadth-first searches to complete its task on almost 200 real-world graphs.

Domaines: Algorithme et structure de données [cs.DS]

Pilu Crescenzi, Roberto Grossi, Michel Habib, Leonardo Lanzi, Andrea Marino. On computing the diameter of real-world undirected graphs. Theoretical Computer Science, 2013, Graph Algorithms and Applications: in Honor of Professor Giorgio Ausiello, 514, pp.84-95. ⟨10.1016/j.tcs.2012.09.018⟩. ⟨hal-00936304⟩