Computing Temporal Twins in Time Logarithmic in History Length

Binh-Minh Bui-Xuan (1) , Hugo Hourcade (2, 1) , Cédric Miachon (2)

1 APR - Algorithmes, Programmes et Résolution
2 Courtanet

A temporal graph G is a sequence of static graphs indexed by a set of integers T representing time instants. For ∆ an integer, a pair of ∆-twins is a pair of vertices u \neg v which, starting at some time instant, have exactly the same neighbourhood outside {u, v} for ∆ consecutive instants. We address the enumeration problem of all pairs of ∆-twins in G, such that the overall runtime depends the least on the history length, namely max{t : G_t ∈ G not empty } − min{t : G_t ∈ G not empty }. We give logarithmic solutions, using red-black tree data structure. Numerical analysis of our implementation on graphs collected from real world data scales up to 10^8 history length.

Mots clés: graph theory; historical data; modular decomposition

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

Binh-Minh Bui-Xuan, Hugo Hourcade, Cédric Miachon. Computing Temporal Twins in Time Logarithmic in History Length. Complex Networks 2020, Dec 2020, Madrid, Spain. ⟨hal-02997890⟩