Boruvka Meets Nearest Neighbors

Mariano Tepper (1) , Marta Mejail (1) , Pablo Musé (2) , Andrés Almansa (3, 4)

1 Departamento de Computación [Buenos Aires]
2 IIE - Instituto de Ingeniería Eléctrica
3 TSI - Département Traitement du Signal et des Images
4 LTCI - Laboratoire Traitement et Communication de l'Information

Computing the minimum spanning tree (MST) is a common task in the pattern recognition and the computer vision fields. However, little work has been done on efficient general methods for solving the problem on large datasets where graphs are complete and edge weights are given implicitly by a distance between vertex attributes. In this work we propose a generic algorithm that extends the classical Boruvka's algorithm by using nearest neighbors search structures to reduce significantly time and memory performances. The algorithm can also compute in a straightforward way approximate MSTs thus further improving speed. Experiments show that the proposed method outperforms classical algorithms on large low-dimensional datasets by several orders of magnitude. Finally, to illustrate the usefulness of the proposed algorithm, we focus on a classical computer vision problem: image segmentation. We modify a state-of-the-art local graph-based clustering algorithm, thus permitting a global scene analysis.

Mots clés: minimum spanning tree; Boruvka; nearest neighbors search; large datasets; global analysis

Domaines: Vision par ordinateur et reconnaissance de formes [cs.CV]

Mariano Tepper, Marta Mejail, Pablo Musé, Andrés Almansa. Boruvka Meets Nearest Neighbors. 2011. ⟨hal-00583120⟩