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1. Introduction In this paper, we consider a connected undi-rected graph with n nodes. An asynchronous distributed algorithm is described which determines a spanning tree of the graph. Moreover, if the edges of the graph are weighted, the same algorithm can compute a minimum-weighted spanning tree. This algorithm can be favourably compared to the one of… (More)

—We propose in this paper a novel clustering algorithm in ultrametric spaces. It has a computational cost of O(n). This method is based on the ultratriangle inequality property. Using the order of ultrametric space we demonstrate that we can deduce the proximities between all data in this space with just a few informations. We present an example of our… (More)

- Said Fouchal, Ivan Lavallée
- 2011

We introduce in this paper a competitive unsupervised clustering algorithm which has two strong features: it is fast and flexible on the processed data type as well as in terms of precision. Our approach has a computational cost, in the worst case, of O(n 2) + ε, and in the average case, of O(n) + ε. This complexity is due to the use of ultrametric distance… (More)

This paper presents an asynchronous distributed algorithm for solving the maximum flow problem which is based on the preflow-push approach of Golberg-Tarjan. Each node in graph initially knows the capacities of outgoing and incoming adjacent arcs, the source nodes knows additionally the number of nodes in graph. Nodes execute the same algorithm, and… (More)

Two types of distributed fully asynchronous probabilistic algorithms are given in the present paper which elect a leader and nd a spanning tree in arbitrary anonymous networks of processes. Our algorithms are simpler than in [11] and slightly improve on those in [9,11] with respect to communication complexity. So far, the present algorithms are very likely… (More)

We assume a link-register communication model under read/write atomicity, where every process can read from but cannot write into its neighbours' registers. The paper presents two self-stabilizing protocols for basic fair and reliable link communication primitives. The first primitive guarantees that any process writes a new value in its register(s) only… (More)

Fast matrix multiplication (FMM) algorithms to multiply two n × n matrices reduce the asymptotic operation count from O(n3) of the traditional algorithm to O(n2.38), thus on distributed memory computers, the association of FMM algorithms and the parallel matrix multiplication algorithms always gives remarkable results. Within this association, the… (More)