Ivan Lavallée

A Distributed Algorithm for the Maximum Flow Problem

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 exchange messages with neighbors until the maximum flow is established. The algorithm is applicable in cases of multiple sources and/or targets. We give also here some ideas to adjust our algorithm to dynamic changes of arc capacities. For a graph of n nodes and m arcs, our algorithm takes O(n2m) message complexity and O(n2 ) time complexity

Competitive clustering algorithms based on ultrametric properties

Abstract We propose in this paper two new competitive unsupervised clustering algorithms: the first algorithm deals with ultrametric data, it has a computational cost of O(n). The second algorithm has two strong features: it is fast and flexible on the processed data type as well as in terms of precision. The second algorithm has a computational cost, in the worst case, of O(n2), and in the average case, of O(n). These complexities are due to exploitation of ultrametric distance properties. In the first method, we use the order induced by an ultrametric in a given space to demonstrate how we can explore quickly data proximity. In the second method, we create an ultrametric space from a sample data, chosen uniformly at random, in order to obtain a global view of proximities in the data set according to the similarity criterion. Then, we use this proximity profile to cluster the global set. We present an example of our algorithms and compare their results with those of a classic clustering method.

An adaptive distributed algorithm for the maximum flow problem in the underlying asynchronous network

This paper presents a new adaptive distributed algorithm which solves the problem of finding a maximum flow in the underlying asynchronous network. Sequential processes, executing the same code over local data, exchange messages with neighbors to establish the max flow, and adapt themselves to any change of arc capacity in the network. This algorithm is derived to the case of multiple sources and/or sinks without adding virtual source and/or virtual sink. For a graph of V nodes and E arcs, the algorithm achieves O(n 2 m) message complexity and O(n 2 ) time complexity.

Optimal clustering method in ultrametric spaces

Resume 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 results and show the efficiency and the consistency of our algorithm compared with another.

Fast and flexible unsupervised custering algorithm based on ultrametric properties

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 properties. We create an ultrametric space from a sample data, chosen uniformly at random, in order to obtain a global view of proximities in the data set according to the similarity criterion. Then, we use this proximity profile to cluster the global set. We present two examples of our algorithm and compare our results with those of a classic clustering method.

A distributed preflow-push for the maximum flow problem

We present a new algorithm that solves the problem of distributively determining the maximum flow in an asynchronous network. This distributed algorithm is based on the preflow-push technique. Sequential processes, executing the same code over local data, exchange messages with neighbors to establish the max flow. This algorithm is derived to the case of multiple sources and/or sinks without modifications. For a network of n nodes and m arcs, the algorithm achieves O(n2m) message complexity and O(n2) time complexity.

A general scalable implementation of fast matrix multiplication algorithms on distributed memory computers

Fast matrix multiplication (FMM) algorithms to multiply two n /spl times/ n matrices reduce the asymptotic operation count from O(n/sup 3/) of the traditional algorithm to O(n/sup 2.38/), thus on distributed memory computers, the association of FMM algorithms and the parallel matrix multiplication algorithms always gives remarkable results. Within this association, the application of FMM algorithms at inter-processor level requires us to solve more difficult problems in designing but it forms the most effective algorithms. In this paper, a general model of these algorithms is presented and we also introduce a scalable method to implement this model on distributed memory computers.

A space aware agent-based modeling process for the study of hierarchical complex systems

Complex systems are composed of many heterogeneous elements organized in a hierarchical way, whose mutual interactions make emergent collective behaviors to appear at the highest levels of observation. In biology, as shown by the integrative physiology theory [2], space and geometry have a significant role in the simulation results. In this paper we expose a process, and its set of formalisms, for modeling and simulation of complex system, going from structural modeling to dynamic simulation while integrating geometrical information in behavior study. Our solution relies on three kind of concepts and techniques: hierarchical graphs for modeling the system structure and organization, Zeiglers formalisms for the specification of components [6] and a space aware Multi Agent System for agent-based simulation.

An O(N) clustering method on ultrametric data

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 induced by an ultrametric in a given space, we demonstrate how we explore quickly data proximities in this space. We present an example of our results and show the efficiency and the consistency of our algorithm compared with another.

Base de données anatomo-fonctionnelle sur le cerveau

Abstract This study proposes a closer look at the neuropsychological method defined as the study of the neural bases of the behavioural and cognitive functions using an organisation–representation model for current data and knowledge of the brain, and the application of an anatomofunctional database. A Centre of Cognitive Anatomy (CAC) was set up for the collection and processing of neuronatomical, neuropsychological, and psycho-behavioural data for patients presenting sequels of focal brain damage. Such a system would allow concurrent treatment of anatomical and functional data. We would expect the results from such a model to produce stable ‘anatomofunctional laws’ that would be independent of all inter-individual variations in the functioning of the brain and could be checked against the entire database of information. A direct application would be the improvement of cognitive and/or behavioural rehabilitation of patients with brain damage.