A realizer of a maximal plane graph is a set of three particular spanning trees. It has been used... more A realizer of a maximal plane graph is a set of three particular spanning trees. It has been used in several graph algorithms and particularly in graph drawing algorithms. We propose colored flips on realizers to generalize Wagner’s theorem on maximal planar graphs to realizers. From this result, it is proved that ξ0 + ξ1 + ξ2 − Δ = n − 1 where ξi is the number of inner nodes in the tree T i, Δ is the number of three colored faces in the realizer and n is the number of vertices. As an application of this formula, we show that orderly spanning trees with at most ë \frac2n + 1-D</font >3 û \left\lfloor {\frac{{2n + 1--\Delta }} {3}} \right\rfloor leaves can be computed in linear time.
2014 Ieee Acm 18th International Symposium on Distributed Simulation and Real Time Applications, Oct 1, 2014
Simulation tools are useful for detailed analysis of distributed systems that are increasingly pr... more Simulation tools are useful for detailed analysis of distributed systems that are increasingly present in our daily lives. ViSiDiA (Visualization and Simulation of Distributed Algorithms) is a platform that aims both to facilitate teaching distributed algorithms and to contribute to the research activities. This paper presents design features and examples of how to implement new ViSiDiA's algorithms. These implementations can be done using the Java language or by using the ViSiDiA's GUI (just drawing the relabelling rules that correspond to considered algorithm). We also present a more complex problem for which ViSiDiA served as a simulation and analysis tool.
The intrinsic characteristics of ad hoc networks, such as the frequent connectivity changes and t... more The intrinsic characteristics of ad hoc networks, such as the frequent connectivity changes and the strict bandwidth and power constraints, impose further challenges, especially for routing tasks. Establishing and maintaining routes are hard tasks in a dynamic environment, in particular for large and dense networks where the control overhead induced by routing packets increases with the number of nodes. To overcome the scalability problem, creating hierarchies among the nodes seems a promising venue and an effective approach to organize the network as the number of nodes increases. In this paper, we investigate the influence of the underlying clustering algorithm on the quality of the routing and illustrate through conducted simulations the gain in network total throughput that can be attained using a clustering scheme that does not rely on periodic exchange of neighborhood information.
A distributed system consists of a collection of processors running simultaneously to achieve a c... more A distributed system consists of a collection of processors running simultaneously to achieve a common task. However, the design of such systems, and the proof of their correctness is a very complex and difficult task. In order to understand, analyze and verify distributed systems and applications, we propose in this paper a general model for proving distributed systems. This model can offer systematic verification of distributed algorithms and also ensure their correct functioning. In other words, the main advantage of this model is the proof of correctness of the distributed algorithms. Moreover, we exploit the refinement technique of Event-B to propose a unified modular development of distributed algorithms. We illustrate this method by investigating examples of the distributed computation of spanning trees, and we implement them by using the Rodin platform. This work has been supported by the french project "Agence Nationale de la Recherche ANR-06-SETI-015"
In a probabilistic graph grammar, each production has a probability attached to it. This induces ... more In a probabilistic graph grammar, each production has a probability attached to it. This induces a probability assigned to each derivation tree, and to each derived graph. Conditions for this probability fkction to be a probabilistic measure are discussed. The statistical properties of the generated language are investigated. We show how to compute the average size of an inductive function, and the probability of an inductive graph predicate. A relationship can be established between production probabilities and some statistical information of the generated language. This way, probabilities can be assigned to productions so that the generated graphs satisfy some statistical conditions. *
Http Dx Doi Org 10 1080 12460125 2012 677645, 2012
Le traitement des requêtes analytiques (OLAP) se base sur deux hypothèses qui semblent contradict... more Le traitement des requêtes analytiques (OLAP) se base sur deux hypothèses qui semblent contradictoires : d'une part on veut que les requêtes soient optimisées (le mieux c'est de les pré-calculer) et d'autre part on suppose que l'on ne connaît pas a priori les requêtes qui sont posées (difficile de les prévoir toutes car elles sont en nombre infini). Dans le présent travail, nous restreignons au cas particulier des cubes de données et à une classe particulière de requêtes (qu'on pourrait qualifier de requêtes de rapports). Malgré ce contexte restrictif, il n'est pas envisageable de matérialiser toutes les requêtes. Nous développons ainsi des techniques basées sur les dépendances fonctionnelles exactes et approximatives afin de sélectionner les meilleures requêtes à matérialiser. Au lieu de fixer une contrainte sur l'espace mémoire disponible, comme c'est fait dans la plupart des travaux, nous supposons une contrainte sur le temps d'exécution des requêtes. Les résultats théoriques sont accompagnés d'expérimentations montrant la faisabilité de notre approche.
The vertex connectivity of a graph is the smallest number of vertices whose deletion separates th... more The vertex connectivity of a graph is the smallest number of vertices whose deletion separates the graph or makes it trivial. This work is devoted to the problem of vertex connectivity test of graphs in a distributed environment based on a general and a constructive approach. The contribution of this paper is threefold. First, using a pre-constructed spanning tree of the considered graph, we present a protocol to test whether a given graph is 2-connected using only local knowledge. Second, we present an encoding of this protocol using graph relabeling systems. The last contribution is the implementation of this protocol in the message passing model. For a given graph G, where M is the number of its edges, N the number of its nodes and Δ is its degree, our algorithms need the following requirements: The first one uses O(Δ×N 2 ) steps and O(Δ×log Δ) bits per node. The second one uses O(Δ × N 2 ) messages, O(N 2 ) time and O(Δ × log Δ) bits per node. Furthermore, the studied network is semi-anonymous: Only the root of the pre-constructed spanning tree needs to be identified.
We propose a probabilistic algorithm for mobile agents which roam around in the network following... more We propose a probabilistic algorithm for mobile agents which roam around in the network following a random walk. We consider the following problem: when two or more agents meet at a node, they merge into a single agent. As the graph is connected, the agents meet in finite time. We are interested in the time it takes for all agents to merge. More precisely, we study a probabilistic model and we analyse the time complexity of a distributed algorithm for all the agents to merge into a single one.
Ad-hoc networks have received significant attention over the last few years as these emerging net... more Ad-hoc networks have received significant attention over the last few years as these emerging networks provide a fast deployable multi-hop wireless infrastructure for a growing number of applications when a wireline network is neither available nor economical to build. To overcome the scalability problem, creating hierarchies among the nodes seems to be a promising approach and an effective way to organize the network as the number of nodes increases. In this paper, we present a novel distributed clustering algorithm for ad-hoc networks. Our algorithm is based on a synchronized and layered process. Its main objective is to minimize the number of control messages exchanged during the clustering process.We evaluate our algorithm using the Visidia simulation test bed and show that it outperforms one of the most known clustering algorithms in minimizing both the number of control messages and the number of elected clusterheads.
Graph traversals are in the basis of many distributed algorithms. In this paper, we use graph rel... more Graph traversals are in the basis of many distributed algorithms. In this paper, we use graph relabelling systems to encode two basic graph traversals which are the broadcast and the convergecast. This encoding allows us to derive formal, modular and simple encoding for many distributed graph algorithms. We illustrate this method by investigating the distributed computation of a breadthfirst spanning tree and the distributed computation of a minimum spanning tree. Our formalism allows to focus on the correctness of a distributed algorithm rather than on the implementation and the communication details.
A realizer of a maximal plane graph is a set of three particular spanning trees. It has been used... more A realizer of a maximal plane graph is a set of three particular spanning trees. It has been used in several graph algorithms and particularly in graph drawing algorithms. We propose colored flips on realizers to generalize Wagner’s theorem on maximal planar graphs to realizers. From this result, it is proved that ξ0 + ξ1 + ξ2 − Δ = n − 1 where ξi is the number of inner nodes in the tree T i, Δ is the number of three colored faces in the realizer and n is the number of vertices. As an application of this formula, we show that orderly spanning trees with at most ë \frac2n + 1-D</font >3 û \left\lfloor {\frac{{2n + 1--\Delta }} {3}} \right\rfloor leaves can be computed in linear time.
2014 Ieee Acm 18th International Symposium on Distributed Simulation and Real Time Applications, Oct 1, 2014
Simulation tools are useful for detailed analysis of distributed systems that are increasingly pr... more Simulation tools are useful for detailed analysis of distributed systems that are increasingly present in our daily lives. ViSiDiA (Visualization and Simulation of Distributed Algorithms) is a platform that aims both to facilitate teaching distributed algorithms and to contribute to the research activities. This paper presents design features and examples of how to implement new ViSiDiA's algorithms. These implementations can be done using the Java language or by using the ViSiDiA's GUI (just drawing the relabelling rules that correspond to considered algorithm). We also present a more complex problem for which ViSiDiA served as a simulation and analysis tool.
The intrinsic characteristics of ad hoc networks, such as the frequent connectivity changes and t... more The intrinsic characteristics of ad hoc networks, such as the frequent connectivity changes and the strict bandwidth and power constraints, impose further challenges, especially for routing tasks. Establishing and maintaining routes are hard tasks in a dynamic environment, in particular for large and dense networks where the control overhead induced by routing packets increases with the number of nodes. To overcome the scalability problem, creating hierarchies among the nodes seems a promising venue and an effective approach to organize the network as the number of nodes increases. In this paper, we investigate the influence of the underlying clustering algorithm on the quality of the routing and illustrate through conducted simulations the gain in network total throughput that can be attained using a clustering scheme that does not rely on periodic exchange of neighborhood information.
A distributed system consists of a collection of processors running simultaneously to achieve a c... more A distributed system consists of a collection of processors running simultaneously to achieve a common task. However, the design of such systems, and the proof of their correctness is a very complex and difficult task. In order to understand, analyze and verify distributed systems and applications, we propose in this paper a general model for proving distributed systems. This model can offer systematic verification of distributed algorithms and also ensure their correct functioning. In other words, the main advantage of this model is the proof of correctness of the distributed algorithms. Moreover, we exploit the refinement technique of Event-B to propose a unified modular development of distributed algorithms. We illustrate this method by investigating examples of the distributed computation of spanning trees, and we implement them by using the Rodin platform. This work has been supported by the french project "Agence Nationale de la Recherche ANR-06-SETI-015"
In a probabilistic graph grammar, each production has a probability attached to it. This induces ... more In a probabilistic graph grammar, each production has a probability attached to it. This induces a probability assigned to each derivation tree, and to each derived graph. Conditions for this probability fkction to be a probabilistic measure are discussed. The statistical properties of the generated language are investigated. We show how to compute the average size of an inductive function, and the probability of an inductive graph predicate. A relationship can be established between production probabilities and some statistical information of the generated language. This way, probabilities can be assigned to productions so that the generated graphs satisfy some statistical conditions. *
Http Dx Doi Org 10 1080 12460125 2012 677645, 2012
Le traitement des requêtes analytiques (OLAP) se base sur deux hypothèses qui semblent contradict... more Le traitement des requêtes analytiques (OLAP) se base sur deux hypothèses qui semblent contradictoires : d'une part on veut que les requêtes soient optimisées (le mieux c'est de les pré-calculer) et d'autre part on suppose que l'on ne connaît pas a priori les requêtes qui sont posées (difficile de les prévoir toutes car elles sont en nombre infini). Dans le présent travail, nous restreignons au cas particulier des cubes de données et à une classe particulière de requêtes (qu'on pourrait qualifier de requêtes de rapports). Malgré ce contexte restrictif, il n'est pas envisageable de matérialiser toutes les requêtes. Nous développons ainsi des techniques basées sur les dépendances fonctionnelles exactes et approximatives afin de sélectionner les meilleures requêtes à matérialiser. Au lieu de fixer une contrainte sur l'espace mémoire disponible, comme c'est fait dans la plupart des travaux, nous supposons une contrainte sur le temps d'exécution des requêtes. Les résultats théoriques sont accompagnés d'expérimentations montrant la faisabilité de notre approche.
The vertex connectivity of a graph is the smallest number of vertices whose deletion separates th... more The vertex connectivity of a graph is the smallest number of vertices whose deletion separates the graph or makes it trivial. This work is devoted to the problem of vertex connectivity test of graphs in a distributed environment based on a general and a constructive approach. The contribution of this paper is threefold. First, using a pre-constructed spanning tree of the considered graph, we present a protocol to test whether a given graph is 2-connected using only local knowledge. Second, we present an encoding of this protocol using graph relabeling systems. The last contribution is the implementation of this protocol in the message passing model. For a given graph G, where M is the number of its edges, N the number of its nodes and Δ is its degree, our algorithms need the following requirements: The first one uses O(Δ×N 2 ) steps and O(Δ×log Δ) bits per node. The second one uses O(Δ × N 2 ) messages, O(N 2 ) time and O(Δ × log Δ) bits per node. Furthermore, the studied network is semi-anonymous: Only the root of the pre-constructed spanning tree needs to be identified.
We propose a probabilistic algorithm for mobile agents which roam around in the network following... more We propose a probabilistic algorithm for mobile agents which roam around in the network following a random walk. We consider the following problem: when two or more agents meet at a node, they merge into a single agent. As the graph is connected, the agents meet in finite time. We are interested in the time it takes for all agents to merge. More precisely, we study a probabilistic model and we analyse the time complexity of a distributed algorithm for all the agents to merge into a single one.
Ad-hoc networks have received significant attention over the last few years as these emerging net... more Ad-hoc networks have received significant attention over the last few years as these emerging networks provide a fast deployable multi-hop wireless infrastructure for a growing number of applications when a wireline network is neither available nor economical to build. To overcome the scalability problem, creating hierarchies among the nodes seems to be a promising approach and an effective way to organize the network as the number of nodes increases. In this paper, we present a novel distributed clustering algorithm for ad-hoc networks. Our algorithm is based on a synchronized and layered process. Its main objective is to minimize the number of control messages exchanged during the clustering process.We evaluate our algorithm using the Visidia simulation test bed and show that it outperforms one of the most known clustering algorithms in minimizing both the number of control messages and the number of elected clusterheads.
Graph traversals are in the basis of many distributed algorithms. In this paper, we use graph rel... more Graph traversals are in the basis of many distributed algorithms. In this paper, we use graph relabelling systems to encode two basic graph traversals which are the broadcast and the convergecast. This encoding allows us to derive formal, modular and simple encoding for many distributed graph algorithms. We illustrate this method by investigating the distributed computation of a breadthfirst spanning tree and the distributed computation of a minimum spanning tree. Our formalism allows to focus on the correctness of a distributed algorithm rather than on the implementation and the communication details.
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Papers by Mohamed Mosbah