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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... 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.
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We present a formal method based on graph rewriting systems for the specifications and the proofs of fault-tolerant distributed algorithms. Our method deals with crash failures. In a crash failure system the process can fail by crashing,... more
We present a formal method based on graph rewriting systems for the specifications and the proofs of fault-tolerant distributed algorithms. Our method deals with crash failures. In a crash failure system the process can fail by crashing, i.e. by permanently halting. The faulty processes are the processes contaminated by the crashes. The methodology is formalized in two phases. In the
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Software Engineering, Distributed System, Distributed Systems, Fault Tolerance, Dependability, and 12 moreFormal Specification, Rewriting, Reliability, Formal method, Graph Rewriting, Message Passing, Formal Model, Fault Localization, Fault Tree Analysis, Fault Tolerant, Spanning Tree, and Distributed Algorithm
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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,... 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 BFS tree
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Abstract We describe a distributed algorithm for computing spanning trees in dynamic networks by using mobile agents. Each agent uses a random walk to move in the network and to construct a spanning subtree for the nodes visited for the... more
Abstract We describe a distributed algorithm for computing spanning trees in dynamic networks by using mobile agents. Each agent uses a random walk to move in the network and to construct a spanning subtree for the nodes visited for the first time. Spanning ...
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In this report1we present a tool for the visualization of distributedcomputations. Special attention is payed to certain distributed algorithmswhich have been coded as rewriting systems by Yves Metivier. In orderto study the behaviour of... more
In this report1we present a tool for the visualization of distributedcomputations. Special attention is payed to certain distributed algorithmswhich have been coded as rewriting systems by Yves Metivier. In orderto study the behaviour of algorithms and tool, several experiments havebeen performed the results of which are presented and discussed. Finally,some important properties of our tool are described and explained. An-version
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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... 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 constructive approach. The contribution of this paper is threefold. First, using a pre-constructed spanning tree of the considered graph,
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Policies, which are widely deployed in networking services (e.g., management, QoS, mobility, etc.), are a promising solution for securing wide distributed systems. However, the adoption of a policy-based approach for security requires an... more
Policies, which are widely deployed in networking services (e.g., management, QoS, mobility, etc.), are a promising solution for securing wide distributed systems. However, the adoption of a policy-based approach for security requires an appropriate policy specification and enforcement tools. In fact, A long-standing problem in distributed systems security is how to specify and enforce correctly security policies. In this paper,
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ABSTRACT In ad hoc networks, hierarchical routing is viewed as an effective solution to face scalability problems. Such routing relies on a subset of nodes to reduce control overhead associated to routing tasks and preserve network... more
ABSTRACT In ad hoc networks, hierarchical routing is viewed as an effective solution to face scalability problems. Such routing relies on a subset of nodes to reduce control overhead associated to routing tasks and preserve network resources. Multipath routing can also be adopted in order to exploit suitably network resources by allowing load balancing and route fault tolerance. Combining the benefits of hierarchical routing and multipath routing can improve significantly the network performances and cope better with mobility. The main contribution of this paper is to propose a multipath extension of a hierarchical routing, which constructs link-disjoint paths and selects less congested and correlated paths for an efficient data transfer and resources use. The performance of our multipath algorithm is witnessed by simulation results. These results indicate that our proposed multipath extension is more effective under various traffic loads in terms of packet delivery ratio and control overhead.