Marc Bui

A self-stabilizing distributed algorithm for spanning tree construction in wireless ad hoc networks

Spanning trees help removing cycles and establishing short paths between a given node and the rest of the nodes in a network. In ad hoc mobile computing networks, however, transient node failures occur due to being out of range or powered off. Therefore, we present a self-stabilized distributed algorithm based on homogeneous agents for constructing a random spanning tree. Our approach makes use of distributed random walks as a network traversal scheme, in order to handle dynamic topology changes in ad hoc wireless networks. Each random walk is represented by a mobile agent annexing a territory over the underlying network. These multiple random walks collapse into a final one that defines the random spanning tree. It will be shown that, compared to deterministically predetermined spanning trees, our algorithm is more resilient to transient failures that occur in ad hoc mobile networks.

A distributed algorithm for constructing a minimum diameter spanning tree

We present a new algorithm, which solves the problem of distributively finding a minimum diameter spanning tree of any (non-negatively) real-weighted graph G=(V, E, ω). As an intermediate step, we use a new, fast, linear-time all-pairs shortest paths distributed algorithm to find an absolute centre of G. The resulting distributed algorithm is asynchronous, it works for named asynchronous arbitrary networks and achieves O(|V|) time complexity and O(|V||E|) message complexity.

RANDOMIZED MOBILE AGENT BASED ROUTING IN WIRELESS NETWORKS

We propose a novel approach for shortest path routing in wireless mobile networks. The approach makes use of n mobile agents initially launched from n mobile nodes forming the network. The agents move randomly from node to node and update routing information as they go. The approach is presented in this paper with two protocols. Both of them exhibit good performance in terms of the network and computing resource consumptions. The first protocol relies on independent mobile agents and imposes a minimum bandwidth requirement on individual mobile agents. Each agent carries the link state of its creator and this information remains unchanged except when the mobile agent returns to the home node. The second protocol is a refinement of the first protocol, with some form of interaction between the mobile agents. Each agent maintains the routing table of its creator instead of link state. The randomly walking agents spread the update information and compute the shortest paths via exchanging network state information between the routing tables they carry and the routing tables at the nodes they traverse. The correctness of the protocols is proven. Our analysis shows that the agent cooperation improves the system performance when dealing with topology and link cost changes.

Random walks in distributed computing: a survey

In this survey, we give an overview of the use of random walks as a traversal scheme to derive distributed control algorithms over a network of computers. It is shown that this paradigm for information exchange can be an attractive technique by using electric network theory as a mathematical tool for performance evaluation.

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

Self-Stabilizing Deterministic Network Decomposition

We present a simple and efficient self-stabilizing protocol for the network partitioning problem. Given a graph with k2 nodes, our decomposition scheme partitions the network into connected and disjoint partitions, with k nodes per partition. The proposed algorithm starts with a spanning tree of the graph, but uses some links which do not belong to the tree, if necessary. The protocol is self-stabilizing meaning that starting from an arbitrary state, it is guaranteed to reach a state where the network is correctly partitioned. The protocol stabilizes in 3(h+1) rounds, where h is the height of the tree. We also propose solutions to the case where the network size is n?k2. Hence our protocol works for dynamic systems in the sense that the protocol can adapt to changes of the network size. We discuss an important application of the proposed protocol.

A new method to automatically compute processing times for random walks based distributed algorithms

Random walks constitute an attractive technique in distributed computing. In this paper, we present an original method using relationship between electrical resistance and random walks, to automatically compute quantities such as cover time, and more generally any processing time measure defined through hitting times. This method comes from electrical theory by using Millmans theorem.

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.

Randomized adaptive routing based on mobile agents

The mobile agent has been shown to be a convenient, efficient, and robust approach to designing distributed protocols. This paper introduces an adaptive, mobile agent-based routing algorithm. While performing a random walk through the network, mobile agents sense changes in the network state, and trigger the computation of updated values for the routing tables. The randomized moving strategy exerts a negligible and balanced impact on the network resources, both in terms of bandwidth and computation. The memory requirement is very moderate. The correctness of the protocol is proven and its complexity is analyzed.

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.