Lélia Blin

Exclusive perpetual ring exploration without chirality

In this paper, we study the exclusive perpetual exploration problem with mobile anonymous and oblivious robots in a discrete space. Our results hold for the most generic settings: robots are asynchronous and are not given any sense of direction, so the left and right sense (i.e. chirality) is decided by the adversary that schedules robots for execution, and may change between invocations of a particular robots (as robots are oblivious). We investigate both the minimal and the maximal number of robots that are necessary and sufficient to solve the exclusive perpetual exploration problem. On the minimal side, we prove that three deterministic robots are necessary and sufficient, provided that the size n of the ring is at least 10, and show that no protocol with three robots can exclusively perpetually explore a ring of size less than 10. On the maximal side, we prove that k = n - 5 robots are necessary and sufficient to exclusively perpetually explore a ring of size n when n is coprime with k.

The first approximated distributed algorithm for the minimum degree spanning tree problem on general graphs

In this paper we present the first distributed algorithm on general graphs for the minimum degree spanning tree problem. The problem is NP-hard in sequential. Our algorithm gives a spanning tree of a degree at most 1 from the optimal. 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.

Self-stabilizing minimum degree spanning tree within one from the optimal degree

We propose a self-stabilizing algorithm for constructing a Minimum Degree Spanning Tree (MDST) in undirected networks. Starting from an arbitrary state, our algorithm is guaranteed to converge to a legitimate state describing a spanning tree whose maximum node degree is at most @D^*+1, where @D^* is the minimum possible maximum degree of a spanning tree of the network. To the best of our knowledge, our algorithm is the first self-stabilizing solution for the construction of a minimum degree spanning tree in undirected graphs. The algorithm uses only local communications (nodes interact only with the neighbors at one hop distance). Moreover, the algorithm is designed to work in any asynchronous message passing network with reliable FIFO channels. Additionally, we use a fine grained atomicity model (i.e., the send/receive atomicity). The time complexity of our solution is O(mn^2logn) where m is the number of edges and n is the number of nodes. The memory complexity is O(@dlogn) in the send-receive atomicity model (@d is the maximal degree of the network).

A new self-stabilizing minimum spanning tree construction with loop-free property

The minimum spanning tree (MST) construction is a classical problem in Distributed Computing for creating a globally minimized structure distributedly. Self-stabilization is versatile technique for forward recovery that permits to handle any kind of transient faults in a unified manner. The loopfree property provides interesting safety assurance in dynamic networks where edge-cost changes during operation of the protocol. We present a new self-stabilizing MST protocol that improves on previous known approaches in several ways. First, it makes fewer system hypotheses as the size of the network (or an upper bound on the size) need not be known to the participants. Second, it is loop-free in the sense that it guarantees that a spanning tree structure is always preserved while edge costs change dynamically and the protocol adjusts to a new MST. Finally, time complexity matches the best known results, while space complexity results show that this protocol is the most efficient to date.

Distributed Chasing of Network Intruders by Mobile Agents

This paper addresses the graph searching problem in a distributed setting. We describe a distributed protocol that enables searchers with logarithmic size memory to clear any network, in a fully decentralized manner. The search strategy for the network in which the searchers are launched is computed online by the searchers themselves without knowing the topology of the network in advance. It performs in an asynchronous environment, i.e., it implements the necessary synchronization mechanism in a decentralized manner. In every network, our protocol performs a connected strategy using at most k + 1 searchers, where k is the minimum number of searchers required to clear the network in a monotone connected way, computed in the centralized and synchronous setting

Loop-free super-stabilizing spanning tree construction

We propose an univesal scheme to design loop-free and super-stabilizing protocols for constructing spanning trees optimizing any tree metrics (not only those that are isomorphic to a shortest path tree). Our scheme combines a novel super-stabilizing loop-free BFS with an existing self-stabilizing spanning tree that optimizes a given metric. The composition result preserves the best properties of both worlds: super-stabilization, loop-freedom, and optimization of the original metric without any stabilization time penalty. As case study we apply our composition mechanism to two well known metric-dependent spanning trees: the maximum-flow tree and the minimum degree spanning tree.

Fast Self-stabilizing Minimum Spanning Tree Construction

We present a novel self-stabilizing algorithm for minimum spanning tree (MST) construction. The space complexity of our solution is O(log2 n) bits and it converges in O(n2) rounds. Thus, this algorithm improves the convergence time of all previously known self-stabilizing asynchronous MST algorithms by a multiplicative factor Θ(n), to the price of increasing the best known space complexity by a factor O(log n). The main ingredient used in our algorithm is the design, for the first time in self-stabilizing settings, of a labeling scheme for computing the nearest common ancestor with only O(log2 n) bits.

Distributed cost management in a selfish multi-operators BGP network

In this paper we deal with inter-domain routing management from an economical point of view. We present a game theory based costing model that maps BGP peers (autonomous systems belonging to different operators) into a strategic (selfish) agents competing for transit traffic as a service provided and charged to their peers. Indeed, in our model each operator fixes a price to each neighbor for each transit traffic unit. Then, BGP routing choice is made based on a minimum cost criterion where the goal of each operator is to minimize its costs. We investigate some particular strategies of updating prices that operators can use locally in order to minimize their costs. We focus on BGP stabilization properties related to such strategies from a simulation point of view.

Compact deterministic self-stabilizing leader election on a ring: the exponential advantage of being talkative

This paper focuses on compact deterministic self-stabilizing solutions for the leader election problem. When the solution is required to be silent (i.e., when the state of each process remains fixed from some point in time during any execution), there exists a lower bound of