Distinguishing Views in Symmetric Networks: A Tight Lower Bound

The view of a node in a port-labeled network is an infinite tree encoding all walks in the network originating from this node. We prove that for any integers $n\geq D\geq 1$, there exists a port-labeled network with at most $n$ nodes and diameter at most $D$ which contains a pair of nodes whose (infinite) views are different, but whose views truncated to depth $\Omega(D\log (n/D))$ are identical

On Simple Back-Off in Unreliable Radio Networks

In this paper, we study local and global broadcast in the dual graph model, which describes communication in a radio network with both reliable and unreliable links. Existing work proved that efficient solutions to these problems are impossible in the dual graph model under standard assumptions. In real networks, however, simple back-off strategies tend to perform well for solving these basic communication tasks. We address this apparent paradox by introducing a new set of constraints to the dual graph model that better generalize the slow/fast fading behavior common in real networks. We prove that in the context of these new constraints, simple back-off strategies now provide efficient solutions to local and global broadcast in the dual graph model. We also precisely characterize how this efficiency degrades as the new constraints are reduced down to non-existent, and prove new lower bounds that establish this degradation as near optimal for a large class of natural algorithms. We conclude with an analysis of a more general model where we propose an enhanced back-off algorithm. These results provide theoretical foundations for the practical observation that simple back-off algorithms tend to work well even amid the complicated link dynamics of real radio networks

On λ-Alert Problem

International audienceIn this paper we introduce and analyse the λ-Alert problem: in a single hop radio network a subset of stations is activated. The aim of the protocol is to decide if the number of activated stations is greater or equal to λ. This problem is similar to the k-Selection problem. It can also be seen as an extension of the standard Alert problem. In our paper we consider the λ-Alert problem in various settings. We describe characteristics of oblivious and adaptive deterministic algorithms for the model with and without collision detection. We also show some results for randomized algorithms. In particular, we present a very efficient Las Vegas- type algorithm which is immune to an adversary

Collision-free network exploration

International audienc

Energy-Efficient Leader Election Protocols for Single-Hop Radio Networks

International audienceIn this paper we investigate leader election protocols for single-hop radio networks from perspective of energetic complexity. We discuss different models of energy consumption and its relation with time complexity. We also present some results about energy consumption in classic protocols optimal with respect to time complexity -- we show that some very basic, intuitive algorithms for simplest models (with known number of stations) do not have to be optimal when energy of stations is restricted. We show that they can be significantly improved by introducing very simple modifications. Our main technical result is however a protocol for solving leader election problem in case of unknown number of stations $n$, working on expectancy within $O(\log^\epsilon n)$ rounds, with each station transmitting $O(1)$ number of times and no station being awake for more than $O(\log \log \log n)$ rounds

k-Selection Protocols from Energetic Complexity Perspective

International audienceIn this paper we discuss energetic complexity aspects of k-Selection protocols for the single-hop radio network (that is equivalent to Multiple Access Channel model). The aim is to grant each of k activated stations exclusive access to communication channel. We consider both deterministic as well as randomized algorithms. Our main goal is to investigate relations between minimal time of execution (time complexity) and energy consumption (energetic complexity). We present lower bound for energetic complexity for some classes of algorithms for k-Selection. We also present randomized algorithm efficient in terms of both time and energetic complexity

Fast Collaborative Graph Exploration

International audienceWe study the following scenario of online graph exploration. A team of $k$ agents is initially located at a distinguished vertex $r$ of an undirected graph. At every time step, each agent can traverse an edge of the graph. All vertices have unique identifiers, and upon entering a vertex, an agent obtains the list of identifiers of all its neighbors. We ask how many time steps are required to complete exploration, i.e., to make sure that every vertex has been visited by some agent. We consider two communication models: one in which all agents have global knowledge of the state of the exploration, and one in which agents may only exchange information when simultaneously located at the same vertex. As our main result, we provide the first strategy which performs exploration of a graph with $n$ vertices at a distance of at most $D$ from $r$ in time $O(D)$, using a team of agents of polynomial size $k = D n^{1+ \epsilon} 0$. Our strategy works in the local communication model, without knowledge of global parameters such as $n$ or $D$. We also obtain almost-tight bounds on the asymptotic relation between exploration time and team size, for large $k$. For any constant $c>1$, we show that in the global communication model, a team of $k = D n^c$ agents can always complete exploration in $D(1+ \frac{1}{c-1} +o(1))$ time steps, whereas at least $D(1+ \frac{1}{c} -o(1))$ steps are sometimes required. In the local communication model, $D(1+ \frac{2}{c-1} +o(1))$ steps always suffice to complete exploration, and at least $D(1+ \frac{2}{c} -o(1))$ steps are sometimes required. This shows a clear separation between the global and local communication models