Bernard Mans

Information Propagation Speed in Mobile and Delay Tolerant Networks

The goal of this paper is to increase our understanding of the fundamental performance limits of mobile and Delay Tolerant Networks (DTNs), where end-to-end multihop paths may not exist and communication routes may only be available through time and mobility. We use analytical tools to derive generic theoretical upper bounds for the information propagation speed in large scale mobile and intermittently connected networks. In other words, we upper-bound the optimal performance, in terms of delay, that can be achieved using any routing algorithm. We then show how our analysis can be applied to specific mobility models to obtain specific analytical estimates. In particular, in 2-D networks, when nodes move at a maximum speed v and their density is small (the network is sparse and asymptotically almost surely disconnected), we prove that the information propagation speed is upper bounded by (1 + O(v2))v in random waypoint-like models, while it is upper bounded by O(√vvv) for other mobility models (random walk, Brownian motion). We also present simulations that confirm the validity of the bounds in these scenarios. Finally, we generalize our results to 1-D and 3-D networks.

Sense of direction in distributed computing

Sense of direction is a property of labeled graphs which has been shown to have a definite impact on computability and complexity in systems of communicating entities, and whose applicability ranges from the analysis of graph classes to distributed object systems. The full consequences of this property are still not known; in fact, the ongoing investigations continue to bring new (often surprising) results, to establish unsuspected links with other research and/or application areas, and to pose more questions than they answer. The aim of this paper is to provide a view of the current status of research, describing some of the relevant results, and providing pointers to future research directions.

Highway Vehicular Delay Tolerant Networks: Information Propagation Speed Properties

In this paper, we provide a full analysis of the information propagation speed in bidirectional vehicular delay tolerant networks such as roads or highways. The provided analysis shows that a phase transition occurs concerning the information propagation speed, with respect to the vehicle densities in each direction of the highway. We prove that under a certain threshold, information propagates on average at vehicle speed, while above this threshold, information propagates dramatically faster at a speed that increases quasi-exponentially when the vehicle density increases. We provide the exact expressions of the threshold and of the average information propagation speed near the threshold, in case of finite or infinite radio propagation speed. Furthermore, we investigate in detail the way information propagates under the threshold, and we prove that delay tolerant routing using cars moving on both directions provides a gain in propagation distance, which is bounded by a sublinear power law with respect to the elapsed time, in the referential of the moving cars. Combining these results, we thus obtain a complete picture of the way information propagates in vehicular networks on roads and highways, which may help designing and evaluating appropriate vehicular ad hoc networks routing protocols. We confirm our analytical results using simulations carried out in several environments (The One and Maple).

Optimal Distributed Algorithms in Unlabeled Tori and Chordal Rings

We study the message complexity of distributed algorithms in tori and chordal Rings when the communication links are unlabeled, which implies that the processors do not have “sense of direction.” We introduce the paradigm ofhandrailwhich allows messages to travel with a consistent direction. We give a distributed algorithm which confirms the conjecture that the leader election problem for unlabeled tori ofNprocessors can be solved using ?(N) messages instead ofO(NlogN). Using the samehandrailparadigm, we solve the election problem using ?(N) messages in unlabeled chordal rings with one chord (of length approximatelyN). This solves the long-standing open problem of the minimal number of unlabeled chords required to decrease theO(NlogN). message complexity. For each topology, we give an algorithm to compute the sense of direction in ?(N) messages (improving theO(NlogN) previous results). This proves the more fundamental result that any global distributed algorithm for these labeled topologies can be used with a similar asymptotic complexity in the respective unlabeled class.

Bandwidth reservation in multihop wireless networks: complexity and mechanisms

We show that link interferences in multihop wireless networks make the problem of selecting a path satisfying bandwidth requirements an NP-complete problem, even under simplified rules for bandwidth reservation. This is in sharp contrast to path selection in wireline networks where efficient polynomial algorithms exist. We also describe a distributed mechanism for the problem of slot allocation according to bandwidth reservation in a wireless slotted environment.

Sense of direction: Definitions, properties, and classes

An extensive body of evidence exists of the impact that specific edge labelings have on the communication complexity of distributed problems. It has been long suspected that these very different labelings share a common property, named sense of direction. In spite of the large number of investigations, and of the obvious practical importance, a formal characterization of this property did not exist. In this paper, we finally provide a formal definition of sense of direction, making explicit the very specific relationship between three factors: the labeling, the topological structure, and the local view that an entity has of the system. In a way, sense of direction is the capability of a node in the system to use the labeling to translate the local view of its neighbors into its own. Using the formal definition as an observational platform, we describe several properties which allow the translation process to be possible beyond the immediate neighborhood. Finally, we identify four general classes of labelings and analyze their properties; these classes include all the labelings used in the literature.

Deterministic Computations in Time-Varying Graphs: Broadcasting under Unstructured Mobility

Most highly dynamic infrastructure-less networks have in common that the assumption of connectivity does not necessarily hold at a given instant. Still, communication routes can be available between any pair of nodes over time and space. These networks (variously called delay-tolerant, disruptive-tolerant, challenged) are naturally modeled as time-varying graphs (or evolving graphs), where the existence of an edge is a function of time. In this paper we study deterministic computations under unstructured mobility, that is when the edges of the graph appear infinitely often but without any (known) pattern. In particular, we focus on the problem of broadcasting with termination detection. We explore the problem with respect to three possible metrics: the date of message arrival (foremost), the time spent doing the broadcast (fastest), and the number of hops used by the broadcast (shortest). We prove that the solvability and complexity of this problem vary with the metric considered, as well as with the type of knowledge a priori available to the entities. These results draw a complete computability map for this problem when mobility is unstructured.

On the impact of sense of direction on message complexity

Abstract In this paper, we prove a general result on the impact of sense of direction. We show that, in arbitrary graphs, any sense of direction has a dramatic effect on the communication complexity of several important distributed problems: Broadcast , Depth First Traversal , Election , and Spanning Tree Construction . In systems with n nodes and e communication links, the solution for the Depth First Traversal and the Broadcast problems require Ω(e) messages with arbitrary labelings; we show that, with any sense of direction, they can be solved exchanging only Θ ( n ) messages, even if the system is anonymous . The problems of Election and of Spanning Tree Construction require Ω(e + n log n) messages with arbitrary labelings; on the other hand, we show that they can be solved with Θ ( n ) messages with any sense of direction. The results presented here completely explain and generalize the existing results which now follow as corollaries for specific labelings.

On routing in circulant graphs

We investigate various problems related to circulant graphs -finding the shortest path between two vertices, finding the shortest loop, and computing the diameter. These problems are related to shortest vector problems in a special class of lattices. We give matching upper and lower bounds on the length of the shortest loop. We claim NP-hardness results, and establish a worst-case/average-case connection for the shortest loop problem. A pseudo-polynomial time algorithm for these problems is also given. Our main tools are results and methods from the geometry of numbers.

HiHCoHP-Toward a realistic communication model for hierarchical hyperclusters of heterogeneous processors

A parameterized model of hyperclusters of processors-clusters of clusters of... of clusters of processors-is formulated under which a hypercluster enjoys generality along three orthogonal axes: (1) Its processors are heterogeneous: they may have different computational powers (speed of computation and memory access). (2) Its constituent clusters are interconnected via a hierarchy of networks of possibly differing bandwidths and speeds. (3) Its clusters at each level of the hierarchy are heterogeneous: they may differ in size. The model accounts for architectural details such as the bandwidths and transit costs of both networks and their ports. The algorithmic tractability of the model is demonstrated via broadcast and reduction algorithms, which are predictably efficient in general and actually optimal in special circumstances.