On Fast and Robust Information Spreading in the Vertex-Congest Model

This paper initiates the study of the impact of failures on the fundamental problem of \emph{information spreading} in the Vertex-Congest model, in which in every round, each of the $n$ nodes sends the same $O(\log{n})$-bit message to all of its neighbors. Our contribution to coping with failures is twofold. First, we prove that the randomized algorithm which chooses uniformly at random the next message to forward is slow, requiring $\Omega(n/\sqrt{k})$ rounds on some graphs, which we denote by $G_{n,k}$, where $k$ is the vertex-connectivity. Second, we design a randomized algorithm that makes dynamic message choices, with probabilities that change over the execution. We prove that for $G_{n,k}$ it requires only a near-optimal number of $O(n\log^3{n}/k)$ rounds, despite a rate of $q=O(k/n\log^3{n})$ failures per round. Our technique of choosing probabilities that change according to the execution is of independent interest.Comment: Appears in SIROCCO 2015 conferenc

Dependability in Aggregation by Averaging

Aggregation is an important building block of modern distributed applications, allowing the determination of meaningful properties (e.g. network size, total storage capacity, average load, majorities, etc.) that are used to direct the execution of the system. However, the majority of the existing aggregation algorithms exhibit relevant dependability issues, when prospecting their use in real application environments. In this paper, we reveal some dependability issues of aggregation algorithms based on iterative averaging techniques, giving some directions to solve them. This class of algorithms is considered robust (when compared to common tree-based approaches), being independent from the used routing topology and providing an aggregation result at all nodes. However, their robustness is strongly challenged and their correctness often compromised, when changing the assumptions of their working environment to more realistic ones. The correctness of this class of algorithms relies on the maintenance of a fundamental invariant, commonly designated as "mass conservation". We will argue that this main invariant is often broken in practical settings, and that additional mechanisms and modifications are required to maintain it, incurring in some degradation of the algorithms performance. In particular, we discuss the behavior of three representative algorithms Push-Sum Protocol, Push-Pull Gossip protocol and Distributed Random Grouping under asynchronous and faulty (with message loss and node crashes) environments. More specifically, we propose and evaluate two new versions of the Push-Pull Gossip protocol, which solve its message interleaving problem (evidenced even in a synchronous operation mode).Comment: 14 pages. Presented in Inforum 200

Randomized permutation routing in multihop ad hoc networks with unknown destinations

A large variety of permutation routing protocols in a single-hop Network are known to day. Since they are single hop, there is always a wireless path connecting two nodes. One way to solve this problem in a multiple hop environment is to partition nodes into clusters, where a node in each cluster called clusterhead is responsible for the routing service. In this paper, we propose a clustering mechanism to perform permutation routing in multi-hop ad hoc Networks having p stations and in which n data items are saved. We first develop a clustering algorithm to partition stations into clusters. Secondly, we run a locally permutation routing to broadcast items to their local destinations in each group. Finally we use a multicast procedure to transmit outgoing items to their final cluster destination.1st IFIP International Conference on Ad-Hoc NetWorkingRed de Universidades con Carreras en Informática (RedUNCI

Randomized Initialization of a Wireless Multihop Network

Address autoconfiguration is an important mechanism required to set the IP address of a node automatically in a wireless network. The address autoconfiguration, also known as initialization or naming, consists to give a unique identifier ranging from 1 to $n$ for a set of $n$ indistinguishable nodes. We consider a wireless network where $n$ nodes (processors) are randomly thrown in a square $X$, uniformly and independently. We assume that the network is synchronous and two nodes are able to communicate if they are within distance at most of $r$ of each other ($r$ is the transmitting/receiving range). The model of this paper concerns nodes without the collision detection ability: if two or more neighbors of a processor $u$ transmit concurrently at the same time, then $u$ would not receive either messages. We suppose also that nodes know neither the topology of the network nor the number of nodes in the network. Moreover, they start indistinguishable, anonymous and unnamed. Under this extremal scenario, we design and analyze a fully distributed protocol to achieve the initialization task for a wireless multihop network of $n$ nodes uniformly scattered in a square $X$. We show how the transmitting range of the deployed stations can affect the typical characteristics such as the degrees and the diameter of the network. By allowing the nodes to transmit at a range r= \sqrt{\frac{(1+\ell) \ln{n} \SIZE}{\pi n}} (slightly greater than the one required to have a connected network), we show how to design a randomized protocol running in expected time $O(n^{3/2} \log^2{n})$ in order to assign a unique number ranging from 1 to $n$ to each of the $n$ participating nodes

Efficient epidemic multicast in heterogeneous networks

The scalability and resilience of epidemic multicast, also called probabilistic or gossip-based multicast, rests on its symmetry: Each participant node contributes the same share of bandwidth thus spreading the load and allowing for redundancy. On the other hand, the symmetry of gossiping means that it does not avoid nodes or links with less capacity. Unfortunately, one cannot naively avoid such symmetry without also endangering scalability and resilience. In this paper we point out how to break out of this dilemma, by lazily deferring message transmission according to a configurable policy. An experimental proof-of-concept illustrates the approach.Fundação para a Ciência e a Tecnologia (FCT) - Project “P-SON: Probabilistically Structured Overlay Networks” (POS C/EIA/60941/2004)

Optimal Initialization and Gossiping Algorithms for Random Radio Networks

The initialization problem, also known as naming, consists to give a unique identifier ranging from $1$ to $n$ to a set of $n$ indistinguishable nodes in a given network. We consider a network where $n$ nodes (processors) are randomly deployed in a square (resp. cube) $X$. We assume that the time is slotted and the network is synchronous, two nodes are able to communicate if they are within distance at most of $r$ of each other ($r$ is the transmitting/receiving range). Moreover, if two or more neighbors of a processor $u$ transmit concurrently at the same time slot, then $u$ would not receive either messages. We suppose also that the anonymous nodes know neither the topology of the network nor the number of nodes in the network. Under this extremal scenario, we first show how the transmitting range of the deployed processors affects the typical characteristics of the network. Then, by allowing the nodes to transmit at various ranges we design sub-linear randomized initialization protocols~: In the two, resp. three, dimensional case, our randomized initialization algorithms run in $O(n^{1/2} \log{n}^{1/2})$, resp. $O(n^{1/3} \log{n}^{2/3})$, time slots. These latter protocols are based upon an optimal gossiping algorithm which is of independent interest

Random Geometric Graphs and the Initialization Problem for Wireless Networks

32 pages. Tutorial invitéInternational audienceThe initialization problem, also known as naming, assigns one unique identifier (ranging from 1 to $n$) to a set of n indistinguishable nodes (stations or processors) in a given wireless network $N$. $N$ is composed of $n$ nodes randomly deployed within a square (or a cube) $X$. We assume the time to be slotted and $N$ to be synchronous; two nodes are able to communicate if they are within a distance at most $r$ of each other ($r$ is the transmitting/receiving range). Moreover, if two or more neighbors of a processor $u$ transmit concurrently at the same round, $u$ does not receive either messages. After the analysis of various critical transmitting/sensing ranges for connectivity and coverage of randomly deployed sensor networks, we design sub-linear randomized initialization and gossip algorithms achieving $O(n^1/2 \log(n)^1/2)$ and $O(n^1/3 \log(n)^2/3) rounds in the two-dimensional and the three-dimensional cases, respectively. Next, we propose energy-efficient initialization and gossip algorithms running in$O(n^3/4 \log (n)^1/4)$rounds, with no station being awake for more than O(n^1/4 \log (n)^3/4)$ rounds