Gathering radio messages in the path

International audienceIn this paper, we address the problem of gathering information in one node (sink) of a radio network where interference constraints are present: when a node transmits, it produces interference in an area bigger than the area in which its message can actually be received. The network is modeled by a graph; a node is able to transmit one unit of information to the set of vertices at distance at most dT in the graph, but when doing so it generates interferences that do not allow nodes at distance up to dI (dI ≥ dT ) to listen to other transmissions. We are interested in finding a gathering protocol, that is an ordered sequence of rounds (each round consists of noninterfering simultaneous transmissions) such that w(u) messages are transmitted from any node u to a fixed node called the sink. Our aim is to find a gathering protocol with the minimum number of rounds (called gathering time). In this article, we focus on the specific case where the network is a path with the sink at an end vertex of the path and where the traffic is unitary (w(u) = 1 for all u); indeed this simple case appears to be already very difficult. We first give a new lower bound and a protocol with a gathering time that differ only by a constant independent of the length of the path. Then we present a method to construct incremental protocols. An incremental protocol for the path on n + 1 vertices is obtained from a protocol for n vertices by adding new rounds and new calls to some rounds but without changing the calls of the original rounds. We show that some of these incremental protocols are optimal for many values of dT and dI (in particular when dT is prime). We conjecture that this incremental construction always gives optimal protocols. Finally, we derive an approximation algorithm when the sink is placed in an arbitrary vertex in the path

Information Gathering in Ad-Hoc Radio Networks with Tree Topology

We study the problem of information gathering in ad-hoc radio networks without collision detection, focussing on the case when the network forms a tree, with edges directed towards the root. Initially, each node has a piece of information that we refer to as a rumor. Our goal is to design protocols that deliver all rumors to the root of the tree as quickly as possible. The protocol must complete this task within its allotted time even though the actual tree topology is unknown when the computation starts. In the deterministic case, assuming that the nodes are labeled with small integers, we give an O(n)-time protocol that uses unbounded messages, and an O(n log n)-time protocol using bounded messages, where any message can include only one rumor. We also consider fire-and-forward protocols, in which a node can only transmit its own rumor or the rumor received in the previous step. We give a deterministic fire-and- forward protocol with running time O(n^1.5), and we show that it is asymptotically optimal. We then study randomized algorithms where the nodes are not labelled. In this model, we give an O(n log n)-time protocol and we prove that this bound is asymptotically optimal

Latency Optimal Broadcasting in Noisy Wireless Mesh Networks

In this paper, we adopt a new noisy wireless network model introduced very recently by Censor-Hillel et al. in [ACM PODC 2017, CHHZ17]. More specifically, for a given noise parameter $p\in [0,1],$ any sender has a probability of $p$ of transmitting noise or any receiver of a single transmission in its neighborhood has a probability $p$ of receiving noise. In this paper, we first propose a new asymptotically latency-optimal approximation algorithm (under faultless model) that can complete single-message broadcasting task in $D+O(\log^2 n)$ time units/rounds in any WMN of size $n,$ and diameter $D$. We then show this diameter-linear broadcasting algorithm remains robust under the noisy wireless network model and also improves the currently best known result in CHHZ17 by a $\Theta(\log\log n)$ factor. In this paper, we also further extend our robust single-message broadcasting algorithm to $k$ multi-message broadcasting scenario and show it can broadcast $k$ messages in $O(D+k\log n+\log^2 n)$ time rounds. This new robust multi-message broadcasting scheme is not only asymptotically optimal but also answers affirmatively the problem left open in CHHZ17 on the existence of an algorithm that is robust to sender and receiver faults and can broadcast $k$ messages in $O(D+k\log n + polylog(n))$ time rounds.Comment: arXiv admin note: text overlap with arXiv:1705.07369 by other author

Fast Structuring of Radio Networks for Multi-Message Communications

We introduce collision free layerings as a powerful way to structure radio networks. These layerings can replace hard-to-compute BFS-trees in many contexts while having an efficient randomized distributed construction. We demonstrate their versatility by using them to provide near optimal distributed algorithms for several multi-message communication primitives. Designing efficient communication primitives for radio networks has a rich history that began 25 years ago when Bar-Yehuda et al. introduced fast randomized algorithms for broadcasting and for constructing BFS-trees. Their BFS-tree construction time was $O(D \log^2 n)$ rounds, where $D$ is the network diameter and $n$ is the number of nodes. Since then, the complexity of a broadcast has been resolved to be $T_{BC} = \Theta(D \log \frac{n}{D} + \log^2 n)$ rounds. On the other hand, BFS-trees have been used as a crucial building block for many communication primitives and their construction time remained a bottleneck for these primitives. We introduce collision free layerings that can be used in place of BFS-trees and we give a randomized construction of these layerings that runs in nearly broadcast time, that is, w.h.p. in $T_{Lay} = O(D \log \frac{n}{D} + \log^{2+\epsilon} n)$ rounds for any constant $\epsilon>0$. We then use these layerings to obtain: (1) A randomized algorithm for gathering $k$ messages running w.h.p. in $O(T_{Lay} + k)$ rounds. (2) A randomized $k$-message broadcast algorithm running w.h.p. in $O(T_{Lay} + k \log n)$ rounds. These algorithms are optimal up to the small difference in the additive poly-logarithmic term between $T_{BC}$ and $T_{Lay}$. Moreover, they imply the first optimal $O(n \log n)$ round randomized gossip algorithm

Minimizing Flow Time in the Wireless Gathering Problem

We address the problem of efficient data gathering in a wireless network through multi-hop communication. We focus on the objective of minimizing the maximum flow time of a data packet. We prove that no polynomial time algorithm for this problem can have approximation ratio less than \Omega(m^{1/3) when $m$ packets have to be transmitted, unless $P = NP$. We then use resource augmentation to assess the performance of a FIFO-like strategy. We prove that this strategy is 5-speed optimal, i.e., its cost remains within the optimal cost if we allow the algorithm to transmit data at a speed 5 times higher than that of the optimal solution we compare to

Broadcasting in Noisy Radio Networks

The widely-studied radio network model [Chlamtac and Kutten, 1985] is a graph-based description that captures the inherent impact of collisions in wireless communication. In this model, the strong assumption is made that node $v$ receives a message from a neighbor if and only if exactly one of its neighbors broadcasts. We relax this assumption by introducing a new noisy radio network model in which random faults occur at senders or receivers. Specifically, for a constant noise parameter $p \in [0,1)$, either every sender has probability $p$ of transmitting noise or every receiver of a single transmission in its neighborhood has probability $p$ of receiving noise. We first study single-message broadcast algorithms in noisy radio networks and show that the Decay algorithm [Bar-Yehuda et al., 1992] remains robust in the noisy model while the diameter-linear algorithm of Gasieniec et al., 2007 does not. We give a modified version of the algorithm of Gasieniec et al., 2007 that is robust to sender and receiver faults, and extend both this modified algorithm and the Decay algorithm to robust multi-message broadcast algorithms. We next investigate the extent to which (network) coding improves throughput in noisy radio networks. We address the previously perplexing result of Alon et al. 2014 that worst case coding throughput is no better than worst case routing throughput up to constants: we show that the worst case throughput performance of coding is, in fact, superior to that of routing -- by a $\Theta(\log(n))$ gap -- provided receiver faults are introduced. However, we show that any coding or routing scheme for the noiseless setting can be transformed to be robust to sender faults with only a constant throughput overhead. These transformations imply that the results of Alon et al., 2014 carry over to noisy radio networks with sender faults.Comment: Principles of Distributed Computing 201

Towards Opportunistic Data Dissemination in Mobile Phone Sensor Networks

Recently, there has been a growing interest within the research community in developing opportunistic routing protocols. Many schemes have been proposed; however, they differ greatly in assumptions and in type of network for which they are evaluated. As a result, researchers have an ambiguous understanding of how these schemes compare against each other in their specific applications. To investigate the performance of existing opportunistic routing algorithms in realistic scenarios, we propose a heterogeneous architecture including fixed infrastructure, mobile infrastructure, and mobile nodes. The proposed architecture focuses on how to utilize the available, low cost short-range radios of mobile phones for data gathering and dissemination. We also propose a new realistic mobility model and metrics. Existing opportunistic routing protocols are simulated and evaluated with the proposed heterogeneous architecture, mobility models, and transmission interfaces. Results show that some protocols suffer long time-to-live (TTL), while others suffer short TTL. We show that heterogeneous sensor network architectures need heterogeneous routing algorithms, such as a combination of Epidemic and Spray and Wait