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Theses

Overcoming interference in the beeping communication model

Abstract : Small inexpensive inter-communicating electronic devices have become widely available. Although the individual device has severely limited capabilities (e.g., basic communication, constant-size memory or limited mobility), multitudes of such weak devices communicating together are able to form a low-cost, easily deployable, yet highly performant network. Such distributed systems present significant challenges however when it comes to the design of efficient, scalable and simple algorithms. In this thesis, we are interested in studying such systems composed of devices with severely limited communication capabilities - using only simple bursts of energy. These distributed systems may be modeled using the beeping model, in which nodes communicate by beeping or listening to their neighbors (according to some undirected communication graph). Simultaneous communications (i.e., collisions) result in non-destructive interference: a node with two or more neighbors beeping simultaneously detects a beep. Its simple, general and energy efficient communication mechanism makes the beeping model widely applicable. However, that simplicity comes at a cost. Due to the poor expressiveness of beeps and the interference caused by simultaneous communications, algorithm design is challenging. Throughout this work, we overcome both difficulties in order to provide efficient communication primitives. A particular focus of the thesis is on deterministic and time-efficient solutions independent of the communication graph's parameters (i.e., uniform). The first part of the thesis considers a setting in which nodes wake up at the same time (i.e., the network has been set up a priori). To obtain efficient solutions to fundamental distributed communication problems, we first focus on efficiently solving problems for local symmetry-breaking: (Δ+1)-vertex coloring and maximal independent set (where Δ is the maximum degree of the communication graph). The solutions we devise are particularly efficient when the communication graph is sparse. They are then used to solve the 2-hop variants of these problems and to simulate message-passing. Finally, combining this simulation with existing results, which assume message-passing, gives the first vertex coloring algorithm using less than Δ+1 colors in the beeping model. Then, we study problems defined on a global scale, such as leader election and multi-broadcast (i.e., information dissemination). Leader election is a crucial building block in the design of distributed algorithms. We give the first two time-optimal leader election algorithms for the beeping model. One is deterministic, but requires unique identifiers. The second one does not need identifiers (useful for security and privacy reasons), but is randomized. Building upon the time-optimal leader election solution, computationally efficient and time-optimal algorithms for multi-broadcast are presented. Although a previous time-optimal solution was available, it required computationally expensive methods. The second part of the thesis considers a more difficult but more general setting, in which nodes wake up at some arbitrary time rounds. We focus on the desynchronization problem, and more precisely on its 2-hop variant, which can be used as medium access control method. We show that it is possible for nodes to communicate in a coherent manner beyond their 1-hop neighborhood. More concretely, a primitive allowing nodes to simulate communication on the square of the communication graph is presented. This primitive is a centerpiece in the design of the 2-hop desynchronization algorithm. Finally, by leveraging this solution, we show that higher-level primitives for sending and receiving messages can be obtained in this difficult setting.
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Submitted on : Tuesday, December 10, 2019 - 1:34:06 PM
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Fabien Dufoulon. Overcoming interference in the beeping communication model. Computational Complexity [cs.CC]. Université Paris Saclay (COmUE), 2019. English. ⟨NNT : 2019SACLS233⟩. ⟨tel-02402275⟩

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