Conflict Resolution and Membership Problem in Beeping Channels

Huang, Bojun; Moscibroda, Thomas

doi:10.1007/978-3-642-41527-2_22

Cited by 9 publications

(6 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The impact of collision detection is studied in [41,28], where it is proved that performances are improved, and in certain cases the improvement can be exponential. The complexity of the conflict resolution problem (where the goal is to let every active node use the channel alone (without collision) at least once) is studied in [21] (they assume that nodes are identified), and an efficient deterministic solution is presented and analysed.…”

Section: Further Related Workmentioning

confidence: 99%

Design patterns in beeping algorithms: Examples, emulation, and analysis

Casteigts

Métivier

Robson

et al. 2019

Information and Computation

View full text Add to dashboard Cite

We consider networks of processes which interact using beeps. In the basic model defined by Cornejo and Kuhn (2010), processes can choose in each round either to beep or to listen. Those who beep are unable to detect simultaneous beeps. Those who listen can only distinguish between silence and the presence of at least one beep. We refer to this model as BL (beep or listen). Stronger models exist where the nodes can detect collision while they are beeping (B cd L), listening (BL cd ), or both (B cd L cd ). Beeping models are weak in essence and even simple tasks are difficult or unfeasible within such models. We present a set of generic building blocks (design patterns) which seem to occur frequently in the design of beeping algorithms. They include multi-slot phases: the fact of dividing the main loop into a number of specialised slots; exclusive beeps: having a single node beep at a time in a neighbourhood (within one or two hops); adaptive probability: increasing or decreasing the probability of beeping to produce more exclusive beeps; internal (resp. peripheral) collision detection: for detecting collision while beeping (resp. listening); and emulation of collision detection when it is not available as a primitive. Based on these patterns, we provide algorithms for a number of basic problems, including colouring, 2-hop colouring, degree computation, 2-hop MIS, and collision detection (in BL). The patterns make it possible to formulate these algorithms in a rather concise and elegant way. Their analyses are more technical; one of them significantly reduces the constant factor in the analysis of the best known MIS algorithm by Jeavons et al. (2016). Finally, inspired by a technique from Afek et al. (2013), our last contribution is to show that any Las Vegas algorithm relying on collision detection can be transposed into a Monte Carlo algorithm without collision detection, through emulation of this primitive at the cost of a logarithmic slowdown. We prove that this is optimal by showing a matching lower bound.

show abstract

Section: Further Related Workmentioning

confidence: 99%

Design patterns in beeping algorithms: Examples, emulation, and analysis

Casteigts

Métivier

Robson

et al. 2019

Information and Computation

View full text Add to dashboard Cite

show abstract

“…Although beep model is almost a newly developed communication protocol, it has been received much attention in recent years and various algorithms have been proposed for different distributed problems in this model. As examples of these problems, we can mention interval coloring and graph coloring [5], [14], [15], [16], leader election [17], [18], [19], [20], [21], [22], [23], maximal independent set [24], [25], [26], [27], [28], [29], minimum connected dominating set [30], network size approximation and counting [31], [32], [33], [34], deterministic rendezvous problem [35], naming problem [36], membership problem [37], [38], broadcasting [39], [40], [41], and consensus [42].…”

Section: A Related Workmentioning

confidence: 99%

Distributed Voting in Beep Model

Ghojogh,

Salehkaleybar

2019

Preprint

View full text Add to dashboard Cite

In this paper, we propose two distributed algorithms, named Distributed Voting with Beeps (DVB), for multi-choice voting in beep model where each node can communicate with its neighbors merely by sending beep signals. The two proposed algorithms have simple structures and can be employed in networks having severe constraints on the size of messages. In the first proposed algorithm, the adjacent nodes having the same value form a set called spot. Afterwards, the spots with majority value try to corrode the spots with non-majority values. The second proposed algorithm is based on pairwise interactions between nodes. The proposed algorithms have a termination detection procedure to check whether voting is achieved. We show that the probability of success of the first algorithm goes to one as the percentage of nodes choosing the majority vote as their initial values gets close to one. The second algorithm returns the correct vote with high probability. Our experiments show that the algorithms are fairly invariant to the network topology, initial distribution of values, and network size.

show abstract

“…The impact of collision detection is studied in [SW10,KP13], where it is proved that performances are improved, and in certain cases the improvement can be exponential. The complexity of the conflict resolution problem (the goal is to let every active vertex use the channel alone (without collision) at least once) is studied in [HM13] (they assume that vertices are identified), and an efficient deterministic solution is presented and analysed.…”

Section: Related Workmentioning

confidence: 99%

On Distributed Computing with Beeps

Métivier,

Robson,

Zemmari

2015

Preprint

View full text Add to dashboard Cite

We consider networks of processes which interact with beeps. Various beeping models are used. The basic one, defined by Cornejo and Kuhn [CK10], assumes that a process can choose either to beep or to listen; if it listens it can distinguish between silence or the presence of at least one beep. The aim of this paper is the study of the resolution of paradigms such as collision detection, computation of the degree of a vertex, colouring, or 2-hop-colouring in the framework of beeping models. For each of these problems we present Las Vegas or Monte Carlo algorithms and we analyse their complexities expressed in terms of the number of slots. We present also efficient randomised emulations of more powerful beeping models on the basic one. We illustrate emulation procedures with an efficient degree computation algorithm in the basic beeping model; this algorithm was given initially in a more powerful model.

show abstract

Conflict Resolution and Membership Problem in Beeping Channels

Cited by 9 publications

References 15 publications

Design patterns in beeping algorithms: Examples, emulation, and analysis

Design patterns in beeping algorithms: Examples, emulation, and analysis

Distributed Voting in Beep Model

On Distributed Computing with Beeps

Contact Info

Product

Resources

About