Multi-Hop Beeping Networks Klaus-Tycho Frster, Jochen Seidel, Roger - - PowerPoint PPT Presentation

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Multi-Hop Beeping Networks Klaus-Tycho Frster, Jochen Seidel, Roger - - PowerPoint PPT Presentation

Dec 08, 2023 28 likes •381 views

Deterministic Leader Election in Multi-Hop Beeping Networks Klaus-Tycho Frster, Jochen Seidel, Roger Wattenhofer ETH Zurich Distributed Computing www.disco.ethz.ch What Algorithm to take? Deterministic Randomization Heuristic Leader

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SLIDE 1 ETH Zurich – Distributed Computing – www.disco.ethz.ch

Klaus-Tycho Förster, Jochen Seidel, Roger Wattenhofer

Deterministic Leader Election in Multi-Hop Beeping Networks

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SLIDE 2

What Algorithm to take? Deterministic Heuristic Randomization

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Leader Election

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LeaderElection

Leader

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Why deterministic leader election?

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Why deterministic leader election?

  

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Single-Hop

  • from Θ log log 𝑜 [Willard, 1986] to Θ 𝑜 log 𝑜 [Clementi et al., 2003] …

– (depending on the model)

Multi-Hop

  • with collision detection

– (deterministic): Θ 𝑜 [Kowalski & Pelc, 2009]

  • without collision detection

– (randomized): O 𝑜 log 𝑜 [Czumaj & Rytter, 2006], Θ 𝑜 [Chlebus et al., 2012] – (deterministic): O 𝑜 log3/2𝑜 log log 𝑜 [Chlebus et al., 2012]

– Ω 𝑜 log 𝑜 [Kowalski & Pelc, 2009] – O 𝑜 log2𝑜 log log 𝑜 [Vaya, 2011]

Leader Election – Wireless Radio Networks

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  • Each round: beep or listen
  • Listen: silence or beep (at least one neighbor beeps)

The Beeping Model

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  • Each round: beep or listen
  • Listen: silence or beep (at least one neighbor beeps)

The Beeping Model

Beep Listen Listen Listen

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  • Each round: beep or listen
  • Listen: silence or beep (at least one neighbor beeps)

The Beeping Model

Beep Listens: Silence Listens: Beep Listens: Beep

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  • Each round: beep or listen
  • Listen: silence or beep (at least one neighbor beeps)

The Beeping Model

Beep Listen Listen Beep

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SLIDE 12
  • Each round: beep or listen
  • Listen: silence or beep (at least one neighbor beeps)

The Beeping Model

Beep Listens: Beep Listens: Beep Beep

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  • Randomized: [Ghaffari & Haeupler, 2013]

– 𝑃 𝐸 + log 𝑜 log log 𝑜 ∗ 𝑛𝑗𝑜 log log 𝑜 , log 𝑜 /𝐸

Leader Election – in the Beeping Model

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  • Deterministic & Uniform: 𝑃 𝐸 log 𝑜 [this paper]

Deterministic Leader Election – in the Beeping Model 1110 1100 1010 1101

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Deterministic Leader Election – in the Beeping Model 1110 1100 1010 1101

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Deterministic Leader Election – in the Beeping Model 1110 1100 1010 1101

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Deterministic Leader Election – in the Beeping Model 1110 1100 1010 1101

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Deterministic Leader Election – in the Beeping Model 1110 1100 1010 1101 

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Deterministic Leader Election – in the Beeping Model 1110 1100 1010 1101 

1111 1111

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Multi-Hop Beeping Model Winner

Listening Not sending

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But what about Uniformity?

I know nothing

(I‘m Jon Snow)

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IDs of different length? 1100 111 10 1 11 10...01 "∞"

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IDs of different length? 1100 111 10 1 11

 

10...01 "∞"

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IDs of different length? 1100 111 10 1 11 10...01

 

"∞"

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SLIDE 25

IDs of different length? 1100 1100 10 1 11 10...01

  

"∞"

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SLIDE 26

IDs of different length? 1100 1100 1100 1 11 10...01

   

"∞"

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SLIDE 27

IDs of different length? 1100 1100 1100 1100 10...01

    

"∞"

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IDs of different length? 1100 111 10 1 11 10...01

 

"∞"

  • 1. Iteration done
  • 1. Iteration running
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IDs of different length? 1100 111 10 1 11 10...01

 

"∞"

  • 1. Iteration done
  • 1. Iteration running
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IDs of different length? 1100 111 10 1 11 10...01

 

"∞"

  • 1. Iteration done
  • 1. Iteration running

I want to start with Iteration 2! But I am still in Iteration 1!

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IDs of different length? 1100 111 10 1 11 10...01

 

"∞"

  • 1. Iteration done
  • 1. Iteration running
Iteration 𝑛𝑝𝑒 3 = 0 ? LISTEN Iteration 𝑛𝑝𝑒 3 = 1 ? LISTEN Iteration 𝑛𝑝𝑒 3 = 2 ? BEEP Iteration 𝑛𝑝𝑒 3 = 0 ? LISTEN Iteration 𝑛𝑝𝑒 3 = 1 ? BEEP Iteration 𝑛𝑝𝑒 3 = 2 ? LISTEN
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  • Repeat the campaigning process 𝐸 times -> 𝑃 𝐸 log 𝑜
  • But how big is 𝐸?
  • How do we stop?

Quiescence?

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Quiescence?

Solution: Overlay Onion Network

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  • Multi-Hop Leader Election in the Beeping Model

– 𝑃 𝐸 log 𝑜 rounds – Deterministic – Uniform – Quiescent

  • Combines

– a local campaigning algorithm – a technique to sequentially execute algorithms – an overlay onion network

Conclusion

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SLIDE 35 ETH Zurich – Distributed Computing – www.disco.ethz.ch

Klaus-Tycho Förster, Jochen Seidel, Roger Wattenhofer

Deterministic Leader Election in Multi-Hop Beeping Networks