1. Deterministic Leader Election in Multi-Hop Beeping Networks

2. What Algorithm to take?
Deterministic
Randomization
Heuristic

3. Leader Election

4. LeaderElection
Leader

5. Why deterministic leader election?

6. Why deterministic leader election?  

7. Leader Election – Wireless Radio Networks
Single-Hop
from Θ log log 𝑛 [Willard, 1986] to Θ 𝑛 log 𝑛 [Clementi et al., 2003] …
(depending on the model)
Multi-Hop
with collision detection
(deterministic): Θ 𝑛 [Kowalski & Pelc, 2009]
without collision detection
(randomized): O 𝑛 log 𝑛 [Czumaj & Rytter, 2006], Θ 𝑛 [Chlebus et al., 2012]
(deterministic): O 𝑛 log 3/2 𝑛 log log 𝑛 [Chlebus et al., 2012]
Ω 𝑛 log 𝑛 [Kowalski & Pelc, 2009]
O 𝑛 log 2 𝑛 log log 𝑛 [Vaya, 2011]

8. The Beeping Model Each round: beep or listen
Listen: silence or beep (at least one neighbor beeps)

9. Listen Listen Beep Listen
The Beeping Model
Each round: beep or listen
Listen: silence or beep (at least one neighbor beeps)
Listen
Listen
Beep
Listen

10. Listens: Beep Beep Listens: Beep
The Beeping Model
Each round: beep or listen
Listen: silence or beep (at least one neighbor beeps)
Listens: Silence
Listens: Beep
Beep
Listens: Beep

11. Listen Listen Beep Beep The Beeping Model Each round: beep or listen
Listen: silence or beep (at least one neighbor beeps)
Listen
Listen
Beep
Beep

12. Listens: Beep Listens: Beep Beep Beep The Beeping Model
Each round: beep or listen
Listen: silence or beep (at least one neighbor beeps)
Listens: Beep
Listens: Beep
Beep
Beep

13. Leader Election – in the Beeping Model
Randomized: [Ghaffari & Haeupler, 2013]
𝑂 𝐷+ log 𝑛 log log 𝑛 ∗𝑚𝑖𝑛 log log 𝑛 , log 𝑛 /𝐷

14. Deterministic Leader Election – in the Beeping Model
Deterministic & Uniform: 𝑂 𝐷 log 𝑛 [this paper]
1110
1010
1101
1100

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

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

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

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

19. Deterministic Leader Election – in the Beeping Model
1110
1111
1010 
1101
1100
1111

20. Multi-Hop Beeping Model
Not sending
Listening
Winner 
110

21. But what about Uniformity?
I know nothing
(I‘m Jon Snow)

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

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

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

25. IDs of different length?
1100
1100 10 11 1   
"∞"

26. IDs of different length?
1100
1100
1100 11 1    
"∞"

27. IDs of different length?
1100
1100
1100
1100     
"∞"

28. IDs of different length?
1100
111 10 11 1  
"∞"
1. Iteration done
1. Iteration running

29. IDs of different length?
1100
111 10 11 1  
"∞"
1. Iteration done
1. Iteration running

30. IDs of different length?
I want to start with Iteration 2!
But I am still in Iteration 1!
1100
111 10 11 1  
"∞"
1. Iteration done
1. Iteration running

31. IDs of different length?
Iteration 𝑚𝑜𝑑 3=0 ? LISTEN
Iteration 𝑚𝑜𝑑 3=1 ? LISTEN
Iteration 𝑚𝑜𝑑 3=2 ? BEEP
Iteration 𝑚𝑜𝑑 3=0 ? LISTEN
Iteration 𝑚𝑜𝑑 3=1 ? BEEP
Iteration 𝑚𝑜𝑑 3=2 ? LISTEN
1100
111 10 11 1  
"∞"
1. Iteration done
1. Iteration running

32. Quiescence? Repeat the campaigning process 𝐷 times -> 𝑂 𝐷 log 𝑛
But how big is 𝐷?
How do we stop?

33. Solution: Overlay Onion Network
Quiescence?
Solution: Overlay Onion Network

34. Conclusion Multi-Hop Leader Election in the Beeping Model Combines
𝑂 𝐷 log 𝑛 rounds
Deterministic
Uniform
Quiescent
Combines
a local campaigning algorithm
a technique to sequentially execute algorithms
an overlay onion network

35. Deterministic Leader Election in Multi-Hop Beeping Networks