Bit Dissemination Problem F O O D ! Bit Dissemination Problem - - PowerPoint PPT Presentation
Self-Stabilizing Broadcast with O(1)-Bit Messages Emanuele Natale joint work with Lucas Boczkowski and Amos Korman 4th Workshop on Biological Distributed Algorithms (BDA) July 25-29, 2016 Chicago, Illinois preprint
Emanuele Natale†
joint work with
Lucas Boczkowski∗ and Amos Korman∗ 4th Workshop on Biological Distributed Algorithms (BDA)
July 25-29, 2016 Chicago, Illinois
† ∗ ⋆preprint at goo.gl/ETNc64
Emanuele Natale†
joint work with
Lucas Boczkowski∗ and Amos Korman∗ 4th Workshop on Biological Distributed Algorithms (BDA)
July 25-29, 2016 Chicago, Illinois
† ∗ ⋆preprint at goo.gl/ETNc64
(Bit Dissemination)
F O O D !
F O O D !
Flocks of birds [Ben-Shahar et al. ’10]
Schools of fish [Sumpter et al. ’08] Flocks of birds [Ben-Shahar et al. ’10]
Schools of fish [Sumpter et al. ’08] Insects colonies [Franks et al. ’02] Flocks of birds [Ben-Shahar et al. ’10]
Animal communication:
PULL(h, ℓ) model [Demers ’88]: at each round each agent can
chosen independently and uniformly at random, and shows ℓ bits to her
Animal communication:
PULL(h, ℓ) model [Demers ’88]: at each round each agent can
chosen independently and uniformly at random, and shows ℓ bits to her
01001
Animal communication:
PULL(h, ℓ) model [Demers ’88]: at each round each agent can
chosen independently and uniformly at random, and shows ℓ bits to her
01001
Animal communication:
PULL(h, ℓ) model [Demers ’88]: at each round each agent can
chosen independently and uniformly at random, and shows ℓ bits to her
01001
Animal communication:
Sources’ bits (and other agents’ states) may change in response to external environment
Sources’ bits (and other agents’ states) may change in response to external environment
Sources’ bits (and other agents’ states) may change in response to external environment
blue vs red: 39/14 ≈ 2.8 Sources’ bits (and other agents’ states) may change in response to external environment
(Probabilistic) Self-stabilizing algorithm: guarantees convergence and closure w.r.t. S (w.h.p.) configuration
S convergence closure (Probabilistic) self-stabilization: S := {“correct configurations of the system” } (= consensus on source’s bit)
system reaches S (w.h.p.)
Self-stablizing algorithms converge from any initial configuration
2-Majority dynamics [Doerr et al. ’11]. Converge to consensus in O(log n) rounds with high probability.
2-Majority dynamics [Doerr et al. ’11]. Converge to consensus in O(log n) rounds with high probability.
1 1 1 1 1 1 1 1 1 1 1 1 1
2-Majority dynamics [Doerr et al. ’11]. Converge to consensus in O(log n) rounds with high probability.
1 1 1 1 1 1 1 1 1 1 1 1 1
2-Majority dynamics [Doerr et al. ’11]. Converge to consensus in O(log n) rounds with high probability.
1 1 1 1 1 1 1 1 1 1 1 1 1
Public
P Emul(P) 1 1 1 1 1 1 0 1 0 1 1 1 0 1 0
Public Private
ℓ bits log ℓ + 1 bits
Message Reduction Lemma
Public
P Emul(P) 1 1 1 1 1 1 0 1 0 1 1 1 0 1 0
Public Private
ℓ bits log ℓ + 1 bits
Message Reduction Lemma Public Private Private Private
1 1 0 0 1 0 1 0 1 0 0 1 0 1 Syn-Clock
Theorem (Self-Stabilizing Bit Dissemination). There is a self-stabilizing Bit Dissemination protocol which converges in ˜ O(log n) rounds w.h.p using 3-bit messages. Theorem (Clock Syncronization). Syn-Clock is a self-stabilizing clock synchronization protocol which synchronizes a clock modulo T in ˜ O(log n log T) rounds w.h.p. using 3-bit messages.
their bit and the 2 bits they pull. If they see only agents of color c for s rounds, they become c-sensitive.
c-frozen if see value c.
f rounds before becoming boosting. BFS(f, s). Agents can boosting, 1/0-frozen or 1/0-sensitive.
their bit and the 2 bits they pull. If they see only agents of color c for s rounds, they become c-sensitive.
c-frozen if see value c.
f rounds before becoming boosting. BFS(f, s). Agents can boosting, 1/0-frozen or 1/0-sensitive.
their bit and the 2 bits they pull. If they see only agents of color c for s rounds, they become c-sensitive.
c-frozen if see value c.
f rounds before becoming boosting. BFS(f, s). Agents can boosting, 1/0-frozen or 1/0-sensitive.
their bit and the 2 bits they pull. If they see only agents of color c for s rounds, they become c-sensitive.
c-frozen if see value c.
f rounds before becoming boosting. BFS(f, s). Agents can boosting, 1/0-frozen or 1/0-sensitive.
their bit and the 2 bits they pull. If they see only agents of color c for s rounds, they become c-sensitive.
c-frozen if see value c.
f rounds before becoming boosting. BFS(f, s). Agents can boosting, 1/0-frozen or 1/0-sensitive.