Brief Announcement: Leader Election with Noisy Reconfigurable Circuits in the Amoebot Model

Abstract

Reconfigurable circuits substantially accelerate coordination tasks in the geometric Amoebot model, but existing circuit-based leader election assumes perfectly reliable circuit beeps and provides only Monte Carlo guarantees. We introduce a natural fault model in which circuit beeps are noisy: whenever at least one amoebot beeps on a circuit in a round, each amoebot hears that beep in the next round independently with probability 1-ε, while direct neighbor-to-neighbor (pin-to-pin) communication remains reliable. In this noisy-circuit model we give a Las Vegas leader election algorithm that terminates in O(√{log n} log n) rounds w.h.p. Moreover, once a leader is elected, we show how to simulate any stationary algorithm that is correct in the noiseless circuit model with only an O(√{log n}) multiplicative overhead in running time. Our techniques combine robust flooding/acknowledgment primitives with a tree-based competition framework (Euler-tour representation, randomized attrition, and deterministic solitude verification).