Abstract
This paper considers the fundamental problem of self-stabilizing leader election (SSLE) in the model of population protocols. In this model an unknown number of asynchronous, anonymous and finite state mobile agents interact in pairs. SSLE has been shown to be impossible in this model without additional assumptions. This impossibility can be circumvented for instance by augmenting the system with an oracle (an external module providing supplementary information useful to solve a problem). Fischer and Jiang have proposed solutions to SSLE, for complete communication graphs and rings, using the oracle \(\varOmega ?\), called the eventual leader detector. In this paper, we investigate the power of \(\varOmega ?\) on larger families of graphs. We present two important results.
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