Friend or Foe? Population Protocols can perform Community Detection

نویسندگان

Luca Becchetti

Andrea E. F. Clementi

Emanuele Natale

Francesco Pasquale

Prasad Raghavendra

Luca Trevisan

چکیده

We present a simple distributed algorithm that, given a regular graph consisting of two communities (or clusters), each inducing a good expander and such that the cut between them has sparsity 1/poly log n, recovers the two communities. More precisely, upon running the protocol, every node assigns itself a binary label of m = Θ(log n) bits, so that with high probability, for all but a small number of outliers, nodes within the same community are assigned labels with Hamming distance o(m), while nodes belonging to di erent communities receive labels with Hamming distance at least m/2− o(m). We refer to such an outcome as a community-sensitive labeling of the graph. Our algorithm uses Θ(log n) local memory and converges after each node performs Θ(log n) steps of local work. Our algorithm and its analysis work in the (random) population protocol model, in which anonymous nodes do not share any global clock (the model is asynchronous) and communication occurs over one single (random) edge per round. We believe, this is the rst provably-e ective protocol for community detection that works in this model.

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