Local Computation of Maximal Independent Set

10/03/2022

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by   Mohsen Ghaffari, et al.

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We present a randomized Local Computation Algorithm (LCA) with query complexity poly(Δ) ·log n for the Maximal Independent Set (MIS) problem. That is, the algorithm determines whether each node is in the computed MIS or not using poly(Δ) ·log n queries to the adjacency lists of the graph, with high probability, and this can be done for different nodes simultaneously and independently. Here Δ and n denote the maximum degree and the number of nodes. This algorithm resolves a key open problem in the study of local computations and sublinear algorithms (attributed to Rubinfeld).