Local Computation of Maximal Independent Set

TL;DR

This paper introduces a randomized local computation algorithm for the Maximal Independent Set problem that efficiently determines node inclusion with poly(Δ)·log n queries, addressing a key open problem in sublinear algorithms.

Contribution

It presents the first efficient LCA for MIS with poly(Δ)·log n query complexity, solving a major open problem in local computation algorithms.

Findings

Achieves high-probability correctness with poly(Δ)·log n queries.

Supports simultaneous, independent queries for different nodes.

Resolves a longstanding open problem in local computation and sublinear algorithms.

Abstract

We present a randomized Local Computation Algorithm (LCA) with query complexity $poly(\Delta) \cdot \log n$ for the Maximal Independent Set (MIS) problem. That is, the algorithm determines whether each node is in the computed MIS or not using $poly(\Delta) \cdot \log n$ queries to the adjacency lists of the graph, with high probability, and this can be done for different nodes simultaneously and independently. Here $\Delta$ 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).