Linear-time MIS size estimation

Develop a maximal independent set size estimation algorithm for the adjacency-matrix query model that runs in $O(n)$ time.

Background

The paper gives a randomized algorithm that estimates the size of a random-greedy maximal independent set within a $(1+\varepsilon)$ multiplicative factor in $O(n^{4/3}/\varepsilon^2)$ time. This improves the previously known $O(n^{3/2}/\varepsilon^2)$ bound.

The authors explicitly ask whether the running time can be reduced further to linear in the number of vertices, which would improve upon the paper’s main MIS estimation result.