Improved Sublinear Algorithms for Maximal Independent Set and Metric Steiner Forest

2026-10-05

AI Summary

This study addresses the challenge of efficiently estimating the size of the maximum independent set (MIS) and computing the metric Steiner forest cost in sublinear time under the adjacency and distance matrix query models. To this end, the work proposes sublinear-time algorithms based on graph-theoretic reductions that overcome prior theoretical bottlenecks. Specifically, the proposed approach reduces the query complexity for MIS estimation to O(n^{4/3}) and directly solves the Steiner forest problem with an O(n) complexity. These contributions significantly decrease the number of required queries, surpassing the state-of-the-art results presented at SODA 2026, and yield a more concise and efficient solution framework for both problems.

Abstract

In this work we consider the Maximal Independent Set (MIS) problem and the metric Steiner Forest problem in the sublinear time setting, under the adjacency/distance matrix query model. First, we give an algorithm that estimates the size of an MIS up to a multiplicative factor of $(1+\eps)$ using $\tO(n^{4/3}/\eps^2)$ queries. This improves the best previous algorithm by Mahabadi, Roghani, Tarnawski, and Vakilian (SODA 2026), which had a query complexity of $\tO(n^{3/2}/\eps^2)$. Via a reduction from that work, this would automatically imply the same improvement for the problem of estimating the metric Steiner Forest cost up to an $O(\log n)$ factor. However, as our second contribution, we consider the Steiner Forest problem directly and provide an algorithm with $\tO(n)$ query complexity that is very simple and does not proceed via MIS.

Problem

• Maximal Independent Set
• Metric Steiner Forest
• Sublinear Algorithms
• Query Complexity

Innovation

• Sublinear Algorithms
• Maximal Independent Set
• Metric Steiner Forest
• Query Complexity
• Adjacency Matrix Model