A New Algorithm for the Robust Semi-random Independent Set Problem

TL;DR

This paper introduces a deterministic algorithm for the semi-random planted independent set problem, improving the size threshold for successful recovery over previous randomized methods, especially in adversarial settings.

Contribution

The paper presents a new deterministic algorithm that reliably finds the planted independent set when its size is at least proportional to n^{2/3}, surpassing prior randomized approaches.

Findings

Deterministic algorithm successfully finds the planted set for size k=Ω(n^{2/3})

Improves recovery threshold compared to previous randomized algorithms

Works in semi-random models with adversarial edges

Abstract

In this paper, we study a general semi-random version of the planted independent set problem in a model initially proposed by Feige and Kilian, which has a large proportion of adversarial edges. We give a new deterministic algorithm that finds a list of independent sets, one of which, with high probability, is the planted one, provided that the planted set has size $k=\Omega(n^{2/3})$. This improves on Feige and Kilian's original randomized algorithm, which with high probability recovers an independent set of size at least $k$ when $k=\alpha n$ where $\alpha$ is a constant.