Exact recovery of planted cliques in semi-random graphs

TL;DR

This paper investigates the Planted Clique problem in a semi-random graph model, proposing an SDP-based algorithm that achieves exact recovery, extending previous models and algorithms for related graph problems.

Contribution

It introduces an SDP-based rounding algorithm for the Planted Clique problem in semi-random graphs, providing guarantees similar to those in purely random models.

Findings

Algorithm achieves exact recovery in semi-random models

Provides an alternative SDP-based approach with guarantees

Extends understanding of planted clique detection in complex models

Abstract

In this paper, we study the Planted Clique problem in a semi-random model. Our model is inspired from the Feige-Kilian model [16] which has been studied in many other works [8,11,17,26,35,38] for a variety of graph problems. Our algorithm and analysis is on similar lines to the one studied for the Densest $k$-subgraph problem in the work of Khanna and Louis [25]. As a by-product of our main result, we give an alternate SDP-based rounding algorithm (with similar guarantees) for solving the Planted Clique problem in a random graph.