Sum-Of-Squares To Approximate Knapsack
Data Structures and Algorithms
2025-02-20 v1 Optimization and Control
Abstract
These notes give a self-contained exposition of Karlin, Mathieu and Nguyen's tight estimate of the integrality gap of the sum-of-squares semidefinite program for solving the knapsack problem. They are based on a sequence of three lectures in CMU course on Advanced Approximation Algorithms in Fall'21 that used the KMN result to introduce the Sum-of-Squares method for algorithm design. The treatment in these notes uses the pseudo-distribution view of solutions to the sum-of-squares SDPs and only rely on a few basic, reusable results about pseudo-distributions.
Cite
@article{arxiv.2502.13292,
title = {Sum-Of-Squares To Approximate Knapsack},
author = {Pravesh K. Kothari and Sherry Sarkar},
journal= {arXiv preprint arXiv:2502.13292},
year = {2025}
}