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The Cartographer
Sum-Of-Squares To Approximate Knapsack
February 18, 2025 Β· Declared Dead Β· π arXiv.org
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Authors
Pravesh K. Kothari, Sherry Sarkar
arXiv ID
2502.13292
Category
cs.DS: Data Structures & Algorithms
Cross-listed
math.OC
Citations
0
Venue
arXiv.org
Last Checked
5 months ago
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.
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