# A Faster Small Treewidth SDP Solver

arXiv: https://arxiv.org/abs/2211.06033 · HTML: https://mlsanity.com/paper/2211.06033/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Nov 2022.

## Built on by (most cited first, 30 of 36)

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## Abstract (arXiv)

Semidefinite programming is a fundamental tool in optimization and theoretical computer science. It has been extensively used as a black-box for solving many problems, such as embedding, complexity, learning, and discrepancy. One natural setting of semidefinite programming is the small treewidth setting. The best previous SDP solver under small treewidth setting is due to Zhang-Lavaei '18, which takes n1.5 τ6.5 time. In this work, we show how to solve a semidefinite programming with n × n variables, m constraints and τ treewidth in n τ2ω+0.5 time, where ω < 2.373 denotes the exponent of matrix multiplication. We give the first SDP solver that runs in time in linear in number of variables under this setting. In addition, we improve the running time that solves a linear programming with tau treewidth from n τ2 (Dong-Lee-Ye '21) to n τ(ω+1)/2.