# AC-Feasibility on Tree Networks is NP-Hard

arXiv: https://arxiv.org/abs/1410.8253 · HTML: https://mlsanity.com/paper/1410.8253/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2014.

## Built on by (most cited first, 3 of 3)

- [OPF-Learn: An Open-Source Framework for Creating Representative AC Optimal Power Flow Datasets](https://mlsanity.com/paper/2111.01228/) (2021)
- [Spatial Network Decomposition for Fast and Scalable AC-OPF Learning](https://mlsanity.com/paper/2101.06768/) (2021)
- [Dual Conic Proxies for AC Optimal Power Flow](https://mlsanity.com/paper/2310.02969/) (2023)

## Abstract (arXiv)

Recent years have witnessed significant interest in convex relaxations of the power flows, several papers showing that the second-order cone relaxation is tight for tree networks under various conditions on loads or voltages. This paper shows that AC-feasibility, i.e., to find whether some generator dispatch can satisfy a given demand, is NP-Hard for tree networks.