# Refining bridge-block decompositions through two-stage and recursive tree partitioning

arXiv: https://arxiv.org/abs/2110.06998 · HTML: https://mlsanity.com/paper/2110.06998/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Oct 2021.

## Built on by (most cited first, 2 of 2)

- [Learning Large-Scale MTP2 Gaussian Graphical Models via Bridge-Block Decomposition](https://mlsanity.com/paper/2309.13405/) (2023)
- [Constant Approximation for Normalized Modularity and Associations Clustering](https://mlsanity.com/paper/2212.14334/) (2022)

## Abstract (arXiv)

In transmission networks power flows and network topology are deeply intertwined due to power flow physics. Recent literature shows that specific network substructures named bridge-blocks prevent line failures from propagating globally. A two-stage and recursive tree partitioning approach have been proposed to create more bridge-blocks in transmission networks, improving their robustness against cascading line failures. In this paper we consider the problem of refining the bridge-block decomposition of a given power network with minimal impact on the maximum congestion. We propose two new solution methods, depending on the preferred power flow model. More specifically, (i) we introduce a novel MILP-based approach that uses the DC approximation to solve more efficiently the second-stage optimization problem of the two-stage approach and (ii) we show how the existing recursive approach can be extended to work with AC power flows, drastically improving the running times when compared to the pre-existing AC-based two-stage method.