# Multi-Priority Graph Sparsification

arXiv: https://arxiv.org/abs/2301.12563 · HTML: https://mlsanity.com/paper/2301.12563/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jan 2023.

## Built on by (most cited first, 1 of 1)

- [Graph Sparsifications using Neural Network Assisted Monte Carlo Tree Search](https://mlsanity.com/paper/2311.10316/) (2023)

## Abstract (arXiv)

A sparsification of a given graph G is a sparser graph (typically a subgraph) which aims to approximate or preserve some property of G. Examples of sparsifications include but are not limited to spanning trees, Steiner trees, spanners, emulators, and distance preservers. Each vertex has the same priority in all of these problems. However, real-world graphs typically assign different ``priorities'' or ``levels'' to different vertices, in which higher-priority vertices require higher-quality connectivity between them. Multi-priority variants of the Steiner tree problem have been studied in prior literature but this generalization is much less studied for other sparsification problems. In this paper, we define a generalized multi-priority problem and present a rounding-up approach that can be used for a variety of graph sparsifications. Our analysis provides a systematic way to compute approximate solutions to multi-priority variants of a wide range of graph sparsification problems given access to a single-priority subroutine.