# Coresets for Clustering in Graphs of Bounded Treewidth

arXiv: https://arxiv.org/abs/1907.04733 · HTML: https://mlsanity.com/paper/1907.04733/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jul 2019.

## Built on by (most cited first, 9 of 9)

- [Towards Optimal Lower Bounds for k-median and k-means Coresets](https://mlsanity.com/paper/2202.12793/) (2022)
- [A Survey on Graph Condensation](https://mlsanity.com/paper/2402.02000/) (2024)
- [Parameterized Approximation Schemes for Clustering with General Norm Objectives](https://mlsanity.com/paper/2304.03146/) (2023)
- [Calibrated Dataset Condensation for Faster Hyperparameter Search](https://mlsanity.com/paper/2405.17535/) (2024)
- [One Backward from Ten Forward, Subsampling for Large-Scale Deep Learning](https://mlsanity.com/paper/2104.13114/) (2021)
- [A Tight VC-Dimension Analysis of Clustering Coresets with Applications](https://mlsanity.com/paper/2501.06588/) (2025)
- [Spectral Greedy Coresets for Graph Neural Networks](https://mlsanity.com/paper/2405.17404/) (2024)
- [Parameterized Approximation for Robust Clustering in Discrete Geometric Spaces](https://mlsanity.com/paper/2305.07316/) (2023)
- [Universal Weak Coreset](https://mlsanity.com/paper/2305.16890/) (2023)

## Abstract (arXiv)

We initiate the study of coresets for clustering in graph metrics, i.e., the shortest-path metric of edge-weighted graphs. Such clustering problems are essential to data analysis and used for example in road networks and data visualization. A coreset is a compact summary of the data that approximately preserves the clustering objective for every possible center set, and it offers significant efficiency improvements in terms of running time, storage, and communication, including in streaming and distributed settings. Our main result is a near-linear time construction of a coreset for k-Median in a general graph G, with size Oε, k(tw(G)) where tw(G) is the treewidth of G, and we complement the construction with a nearly-tight size lower bound. The construction is based on the framework of Feldman and Langberg [STOC 2011], and our main technical contribution, as required by this framework, is a uniform bound of O(tw(G)) on the shattering dimension under any point weights. We validate our coreset on real-world road networks, and our scalable algorithm constructs tiny coresets with high accuracy, which translates to a massive speedup of existing approximation algorithms such as local search for graph k-Median.