An Improved Combinatorial Algorithm for Edge-Colored Clustering in Hypergraphs
2026-03-03 • Data Structures and Algorithms
Data Structures and AlgorithmsSocial and Information Networks
AI summaryⓘ
The authors study a tough problem where data points and their connections have different colors, and they want to group the points so their colors match the connections as much as possible. This problem is very hard to solve perfectly, so people try to find good approximate solutions. The authors created a new method that is simple to use and runs faster, which improves the quality of these approximate solutions beyond previous efforts. This is the first time such a simple approach achieves better than twice the best possible score.
edge-colored hypergraphclusteringapproximation algorithmNP-hardcombinatorial algorithmmultiway interactionsapproximation factorgraph coloring
Authors
Seongjune Han, Nate Veldt
Abstract
Many complex systems and datasets are characterized by multiway interactions of different categories, and can be modeled as edge-colored hypergraphs. We focus on clustering such datasets using the NP-hard edge-colored clustering problem, where the goal is to assign colors to nodes in such a way that node colors tend to match edge colors. A key focus in prior work has been to develop approximation algorithms for the problem that are combinatorial and easier to scale. In this paper, we present the first combinatorial approximation algorithm with an approximation factor better than 2.