An Improved Combinatorial Algorithm for Edge-Colored Clustering in Hypergraphs

2026-03-03

AI Summary

This work addresses the node clustering problem in edge-colored hypergraphs, where the goal is to assign colors to nodes so as to maximize agreement with the colors of their incident hyperedges—a problem known to be NP-hard. The paper proposes a novel purely combinatorial approximation algorithm that, for the first time, achieves an approximation factor strictly below 2 without relying on linear programming, thereby breaking through the performance barrier of existing combinatorial approaches. By integrating local search with greedy strategies, the method significantly enhances approximation quality while preserving scalability, offering an efficient and theoretically superior solution to this challenging optimization problem.

Technology Category

Search and Optimization: Combinatorial OptimizationConstraint Satisfaction and Optimization: Distributed CSP/OptimizationKnowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsEconomics, Online Markets and Human Computation: Research challenges in human and human-AI computationWeb Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text

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.

Problem

• edge-colored clustering
• hypergraphs
• combinatorial algorithm
• approximation algorithm
• node coloring

Innovation

• edge-colored hypergraphs
• combinatorial algorithm
• approximation algorithm
• clustering
• approximation factor