Query Lower Bounds for Correlation Clustering under Memory Constraints

2026-05-21

AI Summary

This work investigates the trade-off between query complexity and memory in correlation clustering under memory constraints, focusing on the minimum number of graph queries required to either estimate the optimal clustering cost or output an approximately correct partition. Operating within standard graph query models—including adjacency, neighbor, and degree queries—the study combines information-theoretic and probabilistic arguments to establish the first lower bounds on query complexity in this setting. The main contributions are twofold: it proves that producing a partition with additive error εn² necessitates Ω(n/ε²) queries, and further demonstrates that even estimating the optimal cost alone requires significantly more than n/ε² queries in the random query model. These results provide fundamental theoretical limits for memory-constrained correlation clustering algorithms.

Abstract

This work initiates the study of memory-query tradeoffs for graph problems, with a focus on correlation clustering. Correlation clustering asks for a partition of the vertices that minimizes disagreements: non-edges inside clusters plus edges across clusters. Our first result is a tight query lower bound: to output a partition whose cost approximates the optimum up to an additive error of $\varepsilon n^2$, any algorithm requires $Ω(n/\varepsilon^2)$ adjacency-matrix queries. Under memory constraints, we show that even for the seemingly easier task of approximating the optimal clustering cost (without producing a partition), any algorithm in the random query model must make $\gg n/\varepsilon^2$ adjacency-matrix queries. Finally, we prove the first general graph model query lower bound for correlation clustering, where algorithms are allowed adjacency-matrix, neighbor, and degree queries. The latter two bounds are not yet tight, leaving room for sharper results.

Problem

• correlation clustering
• query lower bounds
• memory constraints
• graph algorithms
• approximation

Innovation

• correlation clustering
• query complexity
• memory constraints
• lower bounds
• graph algorithms