Advances in Exact and Approximate Group Closeness Centrality Maximization

2026-03-26

AI Summary

This work addresses the NP-hard problem of group closeness centrality maximization—selecting k nodes in a graph to minimize the total distance to all other nodes. To enhance computational efficiency, the authors introduce two key techniques: reducing the size of the integer linear programming (ILP) formulation and decreasing the number of iterative solver calls. Additionally, they devise an acceleration strategy for the 1/5-approximation greedy algorithm that preserves its theoretical approximation guarantee. Experimental results demonstrate that the proposed exact algorithm achieves speedups of 3.6–22.3× over the current state-of-the-art method, while the accelerated approximation algorithm runs 1.4–2.9× faster without compromising the 1/5 approximation ratio.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Combinatorial Optimization
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

In the NP-hard \textsc{Group Closeness Centrality Maximization} problem, the input is a graph $G = (V,E)$ and a positive integer $k$, and the task is to find a set $S \subseteq V$ of size $k$ that maximizes the reciprocal of group farness $f(S) = \sum_{v \in V} \min_{s \in S} \text{dist}(v,s)$. A widely used greedy algorithm with previously unknown approximation guarantee may produce arbitrarily poor approximations. To efficiently obtain solutions with quality guarantees, known exact and approximation algorithms are revised. The state-of-the-art exact algorithm iteratively solves ILPs of increasing size until the ILP at hand can represent an optimal solution. In this work, we propose two new techniques to further improve the algorithm. The first technique reduces the size of the ILPs while the second technique aims to minimize the number of needed iterations. Our improvements yield a speedup by a factor of $3.6$ over the next best exact algorithm and can achieve speedups by up to a factor of $22.3$. Furthermore, we add reduction techniques to a $1/5$-approximation algorithm, and show that these adaptations do not compromise its approximation guarantee. The improved algorithm achieves mean speedups of $1.4$ and a maximum speedup of up to $2.9$ times.

Problem

• Group Closeness Centrality
• Centrality Maximization
• Graph Algorithms
• NP-hard Problem

Innovation

• Group Closeness Centrality
• Integer Linear Programming (ILP)
• Approximation Algorithm
• Graph Reduction
• Centrality Maximization