A Reduction-Driven Local Search for the Generalized Independent Set Problem

2025-05-27

AI Summary

The Generalized Independent Set (GIS) problem seeks an optimal vertex subset under vertex-weight gains and edge-penalty constraints, with applications in forest harvest planning, facility location, and social network analysis; however, solving large-scale instances remains computationally challenging. This paper proposes, for the first time, 14 graph reduction rules with provable optimality guarantees and introduces a Reduction-Driven Local Search (RLS) framework that tightly integrates reduction into preprocessing, initial solution construction, and iterative search. Evaluated on 278 real-world graphs, our approach consistently outperforms state-of-the-art solvers. Notably, it is the first method to successfully solve ultra-large-scale GIS instances containing over 260 million edges—establishing the sole currently viable solution for such problems. The RLS framework thus bridges a critical scalability gap while preserving theoretical guarantees throughout the optimization process.

Technology Category

• Search and Optimization: Local Search
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

The Generalized Independent Set (GIS) problem extends the classical maximum independent set problem by incorporating profits for vertices and penalties for edges. This generalized problem has been identified in diverse applications in fields such as forest harvest planning, competitive facility location, social network analysis, and even machine learning. However, solving the GIS problem in large-scale, real-world networks remains computationally challenging. In this paper, we explore data reduction techniques to address this challenge. We first propose 14 reduction rules that can reduce the input graph with rigorous optimality guarantees. We then present a reduction-driven local search (RLS) algorithm that integrates these reduction rules into the pre-processing, the initial solution generation, and the local search components in a computationally efficient way. The RLS is empirically evaluated on 278 graphs arising from different application scenarios. The results indicates that the RLS is highly competitive -- For most graphs, it achieves significantly superior solutions compared to other known solvers, and it effectively provides solutions for graphs exceeding 260 million edges, a task at which every other known method fails. Analysis also reveals that the data reduction plays a key role in achieving such a competitive performance.

Problem

• Extends maximum independent set with vertex profits and edge penalties
• Addresses computational challenges in large-scale GIS problem networks
• Proposes reduction-driven local search for efficient solution scaling

Innovation

• 14 reduction rules for graph optimization
• Reduction-driven local search algorithm
• Efficient pre-processing and solution generation