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

TL;DR

This paper introduces a reduction-driven local search algorithm for the Generalized Independent Set problem, effectively solving large-scale real-world instances with improved solutions and computational efficiency.

Contribution

It presents 14 new reduction rules with optimality guarantees and integrates them into a local search algorithm, enabling high-performance solutions for large graphs.

Findings

RLS outperforms existing solvers on most test graphs.

Successfully solves graphs with over 260 million edges.

Data reduction is crucial for the algorithm's success.

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.