Optimal Neighborhood Exploration for Dynamic Independent Sets

TL;DR

This paper introduces a novel local search method called optimal neighborhood exploration for dynamic independent set problems, improving solution quality and efficiency in large, real-world graphs.

Contribution

It proposes a new local search technique that solves subproblems optimally to enhance dynamic independent set solutions, with empirical evaluation showing competitive performance.

Findings

The method improves solution quality by adjusting subproblem size.

It matches state-of-the-art performance for the cardinality independent set.

Increasing subproblem size yields significantly better solutions.

Abstract

A dynamic graph algorithm is a data structure that supports edge insertions, deletions, and specific problem queries. While extensive research exists on dynamic algorithms for graph problems solvable in polynomial time, most of these algorithms have not been implemented or empirically evaluated. This work addresses the NP-complete maximum weight and cardinality independent set problems in a dynamic setting, applicable to areas like dynamic map-labeling and vehicle routing. Real-world instances can be vast, with millions of vertices and edges, making it challenging to find near-optimal solutions quickly. Exact solvers can find optimal solutions but have exponential worst-case runtimes. Conversely, heuristic algorithms use local search techniques to improve solutions by optimizing vertices. In this work, we introduce a novel local search technique called optimal neighborhood exploration. This technique creates independent subproblems that are solved to optimality, leading to improved overall solutions. Through numerous experiments, we assess the effectiveness of our approach and compare it with other state-of-the-art dynamic solvers. Our algorithm features a parameter, the subproblem size, that balances running time and solution quality. With this parameter, our configuration matches state-of-the-art performance for the cardinality independent set problem. By increasing the parameter, we significantly enhance solution quality.