Dynamic Approximate Maximum Independent Set on Massive Graphs

TL;DR

This paper introduces a novel framework and algorithms for maintaining an approximate maximum independent set in dynamic graphs, achieving theoretical guarantees and demonstrating efficiency on real-world data.

Contribution

It presents the first non-trivial approximation algorithm for dynamic MaxIS and implements efficient algorithms with proven performance guarantees.

Findings

Achieves a $(rac{ riangle}{2} + 1)$-approximate MaxIS in dynamic graphs.

Demonstrates effectiveness on real and synthetic datasets.

Provides algorithms with near-linear expected time complexity.

Abstract

Computing a maximum independent set (MaxIS) is a fundamental NP-hard problem in graph theory, which has important applications in a wide spectrum of fields. Since graphs in many applications are changing frequently over time, the problem of maintaining a MaxIS over dynamic graphs has attracted increasing attention over the past few years. Due to the intractability of maintaining an exact MaxIS, this paper aims to develop efficient algorithms that can maintain an approximate MaxIS with an accuracy guarantee theoretically. In particular, we propose a framework that maintains a $(\frac{\Delta}{2} + 1)$-approximate MaxIS over dynamic graphs and prove that it achieves a constant approximation ratio in many real-world networks. To the best of our knowledge, this is the first non-trivial approximability result for the dynamic MaxIS problem. Following the framework, we implement an efficient linear-time dynamic algorithm and a more effective dynamic algorithm with near-linear expected time complexity. Our thorough experiments over real and synthetic graphs demonstrate the effectiveness and efficiency of the proposed algorithms, especially when the graph is highly dynamic.