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Mining Large Independent Sets on Massive Graphs

Yu Zhang, Witold Pedrycz, Chanjuan Liu, Enqiang Zhu

TL;DR

Experiments show that ARCIS attains the best or tied-best solution quality in most instances while delivering competitive runtime and low variability, indicating that ARCIS is a practical and robust method for large-scale graph mining.

Abstract

The Maximum Independent Set problem is fundamental for extracting conflict-free structure from large graphs, with applications in scheduling, recommendation, and network analysis. However, existing heuristics can stagnate when search schedules are fixed and information from past solutions is underused, leading to wasted effort in low-quality regions of the search space. We present ARCIS, an efficient algorithm for mining large independent sets on massive graphs. ARCIS couples two main components. The first is an adaptive restart policy that refreshes exploration when progress slows. The second is Consensus-Guided Vertex Fixing, which restricts the search to the non-consensus region of the graph by fixing vertices consistently observed within a round. The consensus is maintained as a running intersection within each round, and because it is recomputed at every restart, the fixing is reversible. Vertices that later lose support are automatically unfixed and their neighborhoods re-enter the working graph, which corrects occasional mistakes while preserving progress. Experiments on 222 graphs from four benchmark suites show that ARCIS attains the best or tied-best solution quality in most instances while delivering competitive runtime and low variability. Ablation studies isolate the impact of each component, indicating that ARCIS is a practical and robust method for large-scale graph mining.

Mining Large Independent Sets on Massive Graphs

TL;DR

Experiments show that ARCIS attains the best or tied-best solution quality in most instances while delivering competitive runtime and low variability, indicating that ARCIS is a practical and robust method for large-scale graph mining.

Abstract

The Maximum Independent Set problem is fundamental for extracting conflict-free structure from large graphs, with applications in scheduling, recommendation, and network analysis. However, existing heuristics can stagnate when search schedules are fixed and information from past solutions is underused, leading to wasted effort in low-quality regions of the search space. We present ARCIS, an efficient algorithm for mining large independent sets on massive graphs. ARCIS couples two main components. The first is an adaptive restart policy that refreshes exploration when progress slows. The second is Consensus-Guided Vertex Fixing, which restricts the search to the non-consensus region of the graph by fixing vertices consistently observed within a round. The consensus is maintained as a running intersection within each round, and because it is recomputed at every restart, the fixing is reversible. Vertices that later lose support are automatically unfixed and their neighborhoods re-enter the working graph, which corrects occasional mistakes while preserving progress. Experiments on 222 graphs from four benchmark suites show that ARCIS attains the best or tied-best solution quality in most instances while delivering competitive runtime and low variability. Ablation studies isolate the impact of each component, indicating that ARCIS is a practical and robust method for large-scale graph mining.
Paper Structure (20 sections, 3 figures, 5 tables, 2 algorithms)

This paper contains 20 sections, 3 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Motivation.
  3. Contributions.
  4. Preliminaries
  5. Notations and Terminologies
  6. The Local Search algorithm ARW
  7. The ARCIS Algorithm
  8. Main-loop complexity.
  9. Main Components of ARCIS
  10. Adaptive restart policy
  11. Consensus-Guided Vertex Fixing
  12. Experimental Evaluation
  13. Experiment Setup
  14. Datasets.
  15. Comparison of Solution Quality
  16. ...and 5 more sections

Figures (3)

  • Figure 1: Comparison of run time of ARCIS and its corresponding competitor.
  • Figure 2: Stability analysis of algorithms.
  • Figure 3: Critical-difference (CD) diagram using Friedman ranks with Nemenyi post-hoc at $\alpha=0.05$ (lower average rank is better). Bars connect methods that are not significantly different.