A Reproducible Benchmark Dataset and Experimental Evaluation for the Minimum s-Club Cover Problem

Abstract The Minimum s-Club Cover (MSCC) problem is an NP-hard and APX-hard combinatorial optimization challenge on graphs with significant applications in social network community detection, computational molecular biology, and telecommunication routing. Despite its theoretical and operational relevance, computational research on MSCC currently suffers from a lack of standardized open benchmark instances, absence of granular per-run execution logs, and inconsistent feasibility reporting. To bridge these critical methodological gaps and promote open science, this paper presents a comprehensive, standardized, and fully reproducible empirical benchmark suite for MSCC ($s=2$). The dataset encompasses 30 standardized benchmark graph instances partitioned into two distinct structural families: 12 real-world complex networks from biological, social, and information domains, and 18 symmetric DIMACS benchmark graphs with varying topological densities. Across these 30 instances, we provide 4,800 complete optimization runs conducted over 20 synchronized paired random seeds and eight comparative algorithms spanning constructive heuristics, static/random evolutionary algorithms, and adaptive learning-augmented baselines. All discovered solutions are strictly verified through breadth-first search and all-pairs shortest path calculations, achieving a verified 100% feasibility rate. We report granular raw logs, aggregated summary metrics, optimal random seed distributions, and non-parametric Wilcoxon signed-rank tests with Holm-Bonferroni correction ($1-\beta > 0.85$). All graph instances, raw/aggregated data, configuration files, and verification scripts are released openly under the permissive Creative Commons Attribution 4.0 International license.