Set Covering Benchmark Dataset

This dataset contains 10,000 reproducible instances of the weighted Set Covering Problem, together with solver-certified integer and linear programming solutions, deterministic greedy solutions, rational certificates, and associated metadata.

For the weighted Set Covering Problem, a collection of elements and a family of available subsets are given, with a positive (integer) cost assigned to each subset. The objective is to select subsets that cover every element while minimising total cost.

The dataset is intended as a benchmark resource for computational experiments in combinatorial optimisation, integer programming, linear programming relaxations, approximation algorithms, greedy heuristics, and preprocessing. It may also be useful for algorithm benchmarking and teaching in operations research and computer science.

The benchmark contains four matrix dimensions:

(m, n) = (24, 40), (40, 70), (60, 100), and (100, 180),

where m denotes the number of elements and n denotes the number of available subsets. Ten instance families are included: sparse random, medium-density random, dense random, block-structured, geometric disk-covering, interval-covering, redundant-column, dominated-column, community-structured, and planted-cover instances. Each family contains 1,000 instances, with 250 at each dimension, giving 10,000 instances in total. 

For each instance, the dataset provides the exact sparse incidence matrix and integer costs, optimal IP and LP objective values and corresponding solution vectors, integrality gaps, two deterministic greedy solutions, generation seed and parameters, structural statistics, solver settings, runtimes, and supporting bounds and certificates.

Every instance is feasible and has solver-certified IP and LP optima. The reference optimisation experiments used AMPL with Gurobi for integer optimisation and HiGHS for the LP relaxation and explicit dual. Exact rational certificates additionally prove 8,480 LP optima and independently establish 5,140 integer optima through integer-rounded dual lower bounds. Numerical solver certification and exact arithmetic proofs are identified separately.

The release consists of five CSV benchmark files, a standalone Python script for deterministic generation and saved-data verification, two AMPL models, a validation report, citation metadata, SHA-256 checksums, and accompanying Markdown documentation. The benchmark inputs and saved results can be read independently of AMPL.