Revisiting a Successful Reduction Rule for Dominating Set (ALENEX 2026): Supplemental Material
Authors/Creators
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1.
Goethe University Frankfurt
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2.
University of Copenhagen
Description
Please use version 2, which includes the complete data set and identical code.
About this Repository
This repository contains the software and data sets to reproduce the experiments in the above mentioned article. Please refer to the README file for more details and instructions.
Article Abstract
Given a graph G = (V, E) with n vertices and m edges, the Dominating Set problem asks for a set D ⊆ V of minimal cardinality such that every vertex either is in D or adjacent to a member of D. Although there is little hope for a kernelization algorithm on general graphs due to the W[2]-hardness of Dominating Set,
in practice data reduction rules are extensively used. In this context, Rule 1 due to Alber, Fellows and Niedermeier [JACM 2004] has been shown to be very
powerful, yet its best-known running time is O(n3) for general graphs. In this work, we propose, to the best of our knowledge, the first O(n+m)-time algorithm for Rule 1 on general graphs. We additionally propose simple, but practically significant, extensions to our algorithmic framework to further prune the input instances.
We complement our theoretical claims with experiments that confirm the practicality of our approach. On average we see significant speedups of over one order of magnitude while removing 59.8× more nodes and 410.9× more edges than the original formulation across a large dataset comprised of real-world and synthetic networks.
Dataset
The data sets included are from two sources and keep their original licensing:
- The majority of instances is derived from graphs obtained from networkrepository.com. These are originally published under Creative Commons Attribution-ShareAlike License (https://networkrepository.com/policy.php) and retain this license. Details of the derivation process can be found in the article (roughly speaking, we interpreted all graphs as undirected graphs, removed multiedges, and extracted connected components). The file names keep the original instance name.
- PACE 2026 downloaded from https://github.com/MarioGrobler/PACE2025-instances
Code
Instructions
Download dataset(s)
Run experiments
Running the experiments should only require two steps (we assume Docker and bash are available):
- Adjust the number of threads in the beginning of `run.sh` (see comments there including the disk space usage)
- Execute `run.sh`.
After building the docker image two (three if large instances were downloaded) experimental campaign are started successively. Each will have their own progress bar. Runtime roughly: 2 to 4 days (the bulk of experiments runs quite quickly and can be parallelized nicely; however 10 instance need roughly 1day each)
External dependencies
The only non-standard external dependency is a Random Hyperbolic Graph generator. Should this become unavailable, any other RHG generator can be used to substitute. For instance, NetworKit offers compatible functionality.