PACE Solver Description: Reductions and Heuristic Search for the Dominating Set Problem and the Hitting Set Problem

Fontan, Florian; Verger, Guillaume

doi:10.4230/LIPIcs.IPEC.2025.36

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Mathematics of computing → Combinatorial optimization

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dominating set
hitting set
unicost set covering
reductions
large neighborhood search
local search

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Abstract

In this paper, we describe the solver we submitted for both heuristic tracks of the PACE challenge 2025 on the dominating set problem and the hitting set problem. We solve both problems as unicost set covering problems. Our solver first performs reductions on the instance. Then greedy algorithms generate an initial solution that serves as starting point of the large neighborhood search and the local search which are executed afterwards. The solver ranked first in the dominating set heuristic track, and second in the hitting set heuristic track.

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Florian Fontan and Guillaume Verger. PACE Solver Description: Reductions and Heuristic Search for the Dominating Set Problem and the Hitting Set Problem. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 36:1-36:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.IPEC.2025.36

Author Details

Florian Fontan

Independent researcher, Grenoble, France

Guillaume Verger

Independent researcher, Lyon, France

References

Chao Gao, Xin Yao, Thomas Weise, and Jinlong Li. An efficient local search heuristic with row weighting for the unicost set covering problem. European Journal of Operational Research, 246(3):750-761, November 2015. URL: https://doi.org/10.1016/j.ejor.2015.05.038.
Weibo Lin, Fuda Ma, Zhouxing Su, Qingyun Zhang, Chumin Li, and Zhipeng Lü. Weighting-based parallel local search for optimal camera placement and unicost set covering. In Proceedings of the 2020 Genetic and Evolutionary Computation Conference Companion, GECCO '20, pages 3-4, Cancún, Mexico, July 2020. Association for Computing Machinery. URL: https://doi.org/10.1145/3377929.3398184.
William Suters, III. Crown Reductions and Decompositions: Theoretical Results and Practical Methods. Masters Theses, December 2004.
Johan M. M. van Rooij and Hans L. Bodlaender. Exact algorithms for dominating set. Discrete Applied Mathematics, 159(17):2147-2164, October 2011. URL: https://doi.org/10.1016/j.dam.2011.07.001.
Mingyu Xiao and Hiroshi Nagamochi. Confining sets and avoiding bottleneck cases: A simple maximum independent set algorithm in degree-3 graphs. Theoretical Computer Science, 469:92-104, January 2013. URL: https://doi.org/10.1016/j.tcs.2012.09.022.

PACE Solver Description: Reductions and Heuristic Search for the Dominating Set Problem and the Hitting Set Problem

Authors Florian Fontan , Guillaume Verger

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