This paper describes our hybrid MaxSAT and mixed integer programming approach for finding minimum hitting sets as submitted to the 2025 PACE challenge. We also discuss hitting set specific challenges, lower bounds, preprocessing and design choices. 2012 ACM Subject Classification Theory of computation -> Discrete optimization; Theory of computation -> Constraint and logic programming; Theory of computation -> Automated reasoning
We investigate the enumeration of dense subgraphs under two well-known relaxations of cliques: k-plexes and k-defective cliques. Our main contribution is a family of algorithms with improved worst-case and output-sensitive complexities, driven by a decomposition technique based on graph degeneracy. We first propose a worst-case output-size near-optimal algorithm to enumerate all maximal k-plexes of size at least 2k - 1, achieving a total time complexity of O(n(dk)(3)2(d)Delta(k)), where d is the degeneracy and Delta the maximum degree of the input graph. We then refine this result to obtain a fixed-parameter tractable output-sensitive algorithm with complexity O(alpha f(k)p(d Delta)), where alpha is the number of solutions, f(k) is an arbitrary function of k, and p is a polynomial. We then extend this framework to the enumeration of k-defective cliques and also show a linear-time O(n) algorithm for the enumeration of 2-plexes for graphs with bounded degeneracy. To the best of our knowledge, these complexities are competitive with or better than the current state of the art. 2012 ACM Subject Classification Theory of computation. Parameterized complexity and exact algorithms
We present and describe the solver OBLX for the Dominating Set problem on graphs. This solver was developed during the PACE challenge 2025 for the Exact track. It first applies several data reduction rules and performs a polynomial time reduction to Max Sat. The resulting Max Sat instance is in turn solved using the EvalMaxSat solver by Florent Avellaneda. 2012 ACM Subject Classification Theory of computation -> Parameterized complexity and exact algorithms
This article briefly describes the most important algorithms and techniques used in HitS&DoSeS, a dominating set and hitting set solver submitted to the PACE 2025 contest (10th Parameterized Algorithms and Computational Experiments Challenge). Used approaches for the exact and heuristic tracks are described, for both the dominating set and the hitting set problems. 2012 ACM Subject Classification Mathematics of computing -> Graph algorithms
Dominating Set and Hitting Set are two well-known NP-hard problems on graphs and hypergraphs, respectively. For Dominating Set, we seek a subset S of vertices of minimum size, such that every vertex has a neighbor in S. For Hitting Set, we require that this minimum size subset S intersects each hyperedge. We present Bad Dominating Set Maker, our solver for both problems posed in the exact tracks of the 2025 PACE Challenge. It uses reduction rules, dynamic programming on tree decompositions, and external Vertex Cover and SAT solvers. 2012 ACM Subject Classification Theory of computation -> Graph algorithms analysis; Theory of computation -> Parameterized complexity and exact algorithms
