André Schidler

AAAI Conference 2026 Conference Paper

Efficient and Reliable Hitting-Set Computations for the Implicit Hitting Set Approach

• Hannes Ihalainen
• Dieter Vandesande
• André Schidler
• Jeremias Berg
• Bart Bogaerts
• Matti Järvisalo

The implicit hitting set (IHS) approach offers a general framework for solving computationally hard combinatorial optimization problems declaratively. IHS iterates between a decision oracle used for extracting sources of inconsistency and an optimizer for computing so-called hitting sets (HSs) over the accumulated sources of inconsistency. While the decision oracle is language-specific, the optimizers is usually instantiated through integer programming. We explore alternative algorithmic techniques for hitting set optimization based on different ways of employing pseudo-Boolean (PB) reasoning as well as stochastic local search. We extensively evaluate the practical feasibility of the alternatives in particular in the context of pseudo-Boolean (0-1 IP) optimization as one of the most recent instantiations of IHS. Highlighting a trade-off between efficiency and reliability, while a commercial IP solver turns out to remain the most effective way to instantiate HS computations, it can cause correctness issues due to numerical instability; in fact, we show that exact HS computations instantiated via PB reasoning can be made competitive with a numerically exact IP solver. Furthermore, the use of PB reasoning as a basis for HS computations allows for obtaining certificates for the correctness of IHS computations, generally applicable to any IHS instantiation in which reasoning in the declarative language at hand can be captured in the PB-based proof format we employ.

AAAI Conference 2026 Conference Paper

Ordered Objectives in Maximum Satisfiability

• Jeremias Berg
• André Schidler
• Matti Järvisalo

Maximum satisfiability (MaxSAT) is a viable approach to solving NP-hard combinatorial optimization problems through propositional encodings. Understanding how problem structure and encodings impact the behaviour of different MaxSAT solving algorithms is an important challenge. In this work, we identify MaxSAT instances in which the constraints entail an ordering of the objective variables as an interesting instance class from the perspectives of problem structure and MaxSAT solving. From the problem structure perspective, we show that a non-negligible percentage of instances in commonly used MaxSAT benchmark sets have ordered objectives and further identify various examples of such problem domains to which MaxSAT solvers have been successfully applied. From the algorithmic perspective, we argue that MaxSAT instances with ordered objectives, provided an ordering, can be solved (at least) as efficiently with a very simplistic algorithmic approach as with modern core-based MaxSAT solving algorithms. We show empirically that state-of-the-art MaxSAT solvers suffer from overheads and are outperformed by the simplistic approach on real-world optimization problems with ordered objectives.

SAT Conference 2025 Conference Paper

Analyzing Reformulation Performance in Core-Guided MaxSAT Solving

• André Schidler
• Stefan Szeider

Core-guided algorithms like OLL are among the best methods for solving the Maximum Satisfiability problem (MaxSAT). Although some performance characteristics of OLL have been studied, a comprehensive experimental analysis of its reformulation behavior is still missing. In this paper, we present a large-scale study on how different reformulations of a MaxSAT instance produced by OLL affect solver performance. By representing these reformulations as a directed acyclic graph (DAG), we isolate the impact of structural features - such as the size and interconnectivity of unsatisfiable cores - on solver runtime. Our extensive experimental evaluation of over 600k solver runs reveals clear correlations between DAG properties and performance outcomes. These results suggest a new avenue for designing heuristics that steer the solver toward more tractable reformulations. All OLL DAGs and performance data from our experiments are publicly available to foster further research.

SAT Conference 2025 Conference Paper

Learn to Unlearn

• Bernhard Gstrein
• Florian Pollitt
• André Schidler
• Mathias Fleury
• Armin Biere

Clause learning is a significant milestone in the development of SAT solving. However, keeping all learned clauses without discrimination gradually slows down the solver. Thus, selectively removing some learned clauses during routine database reduction is essential. In this paper, we reexamine and test several long-standing ideas for clause removal in the modern solver Kissat. Our experiments show that retaining all clauses alters performance in all instances. For satisfiable instances, periodically removing all learned clauses surprisingly yields near state-of-the-art performance. For unsatisfiable instances, it is vital to always keep some learned clauses. Building on the influential Glucose paper, we find that it is crucial to always retain the clauses most likely to help, regardless of whether they are ranked by size or LBD in practice. Another key factor is whether a clause was used recently during conflict resolution steps. Eagerly keeping used clauses improves all unlearning strategies.

ICML Conference 2025 Conference Paper

Learning Minimum-Size BDDs: Towards Efficient Exact Algorithms

• Christian Komusiewicz
• André Schidler
• Frank Sommer
• Manuel Sorge
• Luca Pascal Staus

Binary decision diagrams (BDDs) are widely applied tools to compactly represent labeled data as directed acyclic graphs; for efficiency and interpretability reasons small BDDs are preferred. Given labeled data, minimizing BDDs is NP-complete and thus recent research focused on the influence of parameters such as the solution size $s$ on the complexity [Ordyniak et al. , AAAI 2024]. Our main positive result is an algorithm that is efficient if in particular $s$, the domain size $D$, and the Hamming distance between any two data points is small, improving on previous running-time bounds. This algorithm is inspired by the witness-tree paradigm that was recently successful for computing decision trees [Komusiewicz et al. , ICML 2023], whose extension to BDDs was open. We extend our algorithmic results to the case where we allow a small number of misclassified data points and complement them with lower bounds that show that the running times are tight from multiple points of view. We show that our main algorithm holds practical promise by providing a proof-of-concept implementation.

AIJ Journal 2023 Journal Article

Computing optimal hypertree decompositions with SAT

• André Schidler
• Stefan Szeider

IJCAI Conference 2023 Conference Paper

Computing Twin-width with SAT and Branch & Bound

• André Schidler
• Stefan Szeider

The graph width-measure twin-width recently attracted great attention because of its solving power and generality. Many prominent NP-hard problems are tractable on graphs of bounded twin-width if a certificate for the twin-width bound is provided as an input. Bounded twin-width subsumes other prominent structural restrictions such as bounded treewidth and bounded rank-width. Computing such a certificate is NP-hard itself, already for twin-width 4, and the only known implemented algorithm for twin-width computation is based on a SAT encoding. In this paper, we propose two new algorithmic approaches for computing twin-width that significantly improve the state of the art. Firstly, we develop a SAT encoding that is far more compact than the known encoding and consequently scales to larger graphs. Secondly, we propose a new Branch & Bound algorithm for twin-width that, on many graphs, is significantly faster than the SAT encoding. It utilizes a sophisticated caching system for partial solutions. Both algorithmic approaches are based on new conceptual insights into twin-width computation, including the reordering of contractions.

AAAI Conference 2022 Conference Paper

Tractable Abstract Argumentation via Backdoor-Treewidth

• Wolfgang Dvořák
• Markus Hecher
• Matthias König
• André Schidler
• Stefan Szeider
• Stefan Woltran

Argumentation frameworks (AFs) are a core formalism in the field of formal argumentation. As most standard computational tasks regarding AFs are hard for the first or second level of the Polynomial Hierarchy, a variety of algorithmic approaches to achieve manageable runtimes have been considered in the past. Among them, the backdoor-approach and the treewidth-approach turned out to yield fixed-parameter tractable fragments. However, many applications yield high parameter values for these methods, often rendering them infeasible in practice. We introduce the backdoor-treewidth approach for abstract argumentation, combining the best of both worlds with a guaranteed parameter value that does not exceed the minimum of the backdoor- and treewidth-parameter. In particular, we formally define backdoor-treewidth and establish fixed-parameter tractability for standard reasoning tasks of abstract argumentation. Moreover, we provide systems to find and exploit backdoors of small width, and conduct systematic experiments evaluating the new parameter.

SAT Conference 2022 Conference Paper

Weighted Model Counting with Twin-Width

• Robert Ganian
• Filip Pokrývka
• André Schidler
• Kirill Simonov
• Stefan Szeider

Bonnet et al. (FOCS 2020) introduced the graph invariant twin-width and showed that many NP-hard problems are tractable for graphs of bounded twin-width, generalizing similar results for other width measures, including treewidth and clique-width. In this paper, we investigate the use of twin-width for solving the propositional satisfiability problem (SAT) and propositional model counting. We particularly focus on Bounded-ones Weighted Model Counting (BWMC), which takes as input a CNF formula F along with a bound k and asks for the weighted sum of all models with at most k positive literals. BWMC generalizes not only SAT but also (weighted) model counting. We develop the notion of "signed" twin-width of CNF formulas and establish that BWMC is fixed-parameter tractable when parameterized by the certified signed twin-width of F plus k. We show that this result is tight: it is neither possible to drop the bound k nor use the vanilla twin-width instead if one wishes to retain fixed-parameter tractability, even for the easier problem SAT. Our theoretical results are complemented with an empirical evaluation and comparison of signed twin-width on various classes of CNF formulas.