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Sorting is a foundational problem in computer science that is typically employed on sequences or total orders. More recently, a more general form of sorting on partially ordered sets (or posets), where some pairs of elements are…
We prove that it is NP-hard to properly PAC learn decision trees with queries, resolving a longstanding open problem in learning theory (Bshouty 1993; Guijarro-Lavin-Raghavan 1999; Mehta-Raghavan 2002; Feldman 2016). While there has been a…
We consider the randomized decision tree complexity of the recursive 3-majority function. We prove a lower bound of $(1/2-\delta) \cdot 2.57143^h$ for the two-sided-error randomized decision tree complexity of evaluating height $h$ formulae…
Phylogenetic trees are leaf-labelled trees used to model the evolution of species. In practice it is not uncommon to obtain two topologically distinct trees for the same set of species, and this motivates the use of distance measures to…
Artificial intelligence applications in autonomous driving, medical diagnostics, and financial systems increasingly demand machine learning models that can provide robust uncertainty quantification, interpretability, and noise resilience.…
We propose a tree regularization framework, which enables many tree models to perform feature selection efficiently. The key idea of the regularization framework is to penalize selecting a new feature for splitting when its gain (e.g.…
We investigate the computation of minimum-cost spanning trees satisfying prescribed vertex degree constraints: Given a graph $G$ and a constraint function $D$, we ask for a (minimum-cost) spanning tree $T$ such that for each vertex $v$, $T$…
Missing and incorrect values often cause serious consequences. To deal with these data quality problems, a class of common employed tools are dependency rules, such as Functional Dependencies (FDs), Conditional Functional Dependencies…
Structural parameters of graphs, such as treewidth, play a central role in the study of the parameterized complexity of graph problems. Motivated by the study of parametrized algorithms on phylogenetic networks, scanwidth was introduced…
We introduce tree-width for first order formulae \phi, fotw(\phi). We show that computing fotw is fixed-parameter tractable with parameter fotw. Moreover, we show that on classes of formulae of bounded fotw, model checking is fixed…
Despite their impressive capabilities, aligned large language models (LLMs) often generate outputs that lack diversity. What drives this consistency in the generation? We investigate this phenomenon through the lens of probability…
Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…
Given a DNF formula on n variables, the two natural size measures are the number of terms or size s(f), and the maximum width of a term w(f). It is folklore that short DNF formulas can be made narrow. We prove a converse, showing that…
We generalize the tree doubling and Christofides algorithm, the two most common approximations for TSP, to parameterized approximations for ATSP. The parameters we consider for the respective parameterizations are upper bounded by the…
There are various approaches to exploiting "hidden structure" in instances of hard combinatorial problems to allow faster algorithms than for general unstructured or random instances. For SAT and its counting version #SAT, hidden structure…
We consider a variant of treewidth that we call clique-partitioned treewidth in which each bag is partitioned into cliques. This is motivated by the recent development of FPT-algorithms based on similar parameters for various problems. With…
Training data used for developing machine learning classifiers can exhibit biases against specific protected attributes. Such biases typically originate from historical discrimination or certain underlying patterns that disproportionately…
Compositions of tree-walking tree transducers form a hierarchy with respect to the number of transducers in the composition. As main technical result it is proved that any such composition can be realized as a linear bounded composition,…
In this paper, we initiate a systematic study of the parametrised complexity in the field of Dependence Logics which finds its origin in the Dependence Logic of V\"a\"an\"anen from 2007. We study a propositional variant of this logic (PDL)…
With the rapid progress of Large Language Models (LLMs), it becomes increasingly important to understand their abilities and limitations. In two experiments, we investigate the causal and compositional reasoning abilities of LLMs and humans…