Manuel Sorge
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View article: Improving Decision Trees through the Lens of Parameterized Local Search
Improving Decision Trees through the Lens of Parameterized Local Search Open
Algorithms for learning decision trees often include heuristic local-search operations such as (1) adjusting the threshold of a cut or (2) also exchanging the feature of that cut. We study minimizing the number of classification errors by …
View article: Witty: An Efficient Solver for Computing Minimum-Size Decision Trees
Witty: An Efficient Solver for Computing Minimum-Size Decision Trees Open
Decision trees are a classic model for summarizing and classifying data. To enhance interpretability and generalization properties, it has been proposed to favor small decision trees. Accordingly, in the minimum-size decision tree training…
View article: Optimal Decision Tree Pruning Revisited: Algorithms and Complexity
Optimal Decision Tree Pruning Revisited: Algorithms and Complexity Open
We present a comprehensive classical and parameterized complexity analysis of decision tree pruning operations, extending recent research on the complexity of learning small decision trees. Thereby, we offer new insights into the computati…
View article: Witty: An Efficient Solver for Computing Minimum-Size Decision Trees
Witty: An Efficient Solver for Computing Minimum-Size Decision Trees Open
Decision trees are a classic model for summarizing and classifying data. To enhance interpretability and generalization properties, it has been proposed to favor small decision trees. Accordingly, in the minimum-size decision tree training…
View article: On the Complexity of Establishing Hereditary Graph Properties via Vertex Splitting
On the Complexity of Establishing Hereditary Graph Properties via Vertex Splitting Open
Vertex splitting is a graph operation that replaces a vertex $v$ with two nonadjacent new vertices and makes each neighbor of $v$ adjacent with one or both of the introduced vertices. Vertex splitting has been used in contexts from circuit…
View article: The role of twins in computing planar supports of hypergraphs
The role of twins in computing planar supports of hypergraphs Open
A support or realization of a hypergraph $\mathcal{H}$ is a graph \(G\) on the same vertex set as \(\mathcal{H}\) such that for each hyperedge of $\mathcal{H}$ it holds that its vertices induce a connected subgraph of $G$. The NP-hard prob…
View article: Cluster Editing Parameterized above Modification-disjoint <i>P</i> <sub>3</sub> -packings
Cluster Editing Parameterized above Modification-disjoint <i>P</i> <sub>3</sub> -packings Open
Given a graph G =( V,E ) and an integer k , the Cluster Editing problem asks whether we can transform G into a union of vertex-disjoint cliques by at most k modifications (edge deletions or insertions). In this paper, we study the followin…
View article: The Complexity of Cluster Vertex Splitting and Company
The Complexity of Cluster Vertex Splitting and Company Open
Clustering a graph when the clusters can overlap can be seen from three different angles: We may look for cliques that cover the edges of the graph with bounded overlap, we may look to add or delete few edges to uncover the cluster structu…
View article: Game Implementation: What Are the Obstructions?
Game Implementation: What Are the Obstructions? Open
In many applications, we want to influence the decisions of independent agents by designing incentives for their actions. We revisit a fundamental problem in this area, called GAME IMPLEMENTATION: Given a game in standard form and a set of…
View article: The Influence of Dimensions on the Complexity of Computing Decision Trees
The Influence of Dimensions on the Complexity of Computing Decision Trees Open
A decision tree recursively splits a feature space \mathbb{R}^d and then assigns class labels based on the resulting partition. Decision trees have been part of the basic machine-learning toolkit for decades. A large body of work considers…
View article: On Computing Optimal Tree Ensembles
On Computing Optimal Tree Ensembles Open
Random forests and, more generally, (decision\nobreakdash-)tree ensembles are widely used methods for classification and regression. Recent algorithmic advances allow to compute decision trees that are optimal for various measures such as …
View article: Cluster Editing for Multi-Layer and Temporal Graphs
Cluster Editing for Multi-Layer and Temporal Graphs Open
Motivated by the recent rapid growth of research for algorithms to cluster multi-layer and temporal graphs, we study extensions of the classical Cluster Editing problem. In Multi-Layer Cluster Editing we receive a set of graphs on the same…
View article: The Complexity of Routing Problems in Forbidden-Transition Graphs and Edge-Colored Graphs
The Complexity of Routing Problems in Forbidden-Transition Graphs and Edge-Colored Graphs Open
The notion of forbidden-transition graphs allows for a robust generalization of walks in graphs. In a forbidden-transition graph, every pair of edges incident to a common vertex is permitted or forbidden ; a walk is compatible if all pairs…
View article: Game Implementation: What Are the Obstructions?
Game Implementation: What Are the Obstructions? Open
In many applications, we want to influence the decisions of independent agents by designing incentives for their actions. We revisit a fundamental problem in this area, called GAME IMPLEMENTATION: Given a game in standard form and a set of…
View article: Threshold Treewidth and Hypertree Width
Threshold Treewidth and Hypertree Width Open
Treewidth and hypertree width have proven to be highly successful structural parameters in the context of the Constraint Satisfaction Problem (CSP). When either of these parameters is bounded by a constant, then CSP becomes solvable in pol…
View article: Fixed-parameter tractability of Directed Multicut with three terminal pairs parameterized by the size of the cutset: twin-width meets flow-augmentation
Fixed-parameter tractability of Directed Multicut with three terminal pairs parameterized by the size of the cutset: twin-width meets flow-augmentation Open
We show fixed-parameter tractability of the Directed Multicut problem with three terminal pairs (with a randomized algorithm). This problem, given a directed graph $G$, pairs of vertices (called terminals) $(s_1,t_1)$, $(s_2,t_2)$, and $(s…
View article: The Influence of Dimensions on the Complexity of Computing Decision Trees
The Influence of Dimensions on the Complexity of Computing Decision Trees Open
A decision tree recursively splits a feature space $\mathbb{R}^{d}$ and then assigns class labels based on the resulting partition. Decision trees have been part of the basic machine-learning toolkit for decades. A large body of work treat…
View article: Constant Congestion Brambles in Directed Graphs
Constant Congestion Brambles in Directed Graphs Open
The Directed Grid Theorem, stating that there is a function $f$ such that a\ndirected graphs of directed treewidth at least $f(k)$ contains a directed grid\nof size at least $k$ as a butterfly minor, after being a conjecture for nearly\n20…
View article: Constant Congestion Brambles
Constant Congestion Brambles Open
A bramble in an undirected graph $G$ is a family of connected subgraphs of $G$ such that for every two subgraphs $H_1$ and $H_2$ in the bramble either $V(H_1) \cap V(H_2) \neq \emptyset$ or there is an edge of $G$ with one endpoint in $V(H…
View article: Planarizing Graphs and their Drawings by Vertex Splitting
Planarizing Graphs and their Drawings by Vertex Splitting Open
The splitting number of a graph $G=(V,E)$ is the minimum number of vertex splits required to turn $G$ into a planar graph, where a vertex split removes a vertex $v \in V$, introduces two new vertices $v_1, v_2$, and distributes the edges f…
View article: Turbocharging Heuristics for Weak Coloring Numbers
Turbocharging Heuristics for Weak Coloring Numbers Open
Bounded expansion and nowhere-dense classes of graphs capture the theoretical tractability for several important algorithmic problems. These classes of graphs can be characterized by the so-called weak coloring numbers of graphs, which gen…
View article: Fractional Matchings under Preferences: Stability and Optimality
Fractional Matchings under Preferences: Stability and Optimality Open
We study generalizations of stable matching in which agents may be matched fractionally; this models time-sharing assignments. We focus on the so-called ordinal stability and cardinal stability, and investigate the computational complexity…
View article: On (Coalitional) Exchange-Stable Matching
On (Coalitional) Exchange-Stable Matching Open
We study (coalitional) exchange stability, which Alcalde [Economic Design, 1995] introduced as an alternative solution concept for matching markets involving property rights, such as assigning persons to two-bed rooms. Here, a matching of …
View article: Constant congestion brambles in directed graphs
Constant congestion brambles in directed graphs Open
The Directed Grid Theorem, stating that there is a function $f$ such that a directed graphs of directed treewidth at least $f(k)$ contains a directed grid of size at least $k$ as a butterfly minor, after being a conjecture for nearly 20 ye…
View article: Efficient fully dynamic elimination forests with applications to detecting long paths and cycles
Efficient fully dynamic elimination forests with applications to detecting long paths and cycles Open
We present a data structure that in a dynamic graph of treedepth at most d, which is modified over time by edge insertions and deletions, maintains an optimum-height elimination forest. The data structure achieves worst-case update time , …
View article: Cluster Editing Parameterized Above Modification-Disjoint P₃-Packings
Cluster Editing Parameterized Above Modification-Disjoint P₃-Packings Open
Given a graph G = (V,E) and an integer k, the Cluster Editing problem asks whether we can transform G into a union of vertex-disjoint cliques by at most k modifications (edge deletions or insertions). In this paper, we study the following …
View article: Optimal Discretization is Fixed-parameter Tractable
Optimal Discretization is Fixed-parameter Tractable Open
Given two disjoint sets $W_1$ and $W_2$ of points in the plane, the Optimal Discretization problem asks for the minimum size of a family of horizontal and vertical lines that separate $W_1$ from $W_2$, that is, in every region into which t…