Norbert Zeh

Jannik Schestag, Norbert Zeh

The problem of orienting an unrooted network to obtain a specific class of rooted phylogenetic networks is known to be NP-hard in many cases. In this paper, we introduce two algorithmic frameworks that yield significantly improved fixed-parameter tractable (FPT) algorithms parameterized by the network level $\ell$. Our first main contribution shows that for several prominent network classes, the core algorithmic difficulty lies in finding a directed spanning tree on the network's undirected generator. By enumerating these spanning trees in $O(5.3334^\ell + \ell)$ time and orienting all remaining edges in polynomial time, we solve the orientation problem in $O(5.3334^\ell \cdot n)$ time for tree-based networks and in $O(5.3334^\ell \cdot n^2)$ time for orchards, where $n$ is the number of vertices of the graph. Extending this approach with further branching yields $O(10.6667^\ell \cdot n^2)$-time algorithms for tree-child and normal networks. Our second technique bypasses spanning trees by directly guessing the placement of reticulations on the generator. This framework provides $O(12.2071^\ell \cdot n^2)$-time algorithms for temporal, reticulation-visible, and tree-sibling networks. Finally, we demonstrate the versatility of the reticulation-guessing framework by showing that even computing an orientation with minimum scanwidth is single-exponential FPT with respect to the level. Together, these results significantly improve the best-known running times for phylogenetic network orientation.

Leo van Iersel, Mark Jones, Simone Linz et al.

A directed phylogenetic network is tree-child if every non-leaf vertex has a child that is not a reticulation. As a class of directed phylogenetic networks, tree-child networks are very useful from a computational perspective. For example, several computationally difficult problems in phylogenetics become tractable when restricted to tree-child networks. At the same time, the class itself is rich enough to contain quite complex networks. Furthermore, checking whether a directed network is tree-child can be done in polynomial time. In this paper, we seek a class of undirected phylogenetic networks that is rich and computationally useful in a similar way to the class tree-child directed networks. A natural class to consider for this role is the class of tree-child-orientable networks which contains all those undirected phylogenetic networks whose edges can be oriented to create a tree-child network. However, we show here that recognizing such networks is NP-hard, even for binary networks, and as such this class is inappropriate for this role. Towards finding a class of undirected networks that fills a similar role to directed tree-child networks, we propose new classes called $q$-cuttable networks, for any integer $q\geq 1$. We show that these classes have many of the desirable properties, similar to tree-child networks in the rooted case, including being recognizable in polynomial time, for all $q\geq 1$. Towards showing the computational usefulness of the class, we show that the NP-hard problem Tree Containment is polynomial-time solvable when restricted to $q$-cuttable networks with $q\geq 3$.

Md Rashadul Hasan Rakib, Norbert Zeh, Magdalena Jankowska et al.

Short text clustering is a challenging task due to the lack of signal contained in such short texts. In this work, we propose iterative classification as a method to b o ost the clustering quality (e.g., accuracy) of short texts. Given a clustering of short texts obtained using an arbitrary clustering algorithm, iterative classification applies outlier removal to obtain outlier-free clusters. Then it trains a classification algorithm using the non-outliers based on their cluster distributions. Using the trained classification model, iterative classification reclassifies the outliers to obtain a new set of clusters. By repeating this several times, we obtain a much improved clustering of texts. Our experimental results show that the proposed clustering enhancement method not only improves the clustering quality of different clustering methods (e.g., k-means, k-means--, and hierarchical clustering) but also outperforms the state-of-the-art short text clustering methods on several short text datasets by a statistically significant margin.