Publications
Below you can find my publications sorted by conferences, with links and toggleable abstracts.
Also journal publications are listed that beforehand were published at a certain conference.
This list is sorted by conferences. For sorting by journal or date click here.
International Conference on Research in Computational Molecular Biology (RECOMB)
[15]
preprint
PaNDA: Efficient Optimization of Phylogenetic Diversity in Networks
bioRxiv:10.1101/2025.11.14.688467.
Phylogenetic diversity plays an important role in biodiversity, conservation, and evolutionary studies by measuring the diversity of a set of taxa based on their phylogenetic relationships. In phylogenetic trees, a subset of \(k\) taxa with maximum phylogenetic diversity can be found by a simple and efficient greedy algorithm. However, this algorithmic tractability is lost when considering phylogenetic networks, which incorporate reticulate evolutionary events such as hybridization and horizontal gene transfer. To address this challenge, we introduce PaNDA (Phylogenetic Network Diversity Algorithms), the first software package and interactive graphical user-interface for exploring, visualizing and maximizing diversity in phylogenetic networks. PaNDA includes a novel algorithm to find a subset of \(k\) taxa with maximum diversity, running in polynomial time for networks of bounded canwidth, a measure of tree-likeness of a network that grows slower than the well-known level measure. This algorithm considers the variant of phylogenetic diversity on networks in which the branch lengths of all paths from the root to the selected taxa contribute towards their diversity. We demonstrate the scalability of this algorithm on simulated networks, successfully analyzing level-15 networks with up to 200 taxa in seconds. We also provide a proof-of-concept analysis using a phylogenetic network on Xiphophorus species, illustrating how the tool can support diversity studies based on real genomic data. The software is easily installable and freely available at https://github.com/nholtgrefe/panda. Additionally, we extend the definition of phylogene- tic diversity to semi-directed phylogenetic networks, which are mixed graphs increasingly used in phylogenetic analysis to model uncertainty of the root location. We prove that finding a subset of \(k\) taxa with maximum diversity remains NP-hard on semi-directed networks, but do present a polynomial-time algorithm for networks with bounded level.
@article{holtgrefe2025panda,
title = {{PaNDA: Efficient Optimization of Phylogenetic Diversity in Networks}},
author = {Holtgrefe, Niels and van Iersel, Leo and Meuwese, Ruben and Murakami, Yukihiro and Schestag, Jannik},
year = {2025},
publisher = {Cold Spring Harbor Laboratory},
journal = {bioRxiv: 10.1101/2025.11.14.688467},
doi = {10.1101/2025.11.14.688467}
}
International Symposium on Parameterized and Exact Computation (IPEC)
[14]
conference paper
Parameterized Algorithms for Diversity of Networks with Ecological Dependencies
Proceedings of the 20th International Symposium on Parameterized and Exact Computation (IPEC 2025):11:1-11:21.
For a phylogenetic tree, the phylogenetic diversity of a set \(A\) of taxa is the total weight of edges on paths to \(A\). Finding small sets of maximal diversity is crucial for conservation planning, as it indicates where limited resources can be invested most efficiently. In recent years, efficient algorithms have been developed to find sets of taxa that maximize phylogenetic diversity either in a phylogenetic network or in a phylogenetic tree subject to ecological constraints, such as a food web. However, these aspects have mostly been studied independently. Since both factors are biologically important, it seems natural to consider them together.
In this paper, we introduce decision problems where, given a phylogenetic network, a food web, and integers \(k\), and \(D\), the task is to find a set of \(k\) taxa with phylogenetic diversity of at least \(D\) under the maximize all paths measure, while also satisfying viability conditions within the food web. Here, we consider different definitions of viability, which all demand that a ``sufficient'' number of prey species survive to support surviving predators.
We investigate the parameterized complexity of these problems and present several fixed-parameter tractable (FPT) algorithms. Specifically, we provide a complete complexity dichotomy characterizing which combinations of parameters---out of the size constraint \(k\), the acceptable diversity loss \(\overline{D}\), the scanwidth of the food web \(sw\), the maximum in-degree \(\delta\) in the network, and the network height \(h\)---lead to W[1]-hardness and which admit FPT algorithms.
Our primary methodological contribution is a novel algorithmic framework for solving phylogenetic diversity problems in networks where dependencies (such as those from a food web) impose an order, using a color coding approach.
In this paper, we introduce decision problems where, given a phylogenetic network, a food web, and integers \(k\), and \(D\), the task is to find a set of \(k\) taxa with phylogenetic diversity of at least \(D\) under the maximize all paths measure, while also satisfying viability conditions within the food web. Here, we consider different definitions of viability, which all demand that a ``sufficient'' number of prey species survive to support surviving predators.
We investigate the parameterized complexity of these problems and present several fixed-parameter tractable (FPT) algorithms. Specifically, we provide a complete complexity dichotomy characterizing which combinations of parameters---out of the size constraint \(k\), the acceptable diversity loss \(\overline{D}\), the scanwidth of the food web \(sw\), the maximum in-degree \(\delta\) in the network, and the network height \(h\)---lead to W[1]-hardness and which admit FPT algorithms.
Our primary methodological contribution is a novel algorithmic framework for solving phylogenetic diversity problems in networks where dependencies (such as those from a food web) impose an order, using a color coding approach.
@inproceedings{jones2025parameterized,
title = {{Parameterized Algorithms for Diversity of Networks with Ecological Dependencies}},
author = {Jones, Mark and Schestag, Jannik},
booktitle = {Proceedings of the 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {11:1--11:21},
year = {2025},
organization = {Schloss-Dagstuhl-Leibniz Zentrum f{\"u}r Informatik},
doi = {10.4230/LIPIcs.IPEC.2025.11}
}
[13]
conference paper
Finding Degree-Constrained Acyclic Orientations
Proceedings of the 18th International Symposium on Parameterized and Exact Computation (IPEC 2023):19:1--19:14.
We consider the problem of orienting a given, undirected graph into a (directed) acyclic graph such that the in-degree of each vertex \(v\) is in a prescribed list \(\lambda(v)\). Variants of this problem have been studied for a long time and with various applications, but mostly without the requirement for acyclicity. Without this requirement, the problem is closely related to the classical General Factor problem, which is known to be NP-hard in general, but polynomial-time solvable if no list \(\lambda(v)\) contains large “gaps” [Cornuéjols, J. Comb. Theory B, 1988]. In contrast, we show that deciding if an acyclic orientation exists is NP-hard even in the absence of such “gaps”.
On the positive side, we design parameterized algorithms for various, natural parameterizations of the acyclic orientation problem. A special case of the orientation problem with degree constraints recently came up in the context of reconstructing evolutionary histories (that is, phylogenetic networks). This phylogenetic setting imposes additional structure onto the problem that can be exploited algorithmically, allowing us to show fixed-parameter tractability when parameterized by either the treewidth of \(G\) (a smaller parameter than the frequently employed “level”), by the number of vertices \(v\) for which \(|\lambda(v)| \geq 2\), by the number of vertices \(v\) for which the highest value in \(\lambda(v)\) is at least 2. While the latter result can be extended to the general degree-constraint acyclic orientation problem, we show that the former cannot unless FPT=W[1].
On the positive side, we design parameterized algorithms for various, natural parameterizations of the acyclic orientation problem. A special case of the orientation problem with degree constraints recently came up in the context of reconstructing evolutionary histories (that is, phylogenetic networks). This phylogenetic setting imposes additional structure onto the problem that can be exploited algorithmically, allowing us to show fixed-parameter tractability when parameterized by either the treewidth of \(G\) (a smaller parameter than the frequently employed “level”), by the number of vertices \(v\) for which \(|\lambda(v)| \geq 2\), by the number of vertices \(v\) for which the highest value in \(\lambda(v)\) is at least 2. While the latter result can be extended to the general degree-constraint acyclic orientation problem, we show that the former cannot unless FPT=W[1].
@inproceedings{garvardt2023finding,
title = {{Finding Degree-Constrained Acyclic Orientations}},
author = {Garvardt, Jaroslav and Renken, Malte and Schestag, Jannik and Weller, Mathias},
booktitle = {Proceedings of the 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
pages = {19:1--19:14},
year = {2023},
organization = {Schloss-Dagstuhl-Leibniz Zentrum f{\"u}r Informatik},
doi = {10.4230/LIPIcs.IPEC.2023.19}
}
[12]
conference paper
On the Complexity of Finding a Sparse Connected Spanning Subgraph in a Non-Uniform Failure Model
Proceedings of the 18th International Symposium on Parameterized and Exact Computation (IPEC 2023):4:1--4:12.
We study a generalization of the classic Spanning Tree problem that allows for a non-uniform failure model. More precisely, edges are either safe or unsafe and we assume that failures only affect unsafe edges. In Unweighted Flexible Graph Connectivity we are given an undirected graph \(G = (V,E)\) in which the edge set \(E\) is partitioned into a set \(S\) of safe edges and a set \(U\) of unsafe edges and the task is to find a set \(T\) of at most \(k\) edges such that \(T - u\) is connected and spans \(V\) for any unsafe edge \(u \in T\). Unweighted Flexible Graph Connectivity generalizes both Spanning Tree and Hamiltonian Cycle. We study Unweighted Flexible Graph Connectivity in terms of fixed-parameter tractability (FPT). We show an almost complete dichotomy on which parameters lead to fixed-parameter tractability and which lead to hardness. To this end, we obtain FPT-time algorithms with respect to the vertex deletion distance to cluster graphs and with respect to the treewidth. By exploiting the close relationship to Hamiltonian Cycle, we show that FPT-time algorithms for many smaller parameters are unlikely under standard parameterized complexity assumptions. Regarding problem-specific parameters, we observe that Unweighted Flexible Graph Connectivity admits an FPT-time algorithm when parameterized by the number of unsafe edges. Furthermore, we investigate a below-upper-bound parameter for the number of edges of a solution. We show that this parameter also leads to an FPT-time algorithm.
@inproceedings{bentert2023complexity,
title = {{On the Complexity of Finding a Sparse Connected Spanning Subgraph in a Non-Uniform Failure Model}},
author = {Bentert, Matthias and Schestag, Jannik and Sommer, Frank},
booktitle = {Proceedings of the 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
pages = {4:1--4:12},
year = {2023},
organization = {Schloss-Dagstuhl-Leibniz Zentrum f{\"u}r Informatik},
doi = {10.4230/LIPIcs.IPEC.2023.4}
}
[11]
conference paper
Maximizing All-Paths Phylogenetic Diversity: Parameterized Approaches for Networks
Proceedings of the 18th International Symposium on Parameterized and Exact Computation (IPEC 2023):30:1-30:12.
Phylogenetic Diversity (PD) is a fundamental measure of biodiversity, originally defined on phylogenetic trees and widely used in conservation biology. Phylogenetic trees are often generalised to directed acyclic graphs, called phylogenetic networks. As such, a corresponding generalization of PD is needed. A natural generalization to edge-weighted phylogenetic networks is the all-paths measure, where the diversity of a set \(S\) of species (taxa) is defined as the total weight of all edges that lie on a path from the root to at least one species in \(S\). While maximizing PD on trees can be solved in polynomial time, the corresponding problem on networks is NP-hard and difficult to approximate. We undertake a systematic parameterized complexity study of the Max-All-Paths-PD (MapPD) problem. We establish W[2]-hardness when parameterized by the number of species that are included in a solution, and W[1]-hardness for the number of species that are excluded. On the positive side, we show that the problem is fixed-parameter tractable with respect to the threshold of diversity and the acceptable loss of diversity. We further analyze how the network's proximity to a tree influences algorithmic behavior and present single-exponential fixed-parameter algorithms when parameterized by the number of reticulations and by the treewidth of the underlying graph. Finally, we present a polynomial kernelization for MapPD with respect to the number of reticulation edges.
@inproceedings{jones2023maximize,
title = {{How Can We Maximize Phylogenetic Diversity? Parameterized Approaches for Networks}},
author = {Jones, Mark and Schestag, Jannik},
booktitle = {Proceedings of the 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
pages = {30:1--30:12},
year = {2023},
organization = {Schloss-Dagstuhl-Leibniz Zentrum f{\"u}r Informatik},
doi = {10.4230/LIPIcs.IPEC.2023.30}
}
International Workshop on Algorithms in Bioinformatics (WABI)
[10]
conference paper
Average-Tree Phylogenetic Diversity of Networks
Proceedings of the 25th International Workshop on Algorithms in Bioinformatics (WABI 2025):14:1--14:21.
Phylogenetic diversity is a measure used to quantify the biodiversity of a set of species. Here, we introduce the average-tree phylogenetic diversity score in rooted binary phylogenetic networks and consider algorithms for computing and maximizing the score on a given network. Basically, the score is the weighted average of the phylogenetic diversity scores in all trees displayed by the network, with the weights determined by the inheritance probabilities on the reticulation edges used in the embeddings. We show that computing the score of a given set of taxa in a given network is #P-hard, directly implying #P-hardness of finding a subset of \(k\) taxa achieving maximum diversity score and thereby ruling out polynomial-time algorithms for these problems unless the polynomial hierarchy collapses. However, we show that both problems can be solved efficiently if the input network is close to being a tree in the sense that its reticulation number is small. More precisely, we prove that we can solve the optimization problem in networks with \(n\) leaves and \(r\) reticulations in \(2^{\mathcal{O}(r)} \cdot n \cdot k\) time. Using experiments on data produced by simulating a reticulate-evolution process, we show that our algorithm runs efficiently on networks with hundreds of taxa and tens of reticulations.
@inproceedings{vanIersel2025averagetree,
title = {{Average-Tree Phylogenetic Diversity of Networks}},
author = {van Iersel, Leo and Jones, Mark and Schestag, Jannik and Scornavacca, Celine and Weller, Mathias},
booktitle = {Proceedings of the 25th International Workshop on Algorithms in Bioinformatics (WABI 2025)},
pages = {15:1--15:21},
year = {2025},
organization = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
doi = {10.4230/LIPIcs.WABI.2025.15}
}
Latin American Theoretical Informatics Symposium (LATIN)
[9]
conference paper
Limits of Kernelization and Parametrization for Phylogenetic Diversity with Dependencies
Proceedings of the 17th Latin American Theoretical Informatics Symposium (LATIN 2026).
In the Maximize Phylogenetic Diversity problem, we are given a phylogenetic tree that represents the genetic proximity of species, and we are asked to select a subset of species of maximum phylogenetic diversity to be preserved through conservation efforts, subject to budgetary constraints that allow only \(k\) species to be saved. This neglects that it is futile to preserve a predatory species if we do not also preserve at least a subset of the prey it feeds on. Thus, in the Optimizing PD with Dependencies (\(\varepsilon\)-PDD) problem, we are additionally given a food web that represents the predator–prey relationships between species. The goal is to save a set of \(k\) species of maximum phylogenetic diversity such that for every saved species, at least one of its prey is also saved. This problem is NP-hard even when the phylogenetic tree is a star.
The \(\alpha\)-PDD problem alters \(\varepsilon\)-PDD by requiring that at least some fraction \(\alpha\) of the prey of every saved species are also saved. In this paper, we study the parameterized complexity of \(\alpha\)-PDD. We prove that the problem is W[1]-hard and in XP when parameterized by the solution size \(k\), the diversity threshold \(D\), or their complements. When parameterized by the vertex cover number of the food web, \(\alpha\)-PDD is fixed-parameter tractable (FPT). A key measure of the computational difficulty of a problem that is FPT is the size of the smallest kernel that can be obtained. We prove that, when parameterized by the distance to clique, 1-PDD admits a linear kernel. Our main contribution is to prove that \(\alpha\)-PDD does not admit a polynomial kernel when parameterized by the vertex cover number plus the diversity threshold \(D\), even if the phylogenetic tree is a star. This implies the non-existence of a polynomial kernel for \(\alpha\)-PDD also when parameterized by a range of structural parameters of the food web, such as its distance to cluster, treewidth, pathwidth, feedback vertex set, and others.
The \(\alpha\)-PDD problem alters \(\varepsilon\)-PDD by requiring that at least some fraction \(\alpha\) of the prey of every saved species are also saved. In this paper, we study the parameterized complexity of \(\alpha\)-PDD. We prove that the problem is W[1]-hard and in XP when parameterized by the solution size \(k\), the diversity threshold \(D\), or their complements. When parameterized by the vertex cover number of the food web, \(\alpha\)-PDD is fixed-parameter tractable (FPT). A key measure of the computational difficulty of a problem that is FPT is the size of the smallest kernel that can be obtained. We prove that, when parameterized by the distance to clique, 1-PDD admits a linear kernel. Our main contribution is to prove that \(\alpha\)-PDD does not admit a polynomial kernel when parameterized by the vertex cover number plus the diversity threshold \(D\), even if the phylogenetic tree is a star. This implies the non-existence of a polynomial kernel for \(\alpha\)-PDD also when parameterized by a range of structural parameters of the food web, such as its distance to cluster, treewidth, pathwidth, feedback vertex set, and others.
@inproceedings{holtgrefe2026limits,
title = {{Limits of Kernelization and Parametrization for Phylogenetic Diversity with Dependencies}},
author = {Holtgrefe, Niels and Schestag, Jannik and Zeh, Norbert},
booktitle = {Proceedings of the 17th Latin American Theoretical Informatics Symposium (LATIN 2026)},
organization = {Springer},
year = {2026}
}
IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS)
[8]
conference paper
Maximizing Phylogenetic Diversity under Ecological Constraints: A Parameterized Complexity Study
Proceedings of the 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024):28:1-28:18.
In the NP-hard Optimizing Phylogenetic Diversity with Dependencies (PDD) problem, the input consists of a phylogenetic tree \(\mathcal{T}\) over a set of taxa \(X\), a food-web that describes the prey-predator relationships in \(X\), and integers \(k\) and \(D\). The task is to find a set \(S\) of \(k\) species that is viable in the food-web such that the subtree of \(\mathcal{T}\) obtained by retaining only the vertices of \(S\) has total edge weight at least \(D\). Herein, viable means that for every predator taxon of \(S\), the set \(S\) contains at least one prey taxon.
We provide the first systematic analysis of PDD and its special case with star trees, PDD_s, from a parameterized complexity perspective. For solution-size related parameters, we show that PDD is fixed-parameter tractable (FPT) with respect to \(D\) and with respect to \(k\) plus the height of the phylogenetic tree. Moreover, we consider structural parameterizations of the food-web. For example, we show an FPT-algorithm for the parameter that measures the vertex deletion distance to graphs where every connected component is a complete graph. Finally, we show that PDD_s admits an FPT-algorithm for the treewidth of the food-web. This disproves, unless P = NP, a conjecture of Faller et al. [Annals of Combinatorics, 2011] who conjectured that PDD_s is NP-hard even when the food-web is a tree.
We provide the first systematic analysis of PDD and its special case with star trees, PDD_s, from a parameterized complexity perspective. For solution-size related parameters, we show that PDD is fixed-parameter tractable (FPT) with respect to \(D\) and with respect to \(k\) plus the height of the phylogenetic tree. Moreover, we consider structural parameterizations of the food-web. For example, we show an FPT-algorithm for the parameter that measures the vertex deletion distance to graphs where every connected component is a complete graph. Finally, we show that PDD_s admits an FPT-algorithm for the treewidth of the food-web. This disproves, unless P = NP, a conjecture of Faller et al. [Annals of Combinatorics, 2011] who conjectured that PDD_s is NP-hard even when the food-web is a tree.
@inproceedings{komusiewicz2024maximizing,
title = {{Maximizing Phylogenetic Diversity under Ecological Constraints: A Parameterized Complexity Study}},
author = {Komusiewicz, Christian and Schestag, Jannik},
booktitle = {Proceedings of the 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)},
year = {2024},
pages = {28:1--28:18},
organization = {Schloss-Dagstuhl-Leibniz Zentrum f{\"u}r Informatik},
doi = {10.4230/LIPIcs.FSTTCS.2024.28}
}
International Workshop on Combinatorial Algorithms (IWOCA)
[7]
journal article
On Critical Node Problems with Vulnerable Vertices
Journal of Graph Algorithms and Applications, 28(1):1-26.
A vertex pair in an undirected graph is called connected if the two vertices are connected by a path. In the NP-hard Critical Node Problem (CNP), the input is an undirected graph \(G\) with integers \(k\) and \(x\), and the question is whether one can transform \(G\) by deleting at most \(k\) vertices into a graph whose total number of connected vertex pairs is at most \(x\). In this work, we introduce and study two NP- hard variants of CNP where a subset of the vertices is marked as vulnerable, and we aim to obtain a graph with at most \(x\) connected vertex pairs containing at least one vulnerable vertex. In the first variant, which generalizes CNP, we may delete vulnerable and non-vulnerable vertices. In the second variant, we may only delete non-vulnerable vertices.
We perform a parameterized complexity study of both problems. For example, we show that both problems are FPT with respect to \(k + x\). Furthermore, in the case of deletable vulnerable nodes, we provide a polynomial kernel for the parameter \(vc +k\), where \(vc\) is the vertex cover number. In the case of non-deletable vulnerable nodes, we prove NP-hardness even when there is only one vulnerable node.
We perform a parameterized complexity study of both problems. For example, we show that both problems are FPT with respect to \(k + x\). Furthermore, in the case of deletable vulnerable nodes, we provide a polynomial kernel for the parameter \(vc +k\), where \(vc\) is the vertex cover number. In the case of non-deletable vulnerable nodes, we prove NP-hardness even when there is only one vulnerable node.
@article{schestag2024critical,
title = {{On Critical Node Problems with Vulnerable Vertices}},
author = {Schestag, Jannik and Gruettemeier, Niels and Komusiewicz, Christian and Sommer, Frank},
journal = {Journal of Graph Algorithms and Applications},
volume = {28},
number = {1},
pages = {1--26},
year = {2024},
doi = {10.7155/jgaa.v28i1.2922}
}
Annual Symposium on Combinatorial Pattern Matching (CPM)
[6]
conference paper
On the Complexity of Parameterized Local Search for the Maximum Parsimony Problem
Proceedings of the 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023):18:1-18:18.
Maximum Parsimony is the problem of computing a most parsimonious phylogenetic tree for a taxa set \(X\) from character data for \(X\). A common strategy to attack this notoriously hard problem is to perform a local search over the phylogenetic tree space. Here, one is given a phylogenetic tree \(T\) and wants to find a more parsimonious tree in the neighborhood of \(T\). We study the complexity of this problem when the neighborhood contains all trees within distance \(k\) for several classic distance functions. For the nearest neighbor interchange (NNI), subtree prune and regraft (SPR), tree bisection and reconnection (TBR), and edge contraction and refinement (ECR) distances, we show that, under the exponential time hypothesis, there are no algorithms with running time \(|I|^{o(k)}\) where \(|I|\) is the total input size. Hence, brute-force algorithms with running time \(|X|^{\mathcal{O}(k)} \cdot |I|\) are essentially optimal.
In contrast to the above distances, we observe that for the sECR-distance, where the contracted edges are constrained to form a subtree, a better solution within distance \(k\) can be found in \(k^{\mathcal{O}(k)} \cdot |I|^{\mathcal{O}(1)}\) time.
In contrast to the above distances, we observe that for the sECR-distance, where the contracted edges are constrained to form a subtree, a better solution within distance \(k\) can be found in \(k^{\mathcal{O}(k)} \cdot |I|^{\mathcal{O}(1)}\) time.
@inproceedings{komusiewicz2023complexity,
title = {{On the Complexity of Parameterized Local Search for the Maximum Parsimony Problem}},
author = {Komusiewicz, Christian and Linz, Simone and Morawietz, Nils and Schestag, Jannik},
booktitle = {Proceedings of the 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)},
pages = {18:1--18:18},
year = {2023},
organization = {Schloss-Dagstuhl-Leibniz Zentrum f{\"u}r Informatik},
doi = {10.4230/LIPIcs.CPM.2023.18}
}
International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM)
[5]
conference paper
Weighted Food Webs Make Computing Phylogenetic Diversity So Much Harder
Proceedings of the 51st International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM 2026):187-202.
In a phylogenetic tree, Phylogenetic trees represent certain species and their likely ancestors. In such a tree, present-day species are leaves and an edge from \(u\) to \(v\) indicates that \(u\) is an ancestor of \(v\). Weights on these edges indicate the phylogenetic distance. The phylogenetic diversity (PD) of a set of species \(A\) is the total weight of edges that are on any path between the root of the phylogenetic tree and a species in \(A\).
Selecting a small set of species that maximizes phylogenetic diversity for a given phylogenetic tree is an essential task in preservation planning, where limited resources naturally prevent saving all species. An optimal solution can be found with a greedy algorithm [Steel, Systematic Biology, 2005; Pardi and Goldman, PLoS Genetics, 2005]. However, when a food web representing predator-prey relationships is given, finding a set of species that optimizes phylogenetic diversity subject to the condition that each saved species should be able to find food among the preserved species is NP-hard [Spillner et al., IEEE/ACM, 2008].
We present a generalization of this problem, where, inspired by biological considerations, the food web has weighted edges to represent the importance of predator-prey relationships. We show that this version is NP-hard even when both structures, the food web and the phylogenetic tree, are stars. To cope with this intractability, we proceed in two directions. Firstly, we study special cases where a species can only survive if a given fraction of its prey is preserved. Secondly, we analyze these problems through the lens of parameterized complexity. Our results include that finding a solution is fixed-parameter tractable with respect to the vertex cover number of the food web, assuming the phylogenetic tree is a star.
Selecting a small set of species that maximizes phylogenetic diversity for a given phylogenetic tree is an essential task in preservation planning, where limited resources naturally prevent saving all species. An optimal solution can be found with a greedy algorithm [Steel, Systematic Biology, 2005; Pardi and Goldman, PLoS Genetics, 2005]. However, when a food web representing predator-prey relationships is given, finding a set of species that optimizes phylogenetic diversity subject to the condition that each saved species should be able to find food among the preserved species is NP-hard [Spillner et al., IEEE/ACM, 2008].
We present a generalization of this problem, where, inspired by biological considerations, the food web has weighted edges to represent the importance of predator-prey relationships. We show that this version is NP-hard even when both structures, the food web and the phylogenetic tree, are stars. To cope with this intractability, we proceed in two directions. Firstly, we study special cases where a species can only survive if a given fraction of its prey is preserved. Secondly, we analyze these problems through the lens of parameterized complexity. Our results include that finding a solution is fixed-parameter tractable with respect to the vertex cover number of the food web, assuming the phylogenetic tree is a star.
@inproceedings{schestag2026weighted,
title = {{Weighted Food Webs Make Computing Phylogenetic Diversity So Much Harder}},
author = {Schestag, Jannik},
booktitle = {Proceedings of the 51st International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM 2026)},
pages = {187--202},
year = {2026},
organization = {Springer},
doi = {10.1007/978-3-032-17801-5_14}
}
International Conference on Algorithmic Decision Theory (ADT)
[4]
conference paper
Protective and Nonprotective Subset Sum Games: A Parameterized Complexity Analysis
Proceedings of the 8th International Conference on Algorithmic Decision Theory (ADT 2024):82--97.
In Subset Sum Game as studied by Pieterse and Woeginger [Theory of Computing Systems, 2021], two players alternatingly fill a common knapsack each with items from a private collection. The goal of Player A is to reach a value of at least \(T_A\), whereas Player B may follow different strategies. Subset Sum Game is NP-complete and solvable in pseudopolynomial time if Player B greedily selects the biggest available item in each turn; the game is PSPACE-complete, however, if Player B plays a hostile strategy where the only aim is to avoid that Player A wins. We continue the study of the game with these two strategies for Player B.
First, we provide a faster pseudopolynomial-time algorithm for a greedy Player B and show that the problem with a hostile Player B is fixed-parameter tractable with respect to the knapsack capacity \(C\). Moreover, we study the influence of further parameters such as \(T_A\), the number of rounds in the game, and the number of different numbers in the input on the complexity of the problem. Second, we consider a further variant of the game, called Protective Subset Sum Game, where Player A additionally has the goal that Player B reaches a value of at least \(T_B\). In a nutshell, we show that most algorithms for the nonprotective variant can be transferred to Protective Subset Sum Game.
First, we provide a faster pseudopolynomial-time algorithm for a greedy Player B and show that the problem with a hostile Player B is fixed-parameter tractable with respect to the knapsack capacity \(C\). Moreover, we study the influence of further parameters such as \(T_A\), the number of rounds in the game, and the number of different numbers in the input on the complexity of the problem. Second, we consider a further variant of the game, called Protective Subset Sum Game, where Player A additionally has the goal that Player B reaches a value of at least \(T_B\). In a nutshell, we show that most algorithms for the nonprotective variant can be transferred to Protective Subset Sum Game.
@inproceedings{garvardt2024protective,
title = {{Protective and Nonprotective Subset Sum Games: A Parameterized Complexity Analysis}},
author = {Garvardt, Jaroslav and Komusiewicz, Christian and Lorke, Ber and Schestag, Jannik},
booktitle = {Proceedings of the 8th International Conference on Algorithmic Decision Theory (ADT 2024)},
pages = {82--97},
year = {2024},
organization = {Springer},
doi = {10.1007/978-3-031-73903-3_6}
}
RECOMB International Workshop on Comparative Genomics (RECOMB-CG)
[3]
conference paper
Phylogenetic Network Diversity Parameterized by Reticulation Number and Beyond
Proceedings of the 22nd RECOMB International Workshop on Comparative Genomics (RECOMB-CG 2025):107-130.
Network Phylogenetic Diversity (Network-PD) is a measure for the diversity of a set of species based on a rooted phylogenetic network (with branch lengths and inheritance probabilities on the reticulation edges) describing the evolution of those species. We consider the Maximize Network-PD problem: Given such a network, find \(k\) species with maximum Network-PD score. We show that this problem is fixed-parameter tractable (FPT) for binary networks, by describing an optimal algorithm running in \(\mathcal{O}(2^r \log(k)(n+r))\) time, with \(n\) the total number of species in the network and \(r\) its reticulation number. Furthermore, we show that Maximize Network-PD is NP-hard for level-1 networks, proving that, unless P=NP, the FPT approach cannot be extended by using the level as parameter instead of the reticulation number.
@inproceedings{vanIersel2025phylogenetic,
title = {{Phylogenetic Network Diversity Parameterized by Reticulation Number and Beyond}},
author = {van Iersel, Leo and Jones, Mark and Schestag, Jannik and Scornavacca, Celine and Weller, Mathias},
booktitle = {Proceedings of the 22nd RECOMB International Workshop on Comparative Genomics (RECOMB-CG 2025)},
pages = {107--130},
year = {2025},
organization = {Springer},
doi = {10.1007/978-3-031-94928-9_7}
}
Computability in Europe (CiE)
[2]
journal article
Destroying Bicolored \(P_3\)s by Deleting Few Edges
Discrete Mathematics & Theoretical Computer Science, 23.
We introduce and study the Bicolored \(P_3\) Deletion problem defined as follows. The input is a graph \(G = (V, E)\) where the edge set \(E\) is partitioned into a set \(E_r\) of red edges and a set \(E_b\) of blue edges. The question is whether we can delete at most \(k\) edges such that \(G\) does not contain a bicolored \(P_3\) as an induced subgraph. Here, a bicolored \(P_3\) is a path on three vertices with one blue and one red edge. We show that Bicolored \(P_3\) Deletion is NP-hard and cannot be solved in \(2^{o(|V|+|E|)}\) time on bounded-degree graphs if the ETH is true. Then, we show that Bicolored \(P_3\) Deletion is polynomial-time solvable when \(G\) does not contain a bicolored \(K_3\), that is, a triangle with edges of both colors. We also provide a polynomial-time algorithm for the case that \(G\) contains no blue \(P_3\), red \(P_3\), blue \(K_3\), and red \(K_3\). Finally, we show that Bicolored \(P_3\) Deletion can be solved in \(\mathcal{O}(1.84^k \cdot |V | \cdot |E|)\) time and that it admits a kernel with \(\mathcal{O}(k \Delta min(k, \Delta))\) vertices, where \(\Delta\) is the maximum degree of \(G\).
@article{gruttemeier2021destroying,
title = {{Destroying Bicolored P3s by Deleting Few Edges}},
author = {Gr{\"u}ttemeier, Niels and Komusiewicz, Christian and Schestag, Jannik and Sommer, Frank},
journal = {Discrete Mathematics \& Theoretical Computer Science},
volume = {23},
year = {2021},
publisher = {Episciences.org},
doi = {10.46298/dmtcs.6108}
}
Cologne Twente Workshop on Graphs and Combinatorial Optimization (CTW)
[1]
journal article
A multivariate complexity analysis of the Generalized Noah's Ark Problem
Discrete Applied Mathematics, 382:137-154.
In the Generalized Noah's Ark Problem, one is given a phylogenetic tree on a set of species \(X\) and a set of conservation projects for each species. Each project comes with a cost and raises the survival probability of the corresponding species. The aim is to select a conservation project for each species such that the total cost of the selected projects does not exceed some given threshold and the expected phylogenetic diversity is as large as possible. We study the complexity of Generalized Noah's Ark Problem and some of its special cases with respect to several parameters related to the input structure, such as the number of different costs, the number of different survival probabilities, or the number of species, \(|X|\).
@article{komusiewicz2025multivariate,
title = {{A multivariate complexity analysis of the Generalized Noah's Ark Problem}},
author = {Komusiewicz, Christian and Schestag, Jannik},
journal = {Discrete Applied Mathematics},
volume = {382},
pages = {137--154},
year = {2025},
publisher = {Elsevier},
doi = {10.1016/j.dam.2025.11.037}
}