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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…

Data Structures and Algorithms · Computer Science 2025-10-29 Mark Jones , Jannik Schestag

In this work, we initiate the complexity study of Biclique Contraction and Balanced Biclique Contraction. In these problems, given as input a graph G and an integer k, the objective is to determine whether one can contract at most k edges…

Data Structures and Algorithms · Computer Science 2026-01-15 R. Krithika , V. K. Kutty Malu , Roohani Sharma , Prafullkumar Tale

Parallel parameterized complexity theory studies how fixed-parameter tractable (fpt) problems can be solved in parallel. Previous theoretical work focused on parallel algorithms that are very fast in principle, but did not take into account…

Data Structures and Algorithms · Computer Science 2019-02-21 Max Bannach , Malte Skambath , Till Tantau

We study the complexity of graph modification problems with respect to homomorphism-based colouring properties of edge-coloured graphs. A homomorphism from edge-coloured graph $G$ to edge-coloured graph $H$ is a vertex-mapping from $G$ to…

Data Structures and Algorithms · Computer Science 2022-05-04 Florent Foucaud , Hervé Hocquard , Dimitri Lajou , Valia Mitsou , Théo Pierron

The shortest path problem in graphs is fundamental to AI. Nearly all variants of the problem and relevant algorithms that solve them ignore edge-weight computation time and its common relation to weight uncertainty. This implies that taking…

Data Structures and Algorithms · Computer Science 2024-03-29 Eyal Weiss , Ariel Felner , Gal A. Kaminka

We study the parameterized complexity of a variant of the $F$-free Editing problem: Given a graph $G$ and a natural number $k$, is it possible to modify at most $k$ edges in $G$ so that the resulting graph contains no induced subgraph…

Discrete Mathematics · Computer Science 2019-11-14 René van Bevern , Vincent Froese , Christian Komusiewicz

Given a list of k source-sink pairs in an edge-weighted graph G, the minimum multicut problem consists in selecting a set of edges of minimum total weight in G, such that removing these edges leaves no path from each source to its…

Data Structures and Algorithms · Computer Science 2017-09-18 Cédric Bentz

Temporal graphs are graphs whose edges are labelled with times at which they are active. Their time-sensitivity provides a useful model of real networks, but renders many problems studied on temporal graphs more computationally complex than…

Discrete Mathematics · Computer Science 2026-04-28 Jessica Enright , Samuel D. Hand , Laura Larios-Jones , Kitty Meeks

We study computational complexity of the class of distance-constrained graph labeling problems from the fixed parameter tractability point of view. The parameters studied are neighborhood diversity and clique width. We rephrase the distance…

Discrete Mathematics · Computer Science 2015-12-04 Jiří Fiala , Tomáš Gavenčiak , Dušan Knop , Martin Koutecký , Jan Kratochvíl

The task of the broadcast problem is, given a graph G and a source vertex s, to compute the minimum number of rounds required to disseminate a piece of information from s to all vertices in the graph. It is assumed that, at each round, an…

Data Structures and Algorithms · Computer Science 2023-06-05 Fedor V. Fomin , Pierre Fraigniaud , Petr A. Golovach

In the Disjoint Shortest Paths problem one is given a graph $G$ and a set $\mathcal{T}=\{(s_1,t_1),\dots,(s_k,t_k)\}$ of $k$ vertex pairs. The question is whether there exist vertex-disjoint paths $P_1,\dots,P_k$ in $G$ so that each $P_i$…

Data Structures and Algorithms · Computer Science 2025-05-07 Michał Pilipczuk , Giannos Stamoulis , Michał Włodarczyk

A Fixed-Parameter Tractable (\FPT) $\rho$-approximation algorithm for a minimization (resp. maximization) parameterized problem $P$ is an FPT algorithm that, given an instance $(x, k)\in P$ computes a solution of cost at most $k \cdot…

Data Structures and Algorithms · Computer Science 2013-08-19 Rajesh Chitnis , MohammadTaghi Hajiaghayi , Guy Kortsarz

Tracking of moving objects is crucial to security systems and networks. Given a graph $G$, terminal vertices $s$ and $t$, and an integer $k$, the \textsc{Tracking Paths} problem asks whether there exists at most $k$ vertices, which if…

Data Structures and Algorithms · Computer Science 2020-08-24 Pratibha Choudhary , Venkatesh Raman

A temporal graph is a graph whose edges appear at certain points in time. These graphs are temporally connected (in class TC) if all vertices can reach each other by temporal paths (traversing the edges in chronological order). Reachability…

Discrete Mathematics · Computer Science 2026-04-21 Arnaud Casteigts , Timothée Corsini , Nils Morawietz

It is known that a number of natural graph problems which are FPT parameterized by treewidth become W-hard when parameterized by clique-width. It is therefore desirable to find a different structural graph parameter which is as general as…

Data Structures and Algorithms · Computer Science 2013-08-15 Jakub Gajarský , Michael Lampis , Sebastian Ordyniak

For fixed integers $r,\ell \geq 0$, a graph $G$ is called an {\em $(r,\ell)$-graph} if the vertex set $V(G)$ can be partitioned into $r$ independent sets and $\ell$ cliques. The class of $(r, \ell)$ graphs generalizes $r$-colourable graphs…

Data Structures and Algorithms · Computer Science 2015-12-15 Sudeshna Kolay , Fahad Panolan , Venkatesh Raman , Saket Saurabh

A graph vertex-subset problem defines which subsets of the vertices of an input graph are feasible solutions. We view a feasible solution as a set of tokens placed on the vertices of the graph. A reconfiguration variant of a vertex-subset…

Computational Complexity · Computer Science 2022-04-25 Nicolas Bousquet , Amer E. Mouawad , Naomi Nishimura , Sebastian Siebertz

Consider a vertex-weighted graph $G$ with a source $s$ and a target $t$. Tracking Paths requires finding a minimum weight set of vertices (trackers) such that the sequence of trackers in each path from $s$ to $t$ is unique. In this work, we…

Data Structures and Algorithms · Computer Science 2022-02-25 Václav Blažej , Pratibha Choudhary , Dušan Knop , Jan Matyáš Křišťan , Ondřej Suchý , Tomáš Valla

Neural Networks (NN) have recently emerged as backbone of several sensitive applications like automobile, medical image, security, etc. NNs inherently offer Partial Fault Tolerance (PFT) in their architecture; however, the biased PFT of NNs…

Machine Learning · Computer Science 2019-02-14 Manaar Alam , Arnab Bag , Debapriya Basu Roy , Dirmanto Jap , Jakub Breier , Shivam Bhasin , Debdeep Mukhopadhyay

We study the well-established problem of finding an optimal routing of unsplittable flows in a graph. While by now there is an extensive body of work targeting the problem on graph classes such as paths and trees, we aim at using the…

Data Structures and Algorithms · Computer Science 2024-10-23 Robert Ganian , Mathis Rocton , Daniel Unterberger