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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

The well-known Disjoint Paths problem is to decide if a graph contains k pairwise disjoint paths, each connecting a different terminal pair from a set of k distinct pairs. We determine, with an exception of two cases, the complexity of the…

Combinatorics · Mathematics 2021-05-14 Walter Kern , Barnaby Martin , Daniël Paulusma , Siani Smith , Erik Jan van Leeuwen

For any natural number $d$, a graph $G$ is a (disjoint) $d$-interval graph if it is the intersection graph of (disjoint) $d$-intervals, the union of $d$ (disjoint) intervals on the real line. Two important subclasses of $d$-interval graphs…

Discrete Mathematics · Computer Science 2024-04-30 Virginia Ardévol Martínez , Romeo Rizzi , Abdallah Saffidine , Florian Sikora , Stéphane Vialette

We consider the following question: given an $(X,Y)$-bigraph $G$ and a set $S \subset X$, does $G$ contain two disjoint matchings $M_1$ and $M_2$ such that $M_1$ saturates $X$ and $M_2$ saturates $S$? When $|S|\geq |X|-1$, this question is…

Data Structures and Algorithms · Computer Science 2015-06-23 Gregory J. Puleo

A \emph{mixed interval graph} is an interval graph that has, for every pair of intersecting intervals, either an arc (directed arbitrarily) or an (undirected) edge. We are particularly interested in scenarios where edges and arcs are…

Discrete Mathematics · Computer Science 2024-08-09 Grzegorz Gutowski , Konstanty Junosza-Szaniawski , Felix Klesen , Paweł Rzążewski , Alexander Wolff , Johannes Zink

Let H be a connected bipartite graph with n nodes and m edges. We give an O(nm) time algorithm to decide whether H is an interval bigraph. The best known algorithm has time complexity O(nm^6(m + n) \log n) and it was developed in 1997 [18].…

Data Structures and Algorithms · Computer Science 2018-05-22 Arash Rafiey

Artificial neural networks are functions depending on a finite number of parameters typically encoded as weights and biases. The identification of the parameters of the network from finite samples of input-output pairs is often referred to…

Machine Learning · Computer Science 2022-11-10 Massimo Fornasier , Timo Klock , Marco Mondelli , Michael Rauchensteiner

In the Directed Disjoint Paths problem, we are given a digraph $D$ and a set of requests $\{(s_1, t_1), \ldots, (s_k, t_k)\}$, and the task is to find a collection of pairwise vertex-disjoint paths $\{P_1, \ldots, P_k\}$ such that each…

Data Structures and Algorithms · Computer Science 2021-12-21 Raul Lopes , Ignasi Sau

Given an undirected graph G and a set A \subseteq V(G), an A-path is a path in G that starts and ends at two distinct vertices of A with intermediate vertices in V(G) \setminus A. An A-path is called an (A,\ell)-path if the length of the…

Data Structures and Algorithms · Computer Science 2026-02-17 Susobhan Bandopadhyay , Aritra Banik , Diptapriyo Majumdar , Abhishek Sahu

We study the parameterized complexity of the problems of finding a maximum common (induced) subgraph of two given graphs. Since these problems generalize several NP-complete problems, they are intractable even when parameterized by strongly…

Data Structures and Algorithms · Computer Science 2025-12-09 Tesshu Hanaka , Yuto Okada , Yota Otachi , Lena Volk

The NP-complete Permutation Pattern Matching problem asks whether a permutation P (the pattern) can be matched into a permutation T (the text). A matching is an order-preserving embedding of P into T. In the Generalized Permutation Pattern…

Computational Complexity · Computer Science 2013-01-15 Marie-Louise Bruner , Martin Lackner

We study the design of fixed-parameter algorithms for problems already known to be solvable in polynomial time. The main motivation is to get more efficient algorithms for problems with unattractive polynomial running times. Here, we focus…

Computational Complexity · Computer Science 2021-01-06 Archontia C. Giannopoulou , George B. Mertzios , Rolf Niedermeier

Ordered matchings, defined as graphs with linearly ordered vertices, where each vertex is connected to exactly one edge, play a crucial role in the area of ordered graphs and their homomorphisms. Therefore, we consider related problems from…

Computational Complexity · Computer Science 2025-12-01 Michal Čertík , Andreas Emil Feldmann , Jaroslav Nešetřil , Paweł Rzążewski

Given a graph $G = (V,E)$, $A \subseteq V$, and integers $k$ and $\ell$, the \textsc{$(A,\ell)$-Path Packing} problem asks to find $k$ vertex-disjoint paths of length $\ell$ that have endpoints in $A$ and internal points in $V \setminus A$.…

Data Structures and Algorithms · Computer Science 2020-08-11 Rémy Belmonte , Tesshu Hanaka , Masaaki Kanzaki , Masashi Kiyomi , Yasuaki Kobayashi , Yusuke Kobayashi , Michael Lampis , Hirotaka Ono , Yota Otachi

In this article, we study the problem of finding the longest common separable pattern between several permutations. We give a polynomial-time algorithm when the number of input permutations is fixed and show that the problem is NP-hard for…

Combinatorics · Mathematics 2007-06-13 Mathilde Bouvel , Dominique Rossin , Stephane Vialette

Given a directed graph $D$ on $n$ vertices and a positive integer $k$, the Arc-Disjoint Cycle Packing problem is to determine whether $D$ has $k$ arc-disjoint cycles. This problem is known to be W[1]-hard in general directed graphs. In this…

Data Structures and Algorithms · Computer Science 2018-02-21 R. Krithika , Abhishek Sahu , Saket Saurabh , Meirav Zehavi

We examine ordered graphs, defined as graphs with linearly ordered vertices, from the perspective of homomorphisms (and colorings) and their complexities. We demonstrate the corresponding computational and parameterized complexities, along…

Computational Complexity · Computer Science 2025-12-01 Michal Čertík , Andreas Emil Feldmann , Jaroslav Nešetřil , Paweł Rzążewski

In this work, we study the problem of computing a maximum common contraction of two vertex-labeled graphs, i.e. how to make them identical by contracting as little edges as possible in the two graphs. We study the problem from a…

Data Structures and Algorithms · Computer Science 2025-07-01 Manuel Lafond , Bertrand Marchand

A graph has \emph{diameter} D if every pair of vertices are connected by a path of at most D edges. The Diameter-D Augmentation problem asks how to add the a number of edges to a graph in order to make the resulting graph have diameter D.…

Discrete Mathematics · Computer Science 2009-09-23 James Nastos , Yong Gao

We present completeness results for inference in Bayesian networks with respect to two different parameterizations, namely the number of variables and the topological vertex separation number. For this we introduce the parameterized…

Computational Complexity · Computer Science 2022-06-16 Hans Bodlaender , Nils Donselaar , Johan Kwisthout