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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

We study the parameterized complexity of separating a small set of vertices from a graph by a small vertex-separator. That is, given a graph $G$ and integers $k$, $t$, the task is to find a vertex set $X$ with $|X| \le k$ and $|N(X)| \le…

Data Structures and Algorithms · Computer Science 2013-10-02 Fedor V. Fomin , Petr A. Golovach , Janne H. Korhonen

Let $G$ be a graph such that each vertex has its list of available colors, and assume that each list is a subset of the common set consisting of $k$ colors. For two given list colorings of $G$, we study the problem of transforming one into…

Data Structures and Algorithms · Computer Science 2017-05-23 Tatsuhiko Hatanaka , Takehiro Ito , Xiao Zhou

In this paper we show that the problem of identifying an edge $(i,j)$ in a graph $G$ such that there exists an optimal vertex cover $S$ of $G$ containing exactly one of the nodes $i$ and $j$ is NP-hard. Such an edge is called a weak edge.…

Data Structures and Algorithms · Computer Science 2007-12-21 Qiaoming Han , Abraham P. Punnen

We study the classical problem of computing geometric thickness, i.e., finding a straight-line drawing of an input graph and a partition of its edges into as few parts as possible so that each part is crossing-free. Since the problem is…

Computational Complexity · Computer Science 2024-11-26 Thomas Depian , Simon Dominik Fink , Alexander Firbas , Robert Ganian , Martin Nöllenburg

We consider the parameterised complexity of several list problems on graphs, with parameter treewidth or pathwidth. In particular, we show that List Edge Chromatic Number and List Total Chromatic Number are fixed parameter tractable,…

Computational Complexity · Computer Science 2016-08-05 Kitty Meeks , Alexander Scott

In this work we contribute to the study of the fine-grained complexity of problems parameterized by multi-clique-width, which was initiated by F\"urer [ITCS 2017] and pursued further by Chekan and Kratsch [MFCS 2023]. Multi-clique-width is…

Data Structures and Algorithms · Computer Science 2026-04-29 Benjamin Bergougnoux , Vera Chekan , Stefan Kratsch

The question of the existence of a polynomial kernelization of the Vertex Cover Above LP problem has been a longstanding, notorious open problem in Parameterized Complexity. Five years ago, the breakthrough work by Kratsch and Wahlstrom on…

Data Structures and Algorithms · Computer Science 2017-05-11 Syed Mohammad Meesum , Fahad Panolan , Saket Saurabh , Meirav Zehavi

We survey the field of algorithms and complexity for graph problems parameterized above or below guaranteed values, a research area which was pioneered by Venkatesh Raman. Those problems seek, for a given graph $G$, a solution whose value…

Data Structures and Algorithms · Computer Science 2024-03-21 Gregory Gutin , Matthias Mnich

We investigate the parameterised complexity of the classic coverability problem for vector addition systems (VAS): given a finite set of vectors $V \subseteq\mathbb{Z}^d$, an initial configuration $s\in\mathbb{N}^d$, and a target…

Computational Complexity · Computer Science 2025-12-16 Michał Pilipczuk , Sylvain Schmitz , Henry Sinclair-Banks

After the number of vertices, Vertex Cover is the largest of the classical graph parameters and has more and more frequently been used as a separate parameter in parameterized problems, including problems that are not directly related to…

Data Structures and Algorithms · Computer Science 2013-05-03 Mathieu Chapelle , Mathieu Liedloff , Ioan Todinca , Yngve Villanger

We study the parameterized complexity of the following fundamental geometric problems with respect to the dimension $d$: i) Given $n$ points in $\Rd$, compute their minimum enclosing cylinder. ii) Given two $n$-point sets in $\Rd$, decide…

Computational Geometry · Computer Science 2015-02-18 Panos Giannopoulos , Christian Knauer , Gunter Rote , Daniel Werner

We continue and extend previous work on the parameterized complexity analysis of the NP-hard Stable Roommates with Ties and Incomplete Lists problem, thereby strengthening earlier results both on the side of parameterized hardness as well…

Computational Complexity · Computer Science 2021-03-09 Robert Bredereck , Klaus Heeger , Dušan Knop , Rolf Niedermeier

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

Perturbed graphic matroids are binary matroids that can be obtained from a graphic matroid by adding a noise of small rank. More precisely, r-rank perturbed graphic matroid M is a binary matroid that can be represented in the form I +P,…

Data Structures and Algorithms · Computer Science 2019-02-20 Fedor V. Fomin , Petr A. Golovach , Daniel Lokshtanov , Saket Saurabh , Meirav Zehavi

The fundamental caching problem in networks asks to find an allocation of contents to a network of caches with the aim of maximizing the cache hit rate. Despite the problem's importance to a variety of research areas -- including not only…

Networking and Internet Architecture · Computer Science 2024-12-24 Robert Ganian , Fionn Mc Inerney , Dimitra Tsigkari

We study parameterized Constraint Satisfaction Problem for infinite constraint languages. The parameters that we study are weight of the satisfying assignment, number of constraints, maximum number of occurrences of a variable in the…

Computational Complexity · Computer Science 2017-08-10 Ruhollah Majdoddin

This paper studies the computational complexity of the Edge Packing problem and the Vertex Packing problem. The edge packing problem (denoted by $\bar{EDS}$) and the vertex packing problem (denoted by $\bar{DS} $) are linear programming…

Computational Complexity · Computer Science 2011-04-08 Sameera Muhamed Salam , K. N. Parvathy , K. S. Sudeep , K. Murali Krishnan

We discuss approximability and inapproximability in FPT-time for a large class of subset problems where a feasible solution $S$ is a subset of the input data and the value of $S$ is $|S|$. The class handled encompasses many well-known…

Computational Complexity · Computer Science 2013-10-22 Edouard Bonnet , Vangelis Th. Paschos

We investigate the parameterized complexity of the following edge coloring problem motivated by the problem of channel assignment in wireless networks. For an integer q>1 and a graph G, the goal is to find a coloring of the edges of G with…

Data Structures and Algorithms · Computer Science 2013-06-13 Prachi Goyal , Vikram Kamat , Neeldhara Misra