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Given an integer $k$ and a graph where every edge is colored either red or blue, the goal of the exact matching problem is to find a perfect matching with the property that exactly $k$ of its edges are red. Soon after Papadimitriou and…

Data Structures and Algorithms · Computer Science 2023-10-02 Nicolas {El Maalouly} , Raphael Steiner , Lasse Wulf

We revisit the issue of low-distortion embedding of metric spaces into the line, and more generally, into the shortest path metric of trees, from the parameterized complexity perspective.Let $M=M(G)$ be the shortest path metric of an edge…

Data Structures and Algorithms · Computer Science 2008-04-21 Michael Fellows , Fedor Fomin , Daniel Lokshtanov , Elena Losievskaja , Frances A. Rosamond , Saket Saurabh

We consider the problem of adding a fixed number of new edges to an undirected graph in order to minimize the diameter of the augmented graph, and under the constraint that the number of edges added for each vertex is bounded by an integer.…

Data Structures and Algorithms · Computer Science 2023-02-14 Florian Adriaens , Aristides Gionis

Given a graph G, a matching is a subset of edges of G that do not share an endpoint. A matching M is uniquely restricted if the subgraph induced by the endpoints of the edges of M has exactly one perfect matching. Given a graph G and a…

Data Structures and Algorithms · Computer Science 2025-08-19 Juhi Chaudhary , Ignasi Sau , Meirav Zehavi

The crossing resolution of a non-planar drawing of a graph is the value of the minimum angle formed by any pair of crossing edges. Recent experiments have shown that the larger the crossing resolution is, the easier it is to read and…

Data Structures and Algorithms · Computer Science 2018-09-03 Michael A. Bekos , Henry Förster , Christian Geckeler , Lukas Holländer , Michael Kaufmann , Amadäus M. Spallek , Jan Splett

We propose two fixed-parameter tractable algorithms for the weighted Max-Cut problem on embedded 1-planar graphs parameterized by the crossing number $k$ of the given embedding. A graph is called 1-planar if it can be drawn in the plane…

Data Structures and Algorithms · Computer Science 2020-12-01 Christine Dahn , Nils M. Kriege , Petra Mutzel , Julian Schilling

Drawing network maps automatically comprises two challenging steps, namely laying out the map and placing non-overlapping labels. In this paper we tackle the problem of labeling an already existing network map considering the application of…

Computational Geometry · Computer Science 2015-12-31 Jan-Henrik Haunert , Benjamin Niedermann

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

We introduce a parallel machine scheduling problem in which the processing times of jobs are not given in advance but are determined by a system of linear constraints. The objective is to minimize the makespan, i.e., the maximum job…

Data Structures and Algorithms · Computer Science 2015-10-30 Kameng Nip , Zhenbo Wang , Zizhuo Wang

Computing planar orthogonal drawings with the minimum number of bends is one of the most relevant topics in Graph Drawing. The problem is known to be NP-hard, even when we want to test the existence of a rectilinear planar drawing, i.e., an…

Computational Geometry · Computer Science 2023-09-07 Emilio Di Giacomo , Walter Didimo , Giuseppe Liotta , Fabrizio Montecchiani , Giacomo Ortali

The problem Level Planarity asks for a crossing-free drawing of a graph in the plane such that vertices are placed at prescribed y-coordinates (called levels) and such that every edge is realized as a y-monotone curve. In the variant…

Data Structures and Algorithms · Computer Science 2024-04-26 Boris Klemz , Marie Diana Sieper

In Terminal Monitoring Set (TMS), the input is an undirected graph $G=(V,E)$, together with a collection $T$ of terminal pairs and the goal is to find a subset $S$ of minimum size that hits a shortest path between every pair of terminals.…

Discrete Mathematics · Computer Science 2024-06-05 N. R. Aravind , Roopam Saxena

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

In the minimum constraint removal ($MCR$), there is no feasible path to move from the starting point towards the goal and, the minimum constraints should be removed in order to find a collision-free path. It has been proved that $MCR$…

Computational Geometry · Computer Science 2023-02-21 Bahram Sadeghi Bigham

(see paper for full abstract) Cut problems and connectivity problems on digraphs are two well-studied classes of problems from the viewpoint of parameterized complexity. After a series of papers over the last decade, we now have (almost)…

Data Structures and Algorithms · Computer Science 2019-10-07 Rajesh Chitnis , Andreas Emil Feldmann

Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…

Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…

Computational Complexity · Computer Science 2019-04-29 Andreas Emil Feldmann

We study the minimum Manhattan network problem, which is defined as follows. Given a set of points called \emph{terminals} in $\R^d$, find a minimum-length network such that each pair of terminals is connected by a set of axis-parallel line…

Computational Geometry · Computer Science 2012-04-30 Aparna Das , Emden R. Gansner , Michael Kaufmann , Stephen Kobourov , Joachim Spoerhase , Alexander Wolff

In multistage perfect matching problems we are given a sequence of graphs on the same vertex set and asked to find a sequence of perfect matchings, corresponding to the sequence of graphs, such that consecutive matchings are as similar as…

Data Structures and Algorithms · Computer Science 2021-05-11 Markus Chimani , Niklas Troost , Tilo Wiedera

We study the NP-hard Minimum Shared Edges (MSE) problem on graphs: decide whether it is possible to route $p$ paths from a start vertex to a target vertex in a given graph while using at most $k$ edges more than once. We show that MSE can…

Computational Complexity · Computer Science 2017-06-08 Till Fluschnik , Meike Hatzel , Steffen Härtlein , Hendrik Molter , Henning Seidler