Results 21 to 30 of about 128,668 (237)
Parameterized Complexity of 1-Planarity [PDF]
Journal of Graph Algorithms and Applications, 2017 We consider the problem of drawing graphs with at most one crossing per edge. These drawings, and the graphs that can be drawn in this way, are called $1$-planar. Finding $1$-planar drawings is known to be ${\mathsf{NP}}$-hard, but we prove that it is fixed-parameter tractable with respect to the vertex cover number, tree-depth, and cyclomatic number ...
Michael J. Bannister +2 more
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Parameterized Complexity of Asynchronous Border Minimization
, 2015 Microarrays are research tools used in gene discovery as well as disease and cancer diagnostics. Two prominent but challenging problems related to microarrays are the Border Minimization Problem (BMP) and the Border Minimization Problem with given ...
A Frank +16 more
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Parameterized Complexity of Bandwidth on Trees [PDF]
, 2014 The bandwidth of a $n$-vertex graph $G$ is the smallest integer $b$ such that there exists a bijective function $f : V(G) \rightarrow \{1,...,n\}$, called a layout of $G$, such that for every edge $uv \in E(G)$, $|f(u) - f(v)| \leq b$. In the {\sc Bandwidth} problem we are given as input a graph $G$ and integer $b$, and asked whether the bandwidth of ...
Markus Sortland Dregi, Daniel Lokshtanov
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New Algorithms for Mixed Dominating Set [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 A mixed dominating set is a collection of vertices and edges that dominates all vertices and edges of a graph. We study the complexity of exact and parameterized algorithms for \textsc{Mixed Dominating Set}, resolving some open questions.
Louis Dublois +2 more
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Parameterized Complexity of Diameter [PDF]
Algorithmica, 2019 AbstractDiameter—the task of computing the length of a longest shortest path—is a fundamental graph problem. Assuming the Strong Exponential Time Hypothesis, there is no $$O(n^{1.99})$$ O ( n 1.99
André Nichterlein, Matthias Bentert
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On the parameterized complexity of Grid Contraction
Journal of Computer and System Sciences, 2022 For a family of graphs $\mathcal{G}$, the $\mathcal{G}$-\textsc{Contraction} problem takes as an input a graph $G$ and an integer $k$, and the goal is to decide if there exists $F \subseteq E(G)$ of size at most $k$ such that $G/F$ belongs to $\mathcal{G}$. Here, $G/F$ is the graph obtained from $G$ by contracting all the edges in $F$. In this article,
Saket Saurabh +2 more
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Parameterized Complexity of Broadcasting in Graphs
Theoretical Computer Science, 2023 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 informed vertex can transmit the information to at most one of its neighbors.
Fomin, Fedor +2 more
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On the Descriptive Complexity of Color Coding
Algorithms, 2021 Color coding is an algorithmic technique used in parameterized complexity theory to detect “small” structures inside graphs. The idea is to derandomize algorithms that first randomly color a graph and then search for an easily-detectable, small color ...
Max Bannach, Till Tantau
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Clique Transversal Variants on Graphs: A Parameterized-Complexity Perspective
Mathematics, 2023 The clique transversal problem and its variants have garnered significant attention in the last two decades due to their practical applications in communication networks, social-network theory and transceiver placement for cellular telephones.
Chuan-Min Lee
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