
Multistage Graph Problems on a Global Budget
Timeevolving or temporal graphs gain more and more popularity when stud...
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Multistage Vertex Cover
Covering all edges of a graph by a minimum number of vertices, this is t...
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Extension of vertex cover and independent set in some classes of graphs and generalizations
We consider extension variants of the classical graph problems Vertex Co...
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On Finding Separators in Temporal Split and Permutation Graphs
Removing all connections between two vertices s and z in a graph by remo...
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Consistent polynomialtime unseeded graph matching for Lipschitz graphons
We propose a consistent polynomialtime method for the unseeded node mat...
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A Parameterized View on MultiLayer Cluster Editing
In classical Cluster Editing we seek to transform a given graph into a d...
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On Parameterized Complexity of Liquid Democracy
In liquid democracy, each voter either votes herself or delegates her vo...
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Multistage Problems on a Global Budget
Timeevolving or temporal graphs gain more and more popularity when studying the behavior of complex networks. In this context, the multistage view on computational problems is among the most natural frameworks. Roughly speaking, herein one studies the different (time) layers of a temporal graph (effectively meaning that the edge set may change over time, but the vertex set remains unchanged), and one searches for a solution of a given graph problem for each layer. The twist in the multistage setting is that the found solutions may not differ too much between subsequent layers. We relax on this notion by introducing a global instead of the so far local budget view. More specifically, we allow for few disruptive changes between subsequent layers but request that overall, that is, summing over all layers, the degree of change is upperbounded. Studying several classic graph problems (both NPhard and polynomialtime solvable ones) from a parameterized angle, we encounter both fixedparameter tractability and parameterized hardness results. Somewhat surprisingly, we find that sometimes the global multistage versions of NPhard problems such as Vertex Cover turn out to be computationally easier than the ones of polynomialtime solvable problems such as Matching.
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