
The Complexity of Finding Temporal Separators under Waiting Time Constraints
In this work, we investigate the computational complexity of Restless Te...
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Interferencefree Walks in Time: Temporally Disjoint Paths
We investigate the computational complexity of finding temporally disjoi...
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Algorithmic Aspects of Temporal Betweenness
The betweenness centrality of a graph vertex measures how often this ver...
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Towards Classifying the PolynomialTime Solvability of Temporal Betweenness Centrality
In static graphs, the betweenness centrality of a graph vertex measures ...
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On the Computational Complexity of Length and NeighborhoodConstrained Path Problems
Finding paths in graphs is a fundamental graphtheoretic task. In this w...
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On the Enumeration of Bicriteria Temporal Paths
We discuss the complexity of path enumeration in weighted temporal graph...
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Gerrymandering on graphs: Computational complexity and parameterized algorithms
Partitioning a region into districts to favor a particular candidate or ...
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The Computational Complexity of Finding Temporal Paths under Waiting Time Constraints
Computing a (shortest) path between two vertices in a graph is one of the most fundamental primitive in graph algorithmics. In recent years, the study of paths in temporal graphs, that is, graphs where the vertex set remains static but the edge set may change over time, gained more and more attention. In a nutshell, temporal paths have to respect time, that is, they may only move forward in time. More formally, the time edges used by a temporal path either need to have increasing or nondecreasing time stamps. In is well known that computing temporal paths is polynomialtime solvable. We study a natural variant, where temporal paths may only dwell a certain given amount of time steps in any vertex, which we call restless temporal paths. This small modification creates a significant change in the computational complexity of the task of finding temporal paths. We show that finding restless temporal paths is NPcomplete and give a thorough analysis of the (parameterized) computational complexity of this problem. In particular, we show that problem remains computationally hard on temporal graphs with three layers and is W[1]hard when parameterized by the feedback vertex number of the underlying graph. On the positive side, we give an efficient (FPT) algorithm to find short restless temporal paths that has an asymptotically optimal running time assuming the Exponential Time Hypothesis.
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