Temporal Reachability Minimization: Delaying vs. Deleting

Molter, Hendrik; Renken, Malte; Zschoche, Philipp

doi:10.4230/lipics.mfcs.2021.76

Cited by 6 publications

(5 citation statements)

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“…There has been extensive research on many other connectivity-related problems on temporal graphs [4,9,10,11,12,17,18,20,25]. Delays in temporal graphs have been considered in terms of manipulating reachability sets [7,21]. An individual delay operation considered in the mentioned work delays a single time arc and is similar to our notion.…”

Section: Related Workmentioning

confidence: 99%

Temporal Connectivity: Coping with Foreseen and Unforeseen Delays

Füchsle¹,

Molter²,

Niedermeier³

et al. 2022

Preprint

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Consider planning a trip in a train network. In contrast to, say, a road network, the edges are temporal, i.e., they are only available at certain times. Another important difficulty is that trains, unfortunately, sometimes get delayed. This is especially bad if it causes one to miss subsequent trains. The best way to prepare against this is to have a connection that is robust to some number of (small) delays. An important factor in determining the robustness of a connection is how far in advance delays are announced. We give polynomial-time algorithms for the two extreme cases: delays known before departure and delays occurring without prior warning (the latter leading to a two-player game scenario). Interestingly, in the latter case, we show that the problem becomes PSPACE-complete if the itinerary is demanded to be a path. ACM Subject ClassificationTheory of computation → Graph algorithms analysis; Theory of computation → Problems, reductions and completeness; Mathematics of computing → Discrete mathematics Keywords and phrases Paths and walks in temporal graphs, static expansions of temporal graphs, two-player games, flow computations, dynamic programming, PSPACE-completeness

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Section: Related Workmentioning

confidence: 99%

Temporal Connectivity: Coping with Foreseen and Unforeseen Delays

Füchsle¹,

Molter²,

Niedermeier³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Apart from the already mentioned work on finding temporal walks and paths, there has been extensive research on many other connectivity-related problems on temporal graphs [5,15,23]. Delays in temporal graphs have been considered as a modification operation to manipulate reachability sets [9,26]. The individual delay operation considered in the mentioned work delays a single time arc and is similar to our notion of delays.…”

Section: Related Workmentioning

confidence: 99%

“…The individual delay operation considered in the mentioned work delays a single time arc and is similar to our notion of delays. The deletion of time arcs [12,13,26], the deletion of vertices [17,22,29], as well as reordering of time arcs [14] have also been considered as temporal graph modification operations to manipulate the connectivity properties of the temporal graph. The corresponding computational problems in all mentioned work are NP-hard and can be also considered as computing "robustness measures" for the connectivity in temporal graphs.…”

Section: Related Workmentioning

confidence: 99%

Delay-Robust Routes in Temporal Graphs

Füchsle¹,

Molter²,

Niedermeier³

et al. 2022

Preprint

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Most transportation networks are inherently temporal: Connections (e.g. flights, train runs) are only available at certain, scheduled times. When transporting passengers or commodities, this fact must be considered for the the planning of itineraries. This has already led to several well-studied algorithmic problems on temporal graphs. The difficulty of the described task is increased by the fact that connections are often unreliable -in particular, many modes of transportation suffer from occasional delays. If these delays cause subsequent connections to be missed, the consequences can be severe. Thus, it is a vital problem to design itineraries that are robust to (small) delays. We initiate the study of this problem from a parameterized complexity perspective by proving its NP-completeness as well as several hardness and tractability results for natural parameterizations.

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“…Related to spreading processes, Enright et al [19,20], Deligkas and Potapov [16], and Molter et al [38] studied restricting the set of reachable vertices via various temporal graph modifications-all described decision problems are NP-hard in rather restricted settings.…”

Section: Short Restless Temporal Pathmentioning

confidence: 99%

Restless Temporal Path Parameterized Above Lower Bounds

Zschoche¹

2022

Preprint

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Reachability questions are one of the most fundamental algorithmic primitives in temporal graphsgraphs whose edge set changes over discrete time steps. A core problem here is the NP-hard Short Restless Temporal Path: given a temporal graph G, two distinct vertices s and z, and two numbers δ and k, is there a δ-restless temporal s-z path of length at most k? A temporal path is a path whose edges appear in chronological order and a temporal path is δ-restless if two consecutive path edges appear at most δ time steps apart from each other. Among others, this problem has applications in neuroscience and epidemiology. While Short Restless Temporal Path is known to be computationally hard, e.g., it is NP-hard for only three time steps and W[1]-hard when parameterized by the feedback vertex number of the underlying graph, it is fixed-parameter tractable when parameterized by the path length k. We improve on this by showing that Short Restless Temporal Path can be solved in (randomized) 4 k−d |G| O(1) time, where d is the minimum length of a temporal s-z path.

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Temporal Reachability Minimization: Delaying vs. Deleting

Cited by 6 publications

References 0 publications

Temporal Connectivity: Coping with Foreseen and Unforeseen Delays

Temporal Connectivity: Coping with Foreseen and Unforeseen Delays

Delay-Robust Routes in Temporal Graphs

Restless Temporal Path Parameterized Above Lower Bounds

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