Efficient Algorithms for Temporal Path Computation

Wu, Huanhuan; Cheng, James; Ke, Yiping; Huang, Silu; Huang, Yuzhen; Wu, Hejun

doi:10.1109/tkde.2016.2594065

Cited by 95 publications

(176 citation statements)

References 22 publications

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“…Moreover, our algorithm can compute optimal walks not only for single optimality criteria but also for any linear combination of these. In experiments on real-world data sets, we demonstrate that in terms of efficiency our algorithm can compete with state-of-the-art algorithms by Wu et al [17]. These only run on temporal graphs without waiting-time constraints, which do optimize only one criterion (and not a linear combination).…”

Section: Introductionmentioning

confidence: 86%

“…Two natural motivating examples for the relevance of path (walk) computations in temporal graphs are as follows. First, Wu et al [17] discuss applications in flight networks where every node represents an airport and each edge is labeled with a flight's departure time. Clearly, a "shortest" path may then relate to a most convenient flight connection between two cities.…”

Section: Introductionmentioning

confidence: 99%

“…Our main reference point is the work of Wu et al [17] on efficient algorithms for temporal path computation. These are also implemented in the temporal graph library of Apache Flink [9].…”

Section: Introductionmentioning

confidence: 99%

“…They computed temporal walks under different optimization criteria, namely foremost, fastest, and minimum hop-count 2 on time-evolving graphs-a restricted class of our temporal graph model. Wu et al [17] followed up by introducing algorithms for computing optimal walks for the optimization criteria foremost, reverse-foremost, fastest, and shortest on temporal graphs with no waiting-time constraints. Their algorithms run in linear and quasi-linear time with respect to the number of time-arcs, provided that transmission times are greater than zero on every time-arc.…”

Section: Introductionmentioning

confidence: 99%

“…Finally, in Section 6, we demonstrate the efficiency of our algorithm on real-world data sets. We compare our running times with the running times of the algorithms of Wu et al [17] when neglecting waiting-time constraints. We further examine the impact of different maximum-waiting-time values on the existence and structure of optimal temporal walks.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Efficient Computation of Optimal Temporal Walks Under Waiting-Time Constraints

Himmel

Bentert

Nichterlein

et al. 2019

Studies in Computational Intelligence

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Node connectivity plays a central role in temporal network analysis. We provide a comprehensive study of various concepts of walks in temporal graphs, that is, graphs with fixed vertex sets but edge sets changing over time. Importantly, the temporal aspect results in a rich set of optimization criteria for "shortest" walks. Extending and significantly broadening state-ofthe-art work of Wu et al. [IEEE TKDE 2016], we provide a quasi-linear-time algorithm for shortest walk computation that is capable to deal with various optimization criteria and any linear combination of these. A central distinguishing factor to Wu et al.'s work is that our model allows to, motivated by real-world applications, respect waiting-time constraints for vertices, that is, the minimum and maximum waiting time allowed in intermediate vertices of a walk. Moreover, other than Wu et al. our algorithm does not request a strictly increasing time evolvement of the walk and can optimize a richer set of optimization criteria. Our experimental studies indicate that our richer modeling can be achieved without significantly worsening the running time. * Supported by the DFG, projects DAMM (NI 369/13) and FPTinP (NI 369/16).

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Section: Introductionmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

“…Our main reference point is the work of Wu et al [17] on efficient algorithms for temporal path computation. These are also implemented in the temporal graph library of Apache Flink [9].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Efficient Computation of Optimal Temporal Walks Under Waiting-Time Constraints

Himmel

Bentert

Nichterlein

et al. 2019

Studies in Computational Intelligence

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Maximizing reachability in a temporal graph obtained by assigning starting times to a collection of walks

2022

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We consider the problem of assigning appearing times to the edges of a digraph in order to maximize the (average) temporal reachability between pairs of nodes. Motivated by the application to public transit networks, where edges cannot be scheduled independently one of another, we consider the setting where the edges are grouped into certain walks (called trips) in the digraph and where assigning the appearing time to the first edge of a trip forces the appearing times of the subsequent edges. In this setting, we show that, quite surprisingly, it is NP-complete to decide whether there exists an assignment of times connecting a given pair of nodes. This result allows us to prove that the problem of maximising the temporal reachability cannot be approximated within a factor better than some polynomial term in the size of the graph. We thus focus on the case where, for each pair of nodes, there exists an assignment of times such that one node is reachable from the other. We call this property strong temporalisability. It is a very natural assumption for the application to public transit networks. On the negative side, the problem of maximising the temporal reachability remains hard to approximate within a factor √ n/12 in that setting. Moreover, we show the existence of collections of trips that are strongly temporalisable but for which any assignment of starting times to the trips connects at most an O(1/ √ n) fraction of all pairs of nodes. On the positive side, we show that there must exist an assignment of times that connects a constant fraction of all pairs in the strongly temporalisable and symmetric case, that is, when the set of trips to be scheduled is such that, for each trip, there is a symmetric trip visiting the same nodes in reverse order.

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Temporal Graph Classes: A View Through Temporal Separators

Fluschnik

Molter

Niedermeier

et al. 2018

Graph-Theoretic Concepts in Computer Science

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We investigate the computational complexity of separating two distinct vertices s and z by vertex deletion in a temporal graph. In a temporal graph, the vertex set is fixed but the edges have (discrete) time labels. Since the corresponding Temporal (s, z)-Separation problem is NP-hard, it is natural to investigate whether relevant special cases exist that are computationally tractable. To this end, we study restrictions of the underlying (static) graph-there we observe polynomial-time solvability in the case of bounded treewidth-as well as restrictions concerning the "temporal evolution" along the time steps. Systematically studying partially novel concepts in this direction, we identify sharp borders between tractable and intractable cases. * Supported by the DFG, project DAMM (NI 369/13).

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Efficient Algorithms for Temporal Path Computation

Cited by 95 publications

References 22 publications

Efficient Computation of Optimal Temporal Walks Under Waiting-Time Constraints

Efficient Computation of Optimal Temporal Walks Under Waiting-Time Constraints

Maximizing reachability in a temporal graph obtained by assigning starting times to a collection of walks

Temporal Graph Classes: A View Through Temporal Separators

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