Survivability in time-varying networks

Liang, Qingkai; Modiano, Eytan

doi:10.1109/infocom.2016.7524490

Cited by 14 publications

(9 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We lift the algebraic methods for walk counting to counting temporal walks by means of the directed line graph expansion. Variants of directed line graph expansions have been previously used for survivability and reliability analysis [21,26], and for graph kernels [36]. These variants support only strict temporal walks.…”

Section: Directed Line Graph Expansionmentioning

confidence: 99%

Temporal Walk Centrality: Ranking Nodes in Evolving Networks

Oettershagen¹,

Mutzel²,

Kriege³

2022

Preprint

View full text Add to dashboard Cite

We propose the Temporal Walk Centrality, which quantifies the importance of a node by measuring its ability to obtain and distribute information in a temporal network. In contrast to the widely-used betweenness centrality, we assume that information does not necessarily spread on shortest paths but on temporal random walks that satisfy the time constraints of the network. We show that temporal walk centrality can identify nodes playing central roles in dissemination processes that might not be detected by related betweenness concepts and other common static and temporal centrality measures. We propose exact and approximation algorithms with different running times depending on the properties of the temporal network and parameters of our new centrality measure. A technical contribution is a general approach to lift existing algebraic methods for counting walks in static networks to temporal networks. Our experiments on real-world temporal networks show the efficiency and accuracy of our algorithms. Finally, we demonstrate that the rankings by temporal walk centrality often differ significantly from those of other state-of-the-art temporal centralities. CCS CONCEPTS• Information systems → Social networks; • Theory of computation → Graph algorithms analysis.

show abstract

Section: Directed Line Graph Expansionmentioning

confidence: 99%

Temporal Walk Centrality: Ranking Nodes in Evolving Networks

Oettershagen¹,

Mutzel²,

Kriege³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Temporal graphs are well-established in the literature and are also referred to as time-varying [29] and evolving [17] graphs, temporal networks [26,27,32], link streams [28,38], multidimensional G 1 :…”

Section: Introductionmentioning

confidence: 99%

The complexity of finding small separators in temporal graphs

Zschoche

Fluschnik

Molter

et al. 2020

Journal of Computer and System Sciences

View full text Add to dashboard Cite

Temporal graphs are graphs with time-stamped edges. We study the problem of finding a small vertex set (the separator) with respect to two designated terminal vertices such that the removal of the set eliminates all temporal paths connecting one terminal to the other. Herein, we consider two models of temporal paths: paths that pass through arbitrarily many edges per time step (non-strict) and paths that pass through at most one edge per time step (strict). Regarding the number of time steps of a temporal graph, we show a complexity dichotomy (NPhardness versus polynomial-time solvability) for both problem variants. Moreover we prove both problem variants to be NP-complete even on temporal graphs whose underlying graph is planar. We further show that, on temporal graphs with planar underlying graph, if additionally the number of time steps is constant, then the problem variant for strict paths is solvable in quasi-linear time. Finally, we introduce and motivate the notion of a temporal core (vertices whose incident edges change over time). We prove that the non-strict variant is fixed-parameter tractable when parameterized by the size of the temporal core, while the strict variant remains NP-complete, even for constant-size temporal cores. * Supported by the Stiftung Begabtenförderung berufliche Bildung (SBB). † Supported by the DFG, project DAMM (NI 369/13) and project TORE (NI 369/18). ‡ Supported by DFG, project MATE (NI 369/17). 2 We also refer to Himmel [23] for a thorough discussion and comparison of temporal path concepts. 3 Temporal (s, z)-Separation with τ = 1 is equivalent to (s, z)-Separation on static graphs.

show abstract

“…On the other hand, a growing number of positive results has been developed in recent years for various problems in temporal graphs [1,4,6,7,9,12].…”

Section: Introductionmentioning

confidence: 99%

On Short Fastest Paths in Temporal Graphs

Danda¹,

Ramakrishna

Schmidt

et al. 2021

WALCOM: Algorithms and Computation

View full text Add to dashboard Cite

Temporal graphs equip their directed edges with a departure time and a duration, which allows to model a surprisingly high number of real-world problems. Recently, Wu et al. have shown that a fastest path in a temporal graph G from a given vertex s to a vertex z can be computed in near-linear time, where a fastest path is one that minimizes the arrival time at z minus the departure time at s.Here, we consider the natural problem of computing a fastest path from s to z that is in addition short, i.e. minimizes the sum of durations of its edges; this maximizes the total amount of spare time at stops during the journey. Using a new dominance relation on paths in combination with lexicographic orders on the departure and arrival times of these paths, we derive a near-linear time algorithm for this problem with running time O(n + m log p(G)), where n := |V (G)|, m := |E(G)| and p(G) is upper bounded by both the maximum in-degree and the maximum edge duration of G.The dominance relation is interesting in its own right, and may be of use for several related problems like fastest paths with minimum fare, fastest paths with minimum number of stops, and other pareto-optimal path problems in temporal graphs.

show abstract

Survivability in time-varying networks

Cited by 14 publications

References 34 publications

Temporal Walk Centrality: Ranking Nodes in Evolving Networks

Temporal Walk Centrality: Ranking Nodes in Evolving Networks

The complexity of finding small separators in temporal graphs

On Short Fastest Paths in Temporal Graphs

Contact Info

Product

Resources

About