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Approximating the Temporal Neighbourhood Function of Large Temporal Graphs

1
Institut de Recherche en Informatique Fondamentale, Centre National de la Recherche Scientifique, Université de Paris, F-75013 Paris, France
2
Centre National de la Recherche Scientifique, Laboratoire d’Informatique de Paris 6, Sorbonne Université, F-75005 Paris, France
3
Dipartimento di Statistica, Informatica, Applicazioni “Giuseppe Parenti”, Università degli Studi di Firenze, I-50134 Firenze, Italy
*
Author to whom correspondence should be addressed.
Current Address: On-leave from DiMaI, Università degli Studi di Firenze, I-50134 Firenze, Italy.
Algorithms 2019, 12(10), 211; https://doi.org/10.3390/a12100211
Received: 29 June 2019 / Revised: 25 September 2019 / Accepted: 8 October 2019 / Published: 10 October 2019
Temporal networks are graphs in which edges have temporal labels, specifying their starting times and their traversal times. Several notions of distances between two nodes in a temporal network can be analyzed, by referring, for example, to the earliest arrival time or to the latest starting time of a temporal path connecting the two nodes. In this paper, we mostly refer to the notion of temporal reachability by using the earliest arrival time. In particular, we first show how the sketch approach, which has already been used in the case of classical graphs, can be applied to the case of temporal networks in order to approximately compute the sizes of the temporal cones of a temporal network. By making use of this approach, we subsequently show how we can approximate the temporal neighborhood function (that is, the number of pairs of nodes reachable from one another in a given time interval) of large temporal networks in a few seconds. Finally, we apply our algorithm in order to analyze and compare the behavior of 25 public transportation temporal networks. Our results can be easily adapted to the case in which we want to refer to the notion of distance based on the latest starting time.
Keywords: temporal network; link stream; temporal path; earliest arrival time; temporal reachability; neighborhood function; public transportation system temporal network; link stream; temporal path; earliest arrival time; temporal reachability; neighborhood function; public transportation system
MDPI and ACS Style

Crescenzi, P.; Magnien, C.; Marino, A. Approximating the Temporal Neighbourhood Function of Large Temporal Graphs. Algorithms 2019, 12, 211.

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