4 research outputs found
Link Streams as a Generalization of Graphs and Time Series
A link stream is a set of possibly weighted triplets (t, u, v) modeling that
u and v interacted at time t. Link streams offer an effective model for
datasets containing both temporal and relational information, making their
proper analysis crucial in many applications. They are commonly regarded as
sequences of graphs or collections of time series. Yet, a recent seminal work
demonstrated that link streams are more general objects of which graphs are
only particular cases. It therefore started the construction of a dedicated
formalism for link streams by extending graph theory. In this work, we
contribute to the development of this formalism by showing that link streams
also generalize time series. In particular, we show that a link stream
corresponds to a time-series extended to a relational dimension, which opens
the door to also extend the framework of signal processing to link streams. We
therefore develop extensions of numerous signal concepts to link streams: from
elementary ones like energy, correlation, and differentiation, to more advanced
ones like Fourier transform and filters
Computing Betweenness Centrality in Link Streams
Betweeness centrality is one of the most important concepts in graph
analysis. It was recently extended to link streams, a graph generalization
where links arrive over time. However, its computation raises non-trivial
issues, due in particular to the fact that time is considered as continuous. We
provide here the first algorithms to compute this generalized betweenness
centrality, as well as several companion algorithms that have their own
interest. They work in polynomial time and space, we illustrate them on typical
examples, and we provide an implementation
On Computing Pareto Optimal Paths in Weighted Time-Dependent Networks
International audienceA weighted point-availability time-dependent network is a list of temporal edges, where each temporal edge has an appearing time value, a travel time value, and a cost value. In this paper we consider the single source Pareto problem in weighted point-availability time-dependent networks, which consists of computing, for any destination d, all Pareto optimal pairs (t, c), where t and c are the arrival time and the cost of a path from s to d, respectively (a pair (t, c) is Pareto optimal if there is no path with arrival time smaller than t and cost no worse than c or arrival time no greater than t and better cost). We design and analyse a general algorithm for solving this problem, whose time complexity is O(M log P), where M is the number of temporal edges and P is the maximum number of Pareto optimal pairs for each node of the network. This complexity significantly improves the time complexity of the previously known solution. Our algorithm can be used to solve several different minimum cost path problems in weighted point-availability time-dependent networks with a vast variety of cost definitions, and it can be easily modified in order to deal with the single destination Pareto problem. All our results apply to directed networks, but they can be easily adapted to undirected networks with no edges with zero travel time