Efficient limited-time reachability estimation in temporal networks

Abstract

Time-limited states characterize many dynamical processes on networks: disease-infected individuals recover after some time, people forget news spreading on social networks, or passengers may not wait forever for a connection. These dynamics can be described as limited-waiting-time processes, and they are particularly important for systems modeled as temporal networks. These processes have been studied via simulations, which is equivalent to repeatedly finding all limited-waiting-time temporal paths from a source node and time. We propose a method yielding an orders-of-magnitude more efficient way of tracking the reachability of such temporal paths. Our method gives simultaneous estimates of the in-or out-reachability (with any chosen waiting-time limit) from every possible starting point and time. It works on very large temporal networks with hundreds of millions of events on current commodity computing hardware. This opens up the possibility to analyze reachability and dynamics of spreading processes on large temporal networks in completely new ways. For example, one can now compute centralities based on global reachability for all events or can find with high probability the infected node and time, which would lead to the largest epidemic outbreak.

Data-driven tools for assessing and combating COVID-19 outbreaks in Brazil based on analytics and statistical methods

“…In this sense, the approaches analyzed in [61][62][63] may help to implement improved methodologies in the city for disaster control. Potential uses of machine learning and artificial intelligence will enable us to improve the diagnostic accuracy and tools for COVID-19 [42] (or any new disease or calamity), so obtaining more reliable prognosis, targeted treatments, and increasing the operational efficiency of health systems [64][65][66][67][68].…”

Toward a generalized notion of discrete time for modeling temporal networks

“…The prior is a statical encoding of a temporal graph, that is well suited for computing reachability. This property was exploited in Badie-Modiri et al (2020) to estimate in-or out-reachability with limited waiting times. A temporal event graph is computed by transforming the events in the temporal graph (i.e., interactions between two vertices at some point in time) into vertices and connecting them based on temporal adjacency, that is, two events are connected if they share at least one vertex and they occur within time of each other.…”

Directed Percolation in Random Temporal Network Models with Heterogeneities

“…Many dynamics evolving on top of networks, such as some spreading processes [37][38][39], social contagion [40,41] ad-hoc message passing by mobile agents [42] or routing processes [43], have a limited memory thus can only use paths constrained by limited waiting times. Limited waiting-time reachability can be modeled using the event graph, D, that contains a superposition of all temporal paths [20,26,44]. In a limited waiting-time spreading process unfolding over a temporal network, either the spreading agent (e.g.…”