Time-Dependent Graphs: Definitions, Applications, and Algorithms

Abstract

A time-dependent graph is, informally speaking, a graph structure dynamically changes with time. In such graphs, the weights associated with edges dynamically change over time, that is, the edges in such graphs are activated by sequences of time-dependent elements. Many real-life scenarios can be better modeled by time-dependent graphs, such as bioinformatics networks, transportation networks, and social networks. In particular, the time-dependent graph is a very broad concept, which is reflected in the related research with many names, including temporal graphs, evolving graphs, time-varying graphs, historical graphs, and so on. Though static graphs have been extensively studied, for their time-dependent generalizations, we are still far from a complete and mature theory of models and algorithms. In this paper, we discuss the definition and topological structure of time-dependent graphs, as well as models for their relationship to dynamic systems. In addition, we review some classic problems on time-dependent graphs, e.g., route planning, social analysis, and subgraph problem (including matching and mining). We also introduce existing time-dependent systems and summarize their advantages and limitations. We try to keep the descriptions consistent as much as possible and we hope the survey can help practitioners to understand existing time-dependent techniques.

Data Delivery in a Disaster or Quarantined Area Divided into Triangles Using DTN-Based Algorithms for Unmanned Aerial Vehicles

“…The Dijkstra algorithm is a method used to find the shortest path connecting two nodes in a network [ 43 ]. Our routing problem can be modeled using a time-dependent oriented network [ 44 ]. For the triangle drone network, an algorithm named TD-UAV Dijkstra ( Figure 6 ) is proposed to find a route and its distance dist(d) in seconds from the source s to the destination d starting at the moment “ts”.…”

Distributed temporal graph analytics with GRADOOP

“…Temporal property graphs are property graphs that reflect the graph's evolution, i.e., changes of the graph structure and of properties over time. There are several surveys about such temporal graphs [18,32,45] which have also been called temporal networks [32], time-varying graphs [18], time-dependent graphs [80], evolving graphs and other names [27,55,66,77,82].…”

Recommender System Based on Temporal Models: A Systematic Review

“…Neighborhood: Neighborhood models are CF methods that utilized the collaborative power of the ratings provided by similar users to make recommendations [76]. Generally, the neighborhood model can be adapted to model dynamic changes in RS over time, either by integrating time-dependent algorithms [118][119][120][121][122] or using time-independent algorithms [123][124][125][126]. In this second we present various studies that basically used time-dependent or time-independent algorithms for neighborhood-based RS as shown in Table 5.…”