Reachability and time-based path queries in temporal graphs

Abstract

A temporal graph is a graph in which vertices communicate with each other at specific time, e.g., A calls B at 11 a.m. and talks for 7 minutes, which is modeled by an edge from A to B with starting time "11 a.m." and duration "7 mins". Temporal graphs can be used to model many networks with timerelated activities, but efficient algorithms for analyzing temporal graphs are severely inadequate. We study fundamental problems such as answering reachability and time-based path queries in a temporal graph, and propose an efficient indexing technique specifically designed for processing these queries in a temporal graph. Our results show that our method is efficient and scalable in both index construction and query processing.

Approximating the Temporal Neighbourhood Function of Large Temporal Graphs

“…The method in [16] uses a similar algorithm to [6] for computing spanning trees. The method in [9] proposes to index data to answer reachability and path queries in temporal networks. The problem of finding different types of path (minimum traveling time, earliest arrival time, and minimum number of hops) in the temporal network has also been investigated in a distributed context [17].…”

“…The following definitions are mostly inspired by [3,5,9]. A temporal graph is a pair G = (V, E), where V is the set of nodes and E is the set of temporal edges.…”

“…For example, the left part of Figure 3 shows the earliest arrival path from node 1 to node 3 in the time interval [1,12] in the temporal graph of Figure 2: this path consists of the temporal edges (1, 4, 1), (4,5,3), and (5,3,4), its starting time is 1, and its ending time is 4. The right part of the figure, instead, shows an earliest arrival path from node 1 to node 3 in the time interval [2,12]: it consists of the temporal edges (1,4,6) and (4,3,9), its starting time is 6, and its ending time is 9 (note that another earliest arrival path from node 1 to node 3 in the same interval is the one consisting of the temporal edges (1, 5, 7), (5,4,8), and (4, 3, 9)).…”

“…By assuming that a temporal network is represented by the sequence of its temporal edges, ordered in non-decreasing order with respect to their appearance times, the temporal neighborhood function can be easily computed by making use of the following "scan-based" algorithm [9], which allows us to compute the cardinality of the temporal cone of a node s, which is the set of nodes reachable from s in the interval [t α , t ω ].…”

ATMoN: Adapting the "Temporality" in Large-Scale Dynamic Networks

“…In light of this, several efforts have been made to process and output complex network metrics. In particular, graph measurement techniques now embrace time as another dimension to graphs and develop "temporal" metrics to describe the network reachability [22], connectivity [23] and shortest paths [24]. However, some graph metrics are, in fact, intractable in practice, and cannot scale at will or be efficiently computed [8] [25].…”