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Temporal graphs represent interactions between entities over time. Theseinteractions may be direct, a contact between two vertices at some timeinstant, or indirect, through sequences of contacts called journeys. Decidingwhether an entity can reach another through a journey is useful for variousapplications in complex networks. In this paper, we present a disk-based datastructure that maintains temporal reachability information under the additionof new contacts in a non-chronological order. It represents the \emph{timedtransitive closure} (TTC) by a set of \emph{expanded} R-tuples of the form $(u,v, t^-, t^+)$, which encodes the existence of journeys from vertex $u$ tovertex $v$ with departure at time $t^-$ and arrival at time $t^+$. Let $n$ bethe number of vertices and $\tau$ be the number of timestamps in the lifetimeof the temporal graph. Our data structure explicitly maintains this informationin linear arrays using $O(n^2\tau)$ space so that sequential accesses on diskare prioritized. Furthermore, it adds a new unsorted contact $(u, v, t)$accessing $O\left(\frac{n^2\tau}{B}\right)$ sequential pages in the worst-case,where $B$ is the of pages on disk; it answers whether there is of a journeyfrom a vertex $u$ to a vertex $v$ within a time interval $[t_1, t_2]$ accessinga single page; it answers whether all vertices can reach each other in $[t_1,t_2]$; and it reconstructs a valid journey that validates the reachability froma vertex $u$ to a vertex $v$ within $[t_1, t_1]$ accessing$O\left(\frac{n\tau}{B}\right)$ pages. Our experiments show that our novel datastructure are better that the best known approach for the majority of casesusing synthetic and real world datasets.

A Dynamic Data Structure for Representing Timed Transitive Closures on Disk