Temporal graphs represent interactions between entities over time. Deciding whether entities can reach each other through temporal paths is useful for various applications such as in communication networks and epidemiology. Previous works have studied the scenario in which addition of new interactions can happen at any point in time. A known strategy maintains, incrementally, a Timed Transitive Closure by using a dynamic data structure composed of $O(n^2)$ binary search trees containing non-nested time intervals. However, space usage for storing these trees grows rapidly as more interactions are inserted. In this paper, we present a compact data structures that represent each tree as two dynamic bit-vectors. In our experiments, we observed that our data structure improves space usage while having similar time performance for incremental updates when comparing with the previous strategy in temporally dense temporal graphs.

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