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.

翻译：时序图表示实体间随时间变化的交互关系。判断实体能否通过时序路径相互可达，在通信网络和流行病学等应用中具有重要价值。已有研究探讨了可在任意时间点新增交互的场景。一种已知策略通过由$O(n^2)$个包含非嵌套时间区间的二叉搜索树组成的动态数据结构，增量式维护时序传递闭包。然而，随着更多交互被插入，存储这些树的空间开销急剧增长。本文提出一种紧凑数据结构，将每棵树表示为两个动态位向量。实验表明，与之前策略相比，本数据结构在时序密集图中进行增量更新时，能够在保持相近时间性能的同时有效降低空间占用。