Computing shortest paths is a classical graph theory problem and a central task in many applications. Although many algorithms to solve this problem have been proposed over the years, they are designed to work in the main memory and/or with static graphs, which limits their applicability to many current applications where graphs are highly dynamic, that is, subject to frequent updates. In this paper, we propose novel efficient incremental algorithms for maintaining all-pairs shortest paths and distances in dynamic graphs. We experimentally evaluate our approach on several real-world datasets, showing that it significantly outperforms current algorithms designed for the same problem.
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In this paper, we consider positive real weights.
The time taken to generate all-pairs shortest paths for the original datasets ranges from around 222 seconds for the smallest dataset, namely DIMES, to around 4800 seconds for the biggest dataset, namely Instagram. It is worth noticing that computing all-pairs shortest paths is a task performed only once at the beginning, provided that incremental algorithms are subsequently used to maintain shortest paths and distances.
Clearly, the input of PDR consists of a graph and the corresponding shortest distances, rather than the actual paths.
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This paper was invited as an extended version of Greco et al. (2016b) presented at the 2016 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM), August 18–21, 2016, San Francisco, USA.
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Greco, S., Molinaro, C., Pulice, C. et al. Incremental maintenance of all-pairs shortest paths in relational DBMSs. Soc. Netw. Anal. Min. 7, 36 (2017). https://doi.org/10.1007/s13278-017-0457-y