On Mining Dynamic Graphs for k Shortest Paths

Mining graphs, upon query, for k shortest paths between vertex pairs is a prominent primitive to support several analytics tasks on complex networked datasets. The state-of-the-art method to implement this primitive is KPLL, a framework that provides very fast query answering, even for large inputs and volumes of queries, by pre-computing and exploiting an appropriate index of the graph. However, if the graph's topology undergoes changes over time, such index might become obsolete and thus yield incorrect query results. Re-building the index from scratch, upon every modification, induces unsustainable time overheads, incompatible with applications using k shortest paths for analytics purposes. Motivated by this limitation, in this paper, we introduce DECKPLL, the first dynamic algorithm to maintain a KPLL index under decremental modifications. We assess the effectiveness and scalability of our algorithm through extensive experimentation and show it updates KPLL indices orders of magnitude faster than the re-computation from scratch, while preserving its compactness and query performance. We also combine DECKPLL with INCKPLL, the only known dynamic algorithm to maintain a KPLL index under incremental modifications, and hence showcase, on real-world datasets, the first method to support fast extraction of k shortest paths from graphs that evolve by arbitrary topological changes.