Pré-Publication, Document De Travail Année : 2025

Incremental Reachability

Résumé

In this paper we study the reachability problem in DAGs: given two nodes u and v, is there a path from u to v? While the problem is linear in general, it can be answered faster by using a precomputed index, which gives a compressed representation of the transitive closure of the graph. In this context, algorithms are usually evaluated on three dimensions: the query time that the algorithm needs to answer whether there is a path from one node to another, the memory that the index uses per node, and the indexing time that is required to update the index when a node is added to the graph. In this paper, we add a fourth constraint: we are interested in incremental algorithms, where the index is append-only. In particular, the algorithms guarantee that queries are answered properly even if new nodes are inserted while the query is processed. Combining Jagadish's index with Felsner's incremental chain-decomposition algorithm yields such an incremental algorithm. Its query time is constant, but its index size is heavily dependent on the graph width, and as such is not competitive with recent indexing algorithms (2-hop, tree-chain, ...). We propose an improved version of that algorithm, satisfying incrementality constraints with a much lighter index. In the most compressed version, the query time becomes O(log n). However, constant-time queries can be retained depending on the desired time/memory trade-off.
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Dates et versions

hal-04929088 , version 1 (04-02-2025)

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  • HAL Id : hal-04929088 , version 1

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Laurent Bulteau, Pierre-Yves David, Florian Horn, Euxane Tran-Girard. Incremental Reachability. 2025. ⟨hal-04929088⟩
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