Distinct Shortest Walk Enumeration for RPQs
CoRR(2023)
摘要
We consider the Distinct Shortest Walks problem. Given two vertices $s$ and
$t$ of a graph database $\mathcal{D}$ and a regular path query, enumerate all
walks of minimal length from $s$ to $t$ that carry a label that conforms to the
query.
Usual theoretical solutions turn out to be inefficient when applied to graph
models that are closer to real-life systems, in particular because edges may
carry multiple labels. Indeed, known algorithms may repeat the same answer
exponentially many times.
We propose an efficient algorithm for multi-labelled graph databases. The
preprocessing runs in $O{|\mathcal{D}|\times|\mathcal{A}|}$ and the delay
between two consecutive outputs is in $O(\lambda\times|\mathcal{A}|)$, where
$\mathcal{A}$ is a nondeterministic automaton representing the query and
$\lambda$ is the minimal length. The algorithm can handle
$\varepsilon$-transitions in $\mathcal{A}$ or queries given as regular
expressions at no additional cost.
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