Summary: We consider the information extraction framework known as document spanners, and study the problem of efficiently computing the results of the extraction from an input document, where the extraction task is described as a sequential variable-set automaton (VA). We pose this problem in the setting of enumeration algorithms, where we can first run a preprocessing phase and must then produce the results with a small delay between any two consecutive results. Our goal is to have an algorithm which is tractable in combined complexity, i.e., in the sizes of the input document and the VA; while ensuring the best possible data complexity bounds in the input document size, i.e., constant delay in the document size. Several recent works at [F. Flrenzano et al., in: PODS, 2018. arXiv:1803.05277; D. D. Freydenberger, in: PODS, 2018. arXiv:1703.10350] proposed such algorithms but with linear delay in the document size or with an exponential dependency in size of the (generally nondeterministic) input VA. In particular, Florenzano et al. [loc. cit.] suggest that our desired runtime guarantees cannot be met for general sequential VAs. We refute this and show that, given a nondeterministic sequential VA and an input document, we can enumerate the mappings of the VA on the document with the following bounds: the preprocessing is linear in the document size and polynomial in the size of the VA, and the delay is independent of the document and polynomial in the size of the VA. The resulting algorithm thus achieves tractability in combined complexity and the best possible data complexity bounds. Moreover, it is rather easy to describe, in particular for the restricted case of so-called extended VAs.
For the entire collection see [Zbl 1411.68012].