An absent word of a word y is a word that does not occur in y. It is then called minimal if all its proper factors occur in y. In fact, minimal absent words (MAWs) provide useful information about y and thus have several applications. In this paper, we propose an algorithm that maintains the set of MAWs of a fixed-length window sliding over y online. Our algorithm represents MAWs through nodes of the suffix tree. Specifically, the suffix tree of the sliding window is maintained using modified Senft's algorithm (Senft, 2005), itself generalizing Ukkonen's online algorithm (Ukkonen, 1995). We then apply this algorithm to the approximate pattern-matching problem under the Length Weighted Index distance (Chairungsee and Crochemore, 2012). This results in an online O(σ |y|)-time algorithm for finding approximate occurrences of a word x in y, |x| ≤ |y|, where σ is the alphabet size.

International audienceAn absent (or forbidden) word of a word y is a word that does not occur in y. It is then called minimal if all its proper factors occur in y. There exist linear-time and linear-space algorithms for computing all minimal absent words of y (Crochemore et al. in Inf Process Lett 67:111–117, 1998; Belazzougui et al. in ESA 8125:133–144, 2013; Barton et al. in BMC Bioinform 15:388, 2014). Minimal absent words are used for data compression (Crochemore et al. in Proc IEEE 88:1756–1768, 2000, Ota and Morita in Theoret Comput Sci 526:108–119, 2014) and for alignment-free sequence comparison by utilizing a metric based on minimal absent words (Chairungsee and Crochemore in Theoret Comput Sci 450:109–116, 2012). They are also used in molecular biology; for instance, three minimal absent words of the human genome were found to play a functional role in a coding region in Ebola virus genomes (Silva et al. in Bioinformatics 31:2421–2425, 2015). In this article we introduce a new application of minimal absent words for on-line pattern matching. Specifically, we present an algorithm that, given a pattern x and a text y, computes the distance between x and every window of size |x| on y. The running time is O(σ|y|)O(σ|y|) , where σσ is the size of the alphabet. Along the way, we show an O(σ|y|)O(σ|y|) -time and O(σ|x|)O(σ|x|) -space algorithm to compute the minimal absent words of every window of size |x| on y, together with some new combinatorial insight on minimal absent words

This demonstration showcases ProvSQL, an open-source module for the PostgreSQL database management system that adds support for computation of provenance and probabilities of query results. A large range of provenance formalisms are supported, including all those captured by provenance semirings, provenance semirings with monus, as well as where-provenance. Probabilistic query evaluation is made possible through the use of knowledge compilation tools, in addition to standard approaches such as enumeration of possible worlds and Monte-Carlo sampling. ProvSQL supports a large subset of non-aggregate SQL queries.

We establish a translation between a formalism for dynamic programming over hypergraphs and the computation of semiringbased provenance for Datalog programs. The benefit of this translation is a new method for computing the provenance of Datalog programs for specific classes of semirings, which we apply to provenance-aware querying of graph databases. Theoretical results and practical optimizations lead to an efficient implementation using Soufflé, a state-of-the-art Datalog interpreter. Experimental results on real-world data suggest this approach to be efficient in practical contexts, competing with dedicated solutions for graphs.