Constructing Antidictionaries in OutputSensitive SpaceTools Badkobeh, Golnaz; Ayad, Lorraine; Fici, Gabriele; Heliou, Alice and Pissis, Solon. 2018. 'Constructing Antidictionaries in OutputSensitive Space'. In: Data Compression Conference. Utah, United States 2629 March 2019. [Conference or Workshop Item]
Official URL: https://signalprocessingsociety.org/blog/dcc2019...
Abstract or DescriptionA word x that is absent from a word y is called minimal if all its proper factors occur in y. Given a collection of k words y_1,y_2,...,y_k over an alphabet Σ, we are asked to compute the set M^ℓ_y_1#...#y_k of minimal absent words of length at most ℓ of word y=y_1#y_2#...#y_k, #∉Σ. In data compression, this corresponds to computing the antidictionary of k documents. In bioinformatics, it corresponds to computing words that are absent from a genome of k chromosomes. This computation generally requires Ω(n) space for n=y using any of the plenty available O(n)time algorithms. This is because an Ω(n)sized text index is constructed over y which can be impractical for large n. We do the identical computation incrementally using outputsensitive space. This goal is reasonable when M^ℓ_y_1#...#y_N=o(n), for all N∈[1,k]. For instance, in the human genome, n ≈ 3× 10^9 but M^12_y_1#...#y_k ≈ 10^6. We consider a constantsized alphabet for stating our results. We show that all M^ℓ_y_1,...,M^ℓ_y_1#...#y_k can be computed in O(kn+∑^k_N=1M^ℓ_y_1#...#y_N) total time using O(MaxIn+MaxOut) space, where MaxIn is the length of the longest word in {y_1,...,y_k} and MaxOut={M^ℓ_y_1#...#y_N:N∈[1,k]}. Proofofconcept experimental results are also provided confirming our theoretical findings and justifying our contribution.
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