We consider the problem of retrieving the k documents from a collection of strings where a given pattern P appears least often. This has potential applications in data mining, bioinformatics, security, and big data. We show that adapting the classical linear-space solutions for this problem is trivial, but the compressed-space solutions are not easy to extend. We design a new solution for this ...

Consider an input text string T ≡ T [1, N ] drawn from an unbounded alphabet, so text positions can be accessed using comparisons. We study partial computation in suffix-based problems for Data Compression and Text Indexing such as • retrieve any segment of K ≤ N consecutive symbols from the Burrows-Wheeler transform of T , which is at the heart of the bzip2 family of text compressors, and • re...

We study k-prefix-free, k-suffix-free and k-infix-free languages that generalize prefix-free, suffix-free and infix-free languages by allowing marginal errors. For example, a string x in a k-prefix-free language L can be a prefix of up to k different strings in L. Namely, a code (language) can allow some marginal errors. We also define finitely prefix-free languages in which a string x can be a...

We present a new data structure to index strings that is very similar to a suffix tree. The new structure indexes the factors of a string whose length does not exceed k, and only those. We call such structure the at most k-deep factor tree, or k-factor tree for short. Time and space complexities for constructing the tree are linear in the length of the string. The construction is on-line. Compa...

Suffix trees are by far the most important data structure in stringology, with myriads of applications in fields like bioinformatics, data compression and information retrieval. Classical representations of suffix trees require O(n log n) bits of space, for a string of size n. This is considerably more than the n log 2 σ bits needed for the string itself, where σ is the alphabet size. The size ...

Finite words and their overlap properties are considered in this paper. Let w be a finite word of length n with period p and where the maximum length of its unbordered factors equals k. A word is called unbordered if it possesses no proper prefix that is also a suffix of that word. Suppose k < p in w. It is known that n ≤ 2k − 2, if w has an unbordered prefix u of length k. We show that, if n =...

For a string w over an alphabet Σ, we consider a composite data structure called the all-suffixes directed acyclic word graph (ASDAWG). ASDAWG(w) has |w| + 1 initial nodes, and the dag induced by all reachable nodes from the k-th initial node conforms with DAWG(w[k :]), where w[k :] denotes the k-th suffix of w. We prove that the size of the minimum ASDAWG(w) (MASDAWG(w)) is Θ(|w|) for |Σ| = 1,...

Suffix trees are among the most important data structures in stringology, with a number of applications in flourishing areas like bioinformatics. Their main problem is space usage, which has triggered much research striving for compressed representations that are still functional. A smaller suffix tree representation could fit in a faster memory, outweighing by far the theoretical slowdown brou...