Abstract. Colored range queries are a well-studied topic in computational geometry and database research that, in the past decade, have found exciting applications in information retrieval. In this paper we give improved time and space bounds for three important one-dimensional colored range queries — colored range listing, colored range top-k queries and colored range counting — and, thus, new bounds for various document retrieval problems on general collections of sequences. Specifically, we first describe a framework including almost all recent results on colored range listing and document listing, which suggests new combinations of data structures for these problems. For example, we give the fastest compressed data structures for colored range listing and document listing, and an efficient data structure for document listing whose size is bounded in terms of the high-order entropies of the library of documents. We then show how (approximate) colored top-k queries can be reduced to (approximate) range-mode queries on subsequences, yielding the first efficient data structure for this problem. Finally, we show how a modified wavelet tree can support colored range counting in logarithmic time and space that is succinct whenever the number of colors is superpolylogarithmic in the length of the sequence. 1

Self-indexes aim at representing text collections in a compressed format that allows extracting arbitrary portions and also offers indexed searching on the collection. Current self-indexes are unable of fully exploiting the redundancy of highly repetitive text collections that arise in several applications. Grammar-based compression is well suited to exploit such repetitiveness. We introduce the first grammar-based self-index. It builds on Straight-Line Programs (SLPs), a rather general kind of context-free grammars. If an SLP of n rules represents a text T [1, u], then an SLP-compressed representation of T requires 2n log 2 n bits. For that same SLP, our self-index takes O(n log n) + n log 2 u bits. It extracts any text substring of length m in time O((m + h) log n), and finds occ occurrences of a pattern string of length m in time O((m(m + h) + h occ) log n), where h is the height of the parse tree of the SLP. No previous grammar representation had achieved o(n) search time. As byproducts we introduce (i) a representation of SLPs that takes 2n log 2 n(1 + o(1)) bits and efficiently supports more operations than a plain array of rules; (ii) a representation for binary relations with labels supporting various extended queries; (iii) a generalization of our self-index to grammar

We introduce LZ-End, a new member of the Lempel-Ziv family of text compressors, which achieves compression ratios close to those of LZ77 but performs much faster at extracting arbitrary text substrings. We then build the first self-index based on LZ77 (or LZ-End) compression, which in addition to text extraction offers fast indexed searches on the compressed text. This self-index is particularly effective to represent highly repetitive sequence collections, which arise for example when storing versioned documents, software repositories, periodic publications, and biological sequence databases.

Abstract. We introduce the first grammar-compressed representation of a sequence that supports searches in time that depends only logarithmically on the size of the grammar. Given a text T [1..u] that is represented by a (context-free) grammar of n (terminal and nonterminal) symbols and size N (measured as the sum of the lengths of the right hands of the rules), a basic grammar-based representation of T takes N lg n bits of space. Our representation requires 2N lg n + N lg u + ɛ n lg n + o(N lg n) bits of space, for any 0 < ɛ ≤ 1. It can find the positions of the occ occurrences of a pattern of length m in T in O (m 2 /ɛ) lg lg u lg n + (m + occ) lg n time, and extract any substring of length ℓ of T in time O(ℓ + h lg(N/h)), where h is the height of the grammar tree.

Abstract. The need to index and search huge highly repetitive sequence collections is rapidly arising in various fields, including computational biology, software repositories, versioned collections, and others. In this short survey we briefly describe the progress made along three research lines to address the problem: compressed suffix arrays, grammar compressed indexes, and Lempel-Ziv compressed indexes. 1

Colored range queries are a well-studied topic in computational geometry and database research that, in the past decade, have found exciting applications in information retrieval. In this paper, we give improved time and space bounds for three important one-dimensional colored range queries — colored range listing, colored range top-k queries and colored range counting — and, as a consequence, new bounds for various document retrieval problems on general collections of sequences. Colored range listing is the problem of preprocessing a sequence S [1, n] of colors so that, later, given an interval [i, i + ℓ − 1], we list the different colors in S [i, i + ℓ − 1]. Colored range top-k queries ask instead for k most frequent colors in the interval. Colored range counting asks for the number of different colors in the interval. We first describe a framework including almost all recent results on colored range listing and document listing, which suggests new combinations of data structures for these problems. For example, we give the first compressed data structure (using nHk(S) + o(n log σ) bits, for any k = o(log σ n), where Hk(S) is the k-th order empirical entropy of S and σ the number of different colors in S) that answers colored range listing queries in constant time per returned result. We also give an efficient data structure for document listing whose size is bounded in terms of the k-th order entropy of the library of documents. We then show how (approximate) colored top-k