Related papers: Compressed Data Structures for Dynamic Sequences
We study the problem of evaluating a Monadic Second Order (MSO) query over strings under updates in the setting of direct access. We present an algorithm that, given an MSO query with first-order free variables represented by an unambiguous…
In this paper, we construct a data structure to efficiently compute the longest increasing subsequence of a sequence subject to dynamic updates. Our data structure supports a query for the longest increasing subsequence in $O(r+\log n)$…
The representation of a dynamic ordered set of $n$ integer keys drawn from a universe of size $m$ is a fundamental data structuring problem. Many solutions to this problem achieve optimal time but take polynomial space, therefore preserving…
We propose algorithms that, given the input string of length $n$ over integer alphabet of size $\sigma$, construct the Burrows-Wheeler transform (BWT), the permuted longest-common-prefix (PLCP) array, and the LZ77 parsing in…
We introduce a dynamic data structure for the compact representation of binary relations $\mathcal{R} \subseteq A \times B$. The data structure is a dynamic variant of the k$^2$-tree, a static compact representation that takes advantage of…
Two decades ago, a breakthrough in indexing string collections made it possible to represent them within their compressed space while at the same time offering indexed search functionalities. As this new technology permeated through…
A well-known fact in the field of lossless text compression is that high-order entropy is a weak model when the input contains long repetitions. Motivated by this, decades of research have generated myriads of so-called dictionary…
In a dynamic retrieval system, documents must be ingested as they arrive, and be immediately findable by queries. Our purpose in this paper is to describe an index structure and processing regime that accommodates that requirement for…
The all-pairs suffix-prefix (APSP) problem is a classical problem in string processing which has important applications in bioinformatics. Given a set $\mathcal{S} = \{S_1, \ldots, S_k\}$ of $k$ strings, the APSP problem asks one to compute…
The performance of a dynamic dictionary is measured mainly by its update time, lookup time, and space consumption. In terms of update time and lookup time there are known constructions that guarantee constant-time operations in the worst…
The rise of repetitive datasets has lately generated a lot of interest in compressed self-indexes based on dictionary compression, a rich and heterogeneous family that exploits text repetitions in different ways. For each such compression…
We present an algorithm that, given an index $t$, produces the $t$-th (lexicographically ordered) answer of an MSO query over a string. The algorithm requires linear-time preprocessing, and builds a data structure that answers each of these…
In grammar-based compression a string is represented by a context-free grammar, also called a straight-line program (SLP), that generates only that string. We refine a recent balancing result stating that one can transform an SLP of size…
Shannon's entropy is a definitive lower bound for statistical compression. Unfortunately, no such clear measure exists for the compressibility of repetitive strings. Thus, ad hoc measures are employed to estimate the repetitiveness of…
Let s be a string whose symbols are solely available through access(i), a read-only operation that probes s and returns the symbol at position i in s. Many compressed data structures for strings, trees, and graphs, require two kinds of…
Motivated by computing duplication patterns in sequences, a new fundamental problem called the longest subsequence-repeated subsequence (LSRS) is proposed. Given a sequence $S$ of length $n$, a letter-repeated subsequence is a subsequence…
We present a new algorithm for subsequence matching in grammar compressed strings. Given a grammar of size $n$ compressing a string of size $N$ and a pattern string of size $m$ over an alphabet of size $\sigma$, our algorithm uses…
Given strings $P$ and $Q$ the (exact) string matching problem is to find all positions of substrings in $Q$ matching $P$. The classical Knuth-Morris-Pratt algorithm [SIAM J. Comput., 1977] solves the string matching problem in linear time…
Most of the attention in statistical compression is given to the space used by the compressed sequence, a problem completely solved with optimal prefix codes. However, in many applications, the storage space used to represent the prefix…
In this paper, we design a new succinct static dictionary with worst-case constant query time. A dictionary data structure stores a set of key-value pairs with distinct keys in $[U]$ and values in $[\sigma]$, such that given a query $x\in…