Related papers: Engineering Compact Data Structures for Rank and S…
Bit vectors with support for fast rank and select are a fundamental building block for compressed data structures. We close a gap between theory and practice by analyzing an important part of the design space and experimentally evaluating a…
Rank and select queries on bitmaps are essential building bricks of many compressed data structures, including text indexes, membership and range supporting spatial data structures, compressed graphs, and more. Theoretically considered yet…
Rank and select data structures seek to preprocess a bit vector to quickly answer two kinds of queries: rank(i) gives the number of 1 bits in slots 0 through i, and select(j) gives the first slot s with rank(s) = j. A succinct data…
One of the central problems in the design of compressed data structures is the efficient support for rank and select queries on bitvectors. These two operations form the backbone of more complex data structures (such as wavelet trees) used…
Succinct data structures use space close to the information-theoretic minimum while answering queries directly on the compressed representation. In this paper, we present a practical engineering study of rank and select queries on bit…
The rank problem in succinct data structures asks to preprocess an array A[1..n] of bits into a data structure using as close to n bits as possible, and answer queries of the form rank(k) = Sum_{i=1}^k A[i]. The problem has been intensely…
We consider succinct data structures for representing a set of $n$ horizontal line segments in the plane given in rank space to support \emph{segment access}, \emph{segment selection}, and \emph{segment rank} queries. A segment access query…
Given a text, rank and select queries return the number of occurrences of a character up to a position (rank) or the position of a character with a given rank (select). These queries have applications in, e.g., compression, computational…
Given an $n$-bit array $A$, the succinct rank data structure problem asks to construct a data structure using space $n+r$ bits for $r\ll n$, supporting rank queries of form $\mathtt{rank}(x)=\sum_{i=0}^{x-1} A[i]$. In this paper, we design…
The successor and predecessor problem consists of obtaining the closest value in a set of integers, greater/smaller than a given value. This problem has interesting applications, like the intersection of inverted lists. It can be easily…
Succinct data structures give space-efficient representations of large amounts of data without sacrificing performance. They rely one cleverly designed data representations and algorithms. We present here the formalization in Coq/SSReflect…
Rank and select are fundamental operations in succinct data structures, that is, data structures whose space consumption approaches the information-theoretic optimal. The performance of these primitives is central to the overall performance…
It has been shown in the indexing literature that there is an essential difference between prefix/range searches on the one hand, and predecessor/rank searches on the other hand, in that the former provably allows faster query resolution.…
Rank/Select dictionaries are data structures for an ordered set $S \subset \{0,1,...,n-1\}$ to compute $\rank(x,S)$ (the number of elements in $S$ which are no greater than $x$), and $\select(i,S)$ (the $i$-th smallest element in $S$),…
The problem of answering rank/select queries over a bitmap is of utmost importance for many succinct data structures. When the bitmap does not change, many solutions exist in the theoretical and practical side. In this work we consider the…
A rank-select index for a sequence $B=(b_1,\ldots,b_n)$ of $n$ bits is a data structure that, if provided with an operation to access $\Theta(\log n)$ arbitrary consecutive bits of $B$ in constant time (thus $B$ is stored outside of the…
Let $A$ be a static array storing $n$ elements from a totally ordered set. We present a data structure of optimal size at most $n\log_2(3+2\sqrt{2})+o(n)$ bits that allows us to answer the following queries on $A$ in constant time, without…
We perform experimental studies on data structures that answer path median, path counting, and path reporting queries in weighted trees. These query problems generalize the well-known range median query problem in arrays, as well as the…
Given a string of length $n$ that is composed of $r$ runs of letters from the alphabet $\{0,1,\ldots,\sigma{-}1\}$ such that $2 \le \sigma \le r$, we describe a data structure that, provided $r \le n / \log^{\omega(1)} n$, stores the string…
We consider the problem of supporting Rank() and Select() operations on a bit vector of length m with n 1 bits. The problem is considered in the succinct index model, where the bit vector is stored in "read-only" memory and an additional…