Related papers: SPIDER: Improved Succinct Rank and Select Performa…
Bit vectors are fundamental building blocks of many succinct data structures. They can be used to represent graphs, are an important part of many text indices in the form of the wavelet tree, and can be used to encode ordered sequences of…
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…
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…
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…
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…
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 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…
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…
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…
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.…
The tremendous expanse of search engines, dictionary and thesaurus storage, and other text mining applications, combined with the popularity of readily available scanning devices and optical character recognition tools, has necessitated…
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…
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…
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…
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…
In this paper, a new and novel data structure is proposed to dynamically insert and delete segments. Unlike the standard segment trees[3], the proposed data structure permits insertion of a segment with interval range beyond the interval…
Augmented B-trees (aB-trees) are a broad class of data structures. The seminal work "succincter" by Patrascu showed that any aB-tree can be stored using only two bits of redundancy, while supporting queries to the tree in time proportional…
Recent research has focused on accelerating stencil computations by exploiting emerging hardware like Tensor Cores. To leverage these accelerators, the stencil operation must be transformed to matrix multiplications. However, this…
BERT based ranking models have achieved superior performance on various information retrieval tasks. However, the large number of parameters and complex self-attention operation come at a significant latency overhead. To remedy this, recent…