Related papers: Faster range minimum queries
Range Minimum Query (RMQ) is an important building brick of many compressed data structures and string matching algorithms. Although this problem is essentially solved in theory, with sophisticated data structures allowing for constant time…
Given an array $a[1..n]$, the Range Minimum Query (RMQ) problem is to maintain a data structure that supports RMQ queries: given a range $[l, r]$, find the index of the minimum element among $a[l..r]$, i.e., $\operatorname{argmin}_{i \in…
The range-minimum query (RMQ) problem is a fundamental data structuring task with numerous applications. Despite the fact that succinct solutions with worst-case optimal $2n+o(n)$ bits of space and constant query time are known, it has been…
In the Range Minimum Query (RMQ) problem, we are given an array $A$ of $n$ numbers and we are asked to answer queries of the following type: for indices $i$ and $j$ between $0$ and $n-1$, query $\text{RMQ}_A(i,j)$ returns the index of a…
Range minimum queries (RMQs) are fundamental operations with widespread applications in database management, text indexing and computational biology. While many space-efficient data structures have been designed for RMQs on arrays with…
Given an integer array $A[1..n]$, the Range Minimum Query problem (RMQ) asks to preprocess $A$ into a data structure, supporting RMQ queries: given $a,b\in [1,n]$, return the index $i\in[a,b]$ that minimizes $A[i]$, i.e.,…
Given a string $S$ of $n$ integers in $[0,\sigma)$, a range minimum query RMQ$(i, j)$ asks for the index of the smallest integer in $S[i \dots j]$. It is well known that the problem can be solved with a succinct data structure of size $2n +…
Given an array of distinct integers $A[1\ldots n]$, the Range Minimum Query (RMQ) problem requires us to construct a data structure from $A$, supporting the RMQ query: given an interval $[a,b]\subseteq[1,n]$, return the index of the minimum…
A retrieval data structure for a static function $f:S\rightarrow \{0,1\}^r$ supports queries that return $f(x)$ for any $x \in S$. Retrieval data structures can be used to implement a static approximate membership query data structure…
We consider the problem of encoding range minimum queries (RMQs): given an array A[1..n] of distinct totally ordered values, to pre-process A and create a data structure that can answer the query RMQ(i,j), which returns the index containing…
Range minimum queries are frequently used in string processing and database applications including biological sequence analysis, document retrieval, and web search. Hence, various data structures have been proposed for improving their…
We revisit the range minimum query problem and present a new O(n)-space data structure that supports queries in O(1) time. Although previous data structures exist whose asymptotic bounds match ours, our goal is to introduce a new solution…
We consider the problem of computing a sequence of range minimum queries. We assume a sequence of commands that contains values and queries. Our goal is to quickly determine the minimum value that exists between the current position and a…
During the last decade GPU technology has shifted from pure general purpose computation to the inclusion of application specific integrated circuits (ASICs), such as Tensor Cores and Ray Tracing (RT) cores. Although these special purpose…
Priority queues are abstract data structures which store a set of key/value pairs and allow efficient access to the item with the minimal (maximal) key. Such queues are an important element in various areas of computer science such as…
A retrieval data structure stores a static function f : S -> {0,1}^r . For all x in S, it returns the r-bit value f(x), while for other inputs it may return an arbitrary result. The structure cannot answer membership queries, so it does not…
LSM-tree based key-value (KV) stores organize data in a multi-level structure for high-speed writes. Range queries on traditional LSM-trees must seek and sort-merge data from multiple table files on the fly, which is expensive and often…
Quantum computing is a popular topic in computer science, which has recently attracted many studies in various areas such as machine learning and network. However, the topic of quantum data structures seems neglected. There is an open…
We present bundled references, a new building block to provide linearizable range query operations for highly concurrent linked data structures. Bundled references allow range queries to traverse a path through the data structure that is…
We initiate a study of a query-driven approach to designing partition trees for range-searching problems. Our model assumes that a data structure is to be built for an unknown query distribution that we can access through a sampling oracle,…