Related papers: Faster Linear-Space Data Structures for Path Frequ…
In the static retrieval problem, a data structure must answer retrieval queries mapping a set of $n$ keys in a universe $[U]$ to $v$-bit values. Information-theoretically, retrieval data structures can use as little as $nv$ bits of space.…
In this paper, we present a new data structure called the packed compact trie (packed c-trie) which stores a set $S$ of $k$ strings of total length $n$ in $n \log\sigma + O(k \log n)$ bits of space and supports fast pattern matching queries…
We present a data structure that supports three-dimensional range reporting queries in $O(\log \log U + (\log \log n)^3+k)$ time and uses $O(n\log^{1+\eps} n)$ space, where $U$ is the size of the universe, $k$ is the number of points in the…
We study the following problem: preprocess a set O of objects into a data structure that allows us to efficiently report all pairs of objects from O that intersect inside an axis-aligned query range Q. We present data structures of size…
In this paper we describe a new efficient (in fact optimal) data structure for the {\em top-$K$ color problem}. Each element of an array $A$ is assigned a color $c$ with priority $p(c)$. For a query range $[a,b]$ and a value $K$, we have to…
Navarro and Sadakane [TALG 2014] gave a dynamic succinct data structure for storing an ordinal tree. The structure supports tree queries in either $O(\log n/\log\log n)$ or $O(\log n)$ time, and insertion or deletion of a single node in…
We consider a static data structure problem of computing a linear operator under cell-probe model. Given a linear operator $M \in \mathbb{F}_2^{m \times n}$, the goal is to pre-process a vector $X \in \mathbb{F}_2^n$ into a data structure…
We consider the following problem: Preprocess a set $\mathcal{S}$ of $n$ axis-parallel boxes in $\mathbb{R}^d$ so that given a query of an axis-parallel box in $\mathbb{R}^d$, the pairs of boxes of $\mathcal{S}$ whose intersection…
Let ${\cal{D}}$ = $\{d_1, d_2, d_3, ..., d_D\}$ be a given set of $D$ (string) documents of total length $n$. The top-$k$ document retrieval problem is to index $\cal{D}$ such that when a pattern $P$ of length $p$, and a parameter $k$ come…
Burrows-Wheeler transform (BWT) is an invertible text transformation that, given a text $T$ of length $n$, permutes its symbols according to the lexicographic order of suffixes of $T$. BWT is one of the most heavily studied algorithms in…
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…
In this paper, we explore worst-case solutions for the problems of single and multiple matching on strings in the word RAM model with word length w. In the first problem, we have to build a data structure based on a pattern p of length m…
A (1 + eps)-approximate distance oracle for a graph is a data structure that supports approximate point-to-point shortest-path-distance queries. The most relevant measures for a distance-oracle construction are: space, query time, and…
In this paper we present a new algorithm for solving linear programs that requires only $\tilde{O}(\sqrt{rank(A)}L)$ iterations to solve a linear program with $m$ constraints, $n$ variables, and constraint matrix $A$, and bit complexity…
The task of finding an entry in an unsorted list of $N$ elements famously takes $O(N)$ queries to an oracle for a classical computer and $O(\sqrt{N})$ queries for a quantum computer using Grover's algorithm. Reformulated as a spatial search…
We present a new universal source code for distributions of unlabeled binary and ordinal trees that achieves optimal compression to within lower order terms for all tree sources covered by existing universal codes. At the same time, it…
We introduce a compressed suffix array representation that, on a text $T$ of length $n$ over an alphabet of size $\sigma$, can be built in $O(n)$ deterministic time, within $O(n\log\sigma)$ bits of working space, and counts the number of…
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…
Let $\D = $$ \{d_1,d_2,...d_D\}$ be a given set of $D$ string documents of total length $n$, our task is to index $\D$, such that the $k$ most relevant documents for an online query pattern $P$ of length $p$ can be retrieved efficiently. We…
Let $H$ be a fixed graph and let $G$ be an $H$-minor free $n$-vertex graph with integer edge weights and no negative weight cycles reachable from a given vertex $s$. We present an algorithm that computes a shortest path tree in $G$ rooted…