Related papers: Data Structure Lower Bounds on Random Access to Gr…
We devise a data structure that can answer shortest path queries for two query points in a polygonal domain $P$ on $n$ vertices. For any $\varepsilon > 0$, the space complexity of the data structure is $O(n^{10+\varepsilon })$ and queries…
This paper develops a new technique for proving amortized, randomized cell-probe lower bounds on dynamic data structure problems. We introduce a new randomized nondeterministic four-party communication model that enables "accelerated",…
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 spot a hole in the area of succinct data structures for graph classes from a universe of size at most $n^n$. Very often, the input graph is labeled by the user in an arbitrary and easy-to-use way, and the data structure for the graph…
We describe a data structure that stores a string $S$ in space similar to that of its Lempel-Ziv encoding and efficiently supports access, rank and select queries. These queries are fundamental for implementing succinct and compressed data…
We revisit classic string problems considered in the area of parameterized complexity, and study them through the lens of dynamic data structures. That is, instead of asking for a static algorithm that solves the given instance efficiently,…
Let $\mathcal{D}$ be a collection of $D$ documents, which are strings over an alphabet of size $\sigma$, of total length $n$. We describe a data structure that uses linear space and and reports $k$ most relevant documents that contain a…
Random access to highly compressed strings -- represented by straight-line programs or Lempel-Ziv parses, for example -- is a well-studied topic. Random access to such strings in strongly sublogarithmic time is impossible in the worst case,…
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.…
We show that, given a string $s$ of length $n$, with constant memory and logarithmic passes over a constant number of streams we can build a context-free grammar that generates $s$ and only $s$ and whose size is within an $\Oh{\min (g \log…
A palindromic substring $T[i.. j]$ of a string $T$ is said to be a shortest unique palindromic substring (SUPS) in $T$ for an interval $[p, q]$ if $T[i.. j]$ is a shortest palindromic substring such that $T[i.. j]$ occurs only once in $T$,…
In the range $\alpha$-majority query problem, we are given a sequence $S[1..n]$ and a fixed threshold $\alpha \in (0, 1)$, and are asked to preprocess $S$ such that, given a query range $[i..j]$, we can efficiently report the symbols that…
We consider a range of simply stated dynamic data structure problems on strings. An update changes one symbol in the input and a query asks us to compute some function of the pattern of length $m$ and a substring of a longer text. We give…
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…
Given a string $T$ of length $n$ over an alphabet $\Sigma\subset \{1,2,\ldots,n^{O(1)}\}$ of size $\sigma$, we are to preprocess $T$ so that given a range $[i,j]$, we can return a representation of a shortest string over $\Sigma$ that is…
To store and search genomic databases efficiently, researchers have recently started building compressed self-indexes based on grammars. In this paper we show how, given a straight-line program with $r$ rules for a string (S [1..n]) whose…
Under the word RAM model, we design three data structures that can be constructed in $O(n\sqrt{\lg n})$ time over $n$ points in an $n \times n$ grid. The first data structure is an $O(n\lg^{\epsilon} n)$-word structure supporting orthogonal…
Given a set $S$ of $n$ (distinct) keys from key space $[U]$, each associated with a value from $\Sigma$, the \emph{static dictionary} problem asks to preprocess these (key, value) pairs into a data structure, supporting value-retrieval…
In this paper we present a really simple linear-time algorithm constructing a context-free grammar of size O(g log (N/g)) for the input string, where N is the size of the input string and g the size of the optimal grammar generating this…
In this paper we present new data structures for two extensively studied variants of the orthogonal range searching problem. First, we describe a data structure that supports two-dimensional orthogonal range minima queries in $O(n)$ space…