Related papers: Random Access in Grammar-Compressed Strings: Optim…
Detecting all the strings that occur in a text more frequently or less frequently than expected according to an IID or a Markov model is a basic problem in string mining, yet current algorithms are based on data structures that are either…
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,…
We show that if DTIME[2^{O(n)}] is not included in DSPACE[2^{o(n)}], then, for every set B in PSPACE, all strings x in B of length n can be represented by a string compressed(x) of length at most log (|B^{=n}|) + O(log n), such that a…
Given an array of size $n$ from a total order, we consider the problem of constructing a data structure that supports various queries (range minimum/maximum queries with their variants and next/previous larger/smaller queries) efficiently.…
A compressed self-index stores a string in compressed form while supporting locate queries without decompression. For highly repetitive strings (arising in web crawls, versioned documents, and genomic collections), static self-indexes can…
We consider the problem of querying a string (or, a database) of length $N$ bits to determine all the locations where a substring (query) of length $M$ appears either exactly or is within a Hamming distance of $K$ from the query. We assume…
A well-known fact in the field of lossless text compression is that high-order entropy is a weak model when the input contains long repetitions. Motivated by this, decades of research have generated myriads of so-called dictionary…
The classic exact pattern matching problem, given two strings -- a pattern $P$ of length $m$ and a text $T$ of length $n$ -- asks whether $P$ occurs as a substring of $T$. A property tester for the problem needs to distinguish (with high…
For nearly six decades, the central open question in the study of hash tables has been to determine the optimal achievable tradeoff curve between time and space. State-of-the-art hash tables offer the following guarantee: If keys/values are…
We derive new time-space tradeoff lower bounds and algorithms for exactly computing statistics of input data, including frequency moments, element distinctness, and order statistics, that are simple to calculate for sorted data. We develop…
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 $T$,…
Indexing highly repetitive texts - such as genomic databases, software repositories and versioned text collections - has become an important problem since the turn of the millennium. A relevant compressibility measure for repetitive texts…
A weighted string over an alphabet of size $\sigma$ is a string in which a set of letters may occur at each position with respective occurrence probabilities. Weighted strings, also known as position weight matrices or uncertain sequences,…
We study variable time search, a form of quantum search where queries to different items take different time. Our first result is a new quantum algorithm that performs variable time search with complexity $O(\sqrt{T}\log n)$ where…
Following (Kolpakov et al., 2013; Gawrychowski and Manea, 2015), we continue the study of {\em $\alpha$-gapped repeats} in strings, defined as factors $uvu$ with $|uv|\leq \alpha |u|$. Our main result is the $O(\alpha n)$ bound on the…
We are given a read-only memory for input and a write-only stream for output. For a positive integer parameter s, an s-workspace algorithm is an algorithm using only $O(s)$ words of workspace in addition to the memory for input. In this…
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,…
We study the problem of reaching agreement in a synchronous distributed system by $n$ autonomous parties, when the communication links from/to faulty parties can omit messages. The faulty parties are selected and controlled by an adaptive,…
We give an $\mathcal{O}(n \log n)$-time, $\mathcal{O}(n)$-space algorithm for factoring a string into the minimum number of palindromic substrings. That is, given a string $S [1..n]$, in $\mathcal{O}(n \log n)$ time our algorithm returns…
We present an efficient algorithm for finding all approximate occurrences of a given pattern $p$ of length $m$ in a text $t$ of length $n$ allowing for translocations of equal length adjacent factors and inversions of factors. The algorithm…