Related papers: Lower bounds for text indexing with mismatches and…
We introduce a new variant of the $k$-deck problem, which in its traditional formulation asks for determining the smallest $k$ that allows one to reconstruct any binary sequence of length $n$ from the multiset of its $k$-length…
The rise of repetitive datasets has lately generated a lot of interest in compressed self-indexes based on dictionary compression, a rich and heterogeneous family that exploits text repetitions in different ways. For each such compression…
The classic string indexing problem is to preprocess a string $S$ into a compact data structure that supports efficient subsequent pattern matching queries, that is, given a pattern string $P$, report all occurrences of $P$ within $S$. In…
When persons are mentioned in texts with their first name, last name and/or middle names, there can be a high variation which of their names are used, how their names are ordered and if their names are abbreviated. If multiple persons are…
Many tasks in natural language processing, ranging from machine translation to question answering, can be reduced to the problem of matching two sentences or more generally two short texts. We propose a new approach to the problem, called…
In the standard trace reconstruction problem, the goal is to \emph{exactly} reconstruct an unknown source string $\mathsf{x} \in \{0,1\}^n$ from independent "traces", which are copies of $\mathsf{x}$ that have been corrupted by a…
We study the fundamental question of how efficiently suffix array entries can be accessed when the array cannot be stored explicitly. The suffix array $SA_T[1..n]$ of a text $T$ of length $n$ encodes the lexicographic order of its suffixes…
Motivated by an application where we try to make proofs for Description Logic inferences smaller by rewriting, we consider the following decision problem, which we call the small term reachability problem: given a term rewriting system $R$,…
In this work, we study the relative hardness of fundamental problems with state-of-the-art word RAM algorithms that take $O(n\sqrt{\log n})$ time for instances described in $\Theta(n)$ machine words ($\Theta(n\log n)$ bits). This complexity…
The Element Distinctness problem is to decide whether each character of an input string is unique. The quantum query complexity of Element Distinctness is known to be $\Theta(N^{2/3})$; the polynomial method gives a tight lower bound for…
String matching is the problem of deciding whether a given $n$-bit string contains a given $k$-bit pattern. We study the complexity of this problem in three settings. Communication complexity. For small $k$, we provide near-optimal upper…
Motivated by the imminent growth of massive, highly redundant genomic databases, we study the problem of compressing a string database while simultaneously supporting fast random access, substring extraction and pattern matching to the…
This paper introduces the notion of distributed verification without preprocessing. It focuses on the Minimum-weight Spanning Tree (MST) verification problem and establishes tight upper and lower bounds for the time and message complexities…
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,…
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…
Text embeddings from large language models (LLMs) have achieved excellent results in tasks such as information retrieval, semantic textual similarity, etc. In this work, we show an interesting finding: when feeding a text into the LLM-based…
We revisit the longest common extension (LCE) problem, that is, preprocess a string $T$ into a compact data structure that supports fast LCE queries. An LCE query takes a pair $(i,j)$ of indices in $T$ and returns the length of the longest…
We show quantum lower bounds for two problems. First, we consider the problem of determining if a sequence of parentheses is a properly balanced one (a Dyck word), with a depth of at most $k$. It has been known that, for any $k$,…
We give a simplified and improved lower bound for the simplex range reporting problem. We show that given a set $P$ of $n$ points in $\mathbb{R}^d$, any data structure that uses $S(n)$ space to answer such queries must have…
Many machine learning approaches are characterized by information constraints on how they interact with the training data. These include memory and sequential access constraints (e.g. fast first-order methods to solve stochastic…