Related papers: Bit catastrophes for the Burrows-Wheeler Transform
We first review how we can store a run-length compressed suffix array (RLCSA) for a text $T$ of length $n$ over an alphabet of size $\sigma$ whose Burrows-Wheeler Transform (BWT) consists of $r$ runs in $O \left( \rule{0ex}{2ex} r \log (n /…
The move structure represents permutations with long contiguously permuted intervals in compressed space with optimal query time. They have become an important feature of compressed text indexes using space proportional to the number of…
We characterize those strings whose suffix arrays are based on arithmetic progressions, in particular, arithmetically progressed permutations where all pairs of successive entries of the permutation have the same difference modulo the…
In highly repetitive strings, like collections of genomes from the same species, distinct measures of repetition all grow sublinearly in the length of the text, and indexes targeted to such strings typically depend only on one of these…
The string repetitiveness measures $\chi$ (the size of a smallest suffixient set of a string) and $r$ (the number of runs in the Burrows--Wheeler Transform) are related. Recently, we have shown that the bound $\chi \leq 2r$, proved by…
The notion of string attractor has been introduced in [Kempa and Prezza, 2018] in the context of Data Compression and it represents a set of positions of a finite word in which all of its factors can be "attracted". The smallest size…
A substring $u$ of a string $T$ is called a minimal unique substring (MUS) of $T$ if $u$ occurs exactly once in $T$ and any proper substring of $u$ occurs at least twice in $T$. A string $w$ is called a minimal absent word (MAW) of $T$ if…
The run-length compressed Burrows-Wheeler transform (RLBWT) used in conjunction with the backward search introduced in the FM index is the centerpiece of most compressed indexes working on highly-repetitive data sets like biological…
Cartesian tree matching is a form of generalized pattern matching where a substring of the text matches with the pattern if they share the same Cartesian tree. This form of matching finds application for time series of stock prices and can…
We show how to merge two run-length compressed Burrows-Wheeler Transforms (RLBWTs) into a run-length compressed extended Burrows-Wheeler Transform (eBWT) in $O (r)$ space and $O ((r + L) \log (m + n))$ time, where $m$ and $n$ are the…
Nishimoto and Tabei [CPM, 2021] proposed r-enum, an algorithm to enumerate various characteristic substrings, including maximal repeats, in a string $T$ of length $n$ in $O(r)$ words of compressed working space, where $r \le n$ is the…
Knowing which strings in a massive text are significant -- that is, which strings are common and distinct from other strings -- is valuable for several applications, including text compression and tokenization. Frequency in itself is not…
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…
When building Burrows-Wheeler Transforms (BWTs) of truly huge datasets, prefix-free parsing (PFP) can use an unreasonable amount of memory. In this paper we show how if a dataset can be broken down into small datasets that are not very…
An absent factor of a string $w$ is a string $u$ which does not occur as a contiguous substring (a.k.a. factor) inside $w$. We extend this well-studied notion and define absent subsequences: a string $u$ is an absent subsequence of a string…
A string $w$ is called a minimal absent word (MAW) for another string $T$ if $w$ does not occur (as a substring) in $T$ and any proper substring of $w$ occurs in $T$. State-of-the-art data structures for reporting the set $\mathsf{MAW}(T)$…
We prove conjecturally sharp upper bounds for the Dirichlet character moments $\frac{1}{r-1} \sum_{\chi \; \text{mod} \; r} |\sum_{n \leq x} \chi(n)|^{2q}$, where $r$ is a large prime, $1 \leq x \leq r$, and $0 \leq q \leq 1$ is real. In…
Motivation: Burrows-Wheeler Transform (BWT) is a common component in full-text indices. Initially developed for data compression, it is particularly powerful for encoding redundant sequences such as pangenome data. However, BWT construction…
Compact directed acyclic word graphs (CDAWGs) [Blumer et al. 1987] are a fundamental data structure on strings with applications in text pattern searching, data compression, and pattern discovery. Intuitively, the CDAWG of a string $T$ is…
Despite massive investments in scale, deep models for click-through rate (CTR) prediction often exhibit rapidly diminishing returns - a stark contrast to the smooth, predictable gains seen in large language models. We identify the root…