相关论文: Partial Data Compression and Text Indexing via Opt…
We consider the problem of recovering a function over the space of permutations (or, the symmetric group) over $n$ elements from given partial information; the partial information we consider is related to the group theoretic Fourier…
Lexicographically minimal string rotation is a fundamental problem in string processing that has recently garnered significant attention in quantum computing. Near-optimal quantum algorithms have been proposed for solving this problem,…
Recovering a low-rank tensor from incomplete information is a recurring problem in signal processing and machine learning. The most popular convex relaxation of this problem minimizes the sum of the nuclear norms of the unfoldings of the…
The Burrows-Wheeler Transform (BWT) is among the most influential discoveries in text compression and DNA storage. It is a reversible preprocessing step that rearranges an $n$-letter string into runs of identical characters (by exploiting…
This paper presents a general technique for optimally transforming any dynamic data structure that operates on atomic and indivisible keys by constant-time comparisons, into a data structure that handles unbounded-length keys whose…
The problem called "String reconstruction from substrings" is a mathematical model of sequencing by hybridization that plays an important role in DNA sequencing. In this problem, we are given a blackbox oracle holding an unknown string…
Given a string $T$ on an alphabet of size $\sigma$, we describe a bidirectional Burrows-Wheeler index that takes $O(|T|\log{\sigma})$ bits of space, and that supports the addition \emph{and removal} of one character, on the left or right…
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…
Given an unordered array of $N$ elements drawn from a totally ordered set and an integer $k$ in the range from $1$ to $N$, in the classic selection problem the task is to find the $k$-th smallest element in the array. We study the…
We consider the problem of maintaining a collection of strings while efficiently supporting splits and concatenations on them, as well as comparing two substrings, and computing the longest common prefix between two suffixes. This problem…
In the field of algorithmic analysis, one of the more well-known exercises is the subset sum problem. That is, given a set of integers, determine whether one or more integers in the set can sum to a target value. Aside from the brute-force…
Most of the attention in statistical compression is given to the space used by the compressed sequence, a problem completely solved with optimal prefix codes. However, in many applications, the storage space used to represent the prefix…
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…
We consider construction of the suffix tree and the directed acyclic word graph (DAWG) indexing data structures for a collection $\mathcal{T}$ of texts, where a new symbol may be appended to any text in $\mathcal{T} = \{T_1, \ldots, T_K\}$,…
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…
Indexing of very large collections of strings such as those produced by the widespread sequencing technologies, heavily relies on multi-string generalizations of the Burrows-Wheeler Transform (BWT), and for this problem various in-memory…
The longest common prefix array is a very advantageous data structure that, combined with the suffix array and the Burrows-Wheeler transform, allows to efficiently compute some combinatorial properties of a string useful in several…
We propose a B tree representation storing $n$ keys, each of $k$ bits, in either (a) $nk + O(nk / \lg n)$ bits or (b) $nk + O(nk \lg \lg n/ \lg n)$ bits of space supporting all B tree operations in either (a) $O(\lg n )$ time or (b) $O(\lg…
In today's data-centric world, fast and effective compression of data is paramount. To measure success towards the second goal, Kempa and Prezza [STOC2018] introduce the string attractor, a combinatorial object unifying dictionary-based…
This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its…