Related papers: Constructing LZ78 Tries and Position Heaps in Line…
We present first algorithmic ideas for a practical and lightweight adaption of the DCX suffix array construction algorithm [Sanders et al., 2003] to the distributed-memory setting. Our approach relies on a bucketing technique which enables…
In this paper, we present a toolbox for a specific optimization problem that frequently arises in bioinformatics or genomics. In this specific optimisation problem, the state space is a set of words of specified length over a finite…
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…
Let $P = \{p(i)\}$ be a measure of strictly positive probabilities on the set of nonnegative integers. Although the countable number of inputs prevents usage of the Huffman algorithm, there are nontrivial $P$ for which known methods find a…
Lempel-Ziv-Double (LZD) is a variation of the LZ78 compression scheme that achieves better compression on repetitive datasets. Nevertheless, prior research has identified computational inefficiencies and a weakness in its compressibility…
We consider the problem of learning low-rank tensors from partial observations with structural constraints, and propose a novel factorization of such tensors, which leads to a simpler optimization problem. The resulting problem is an…
An instance of the NP-hard Quadratic Shortest Path Problem (QSPP) is called linearizable iff it is equivalent to an instance of the classic Shortest Path Problem (SPP) on the same input digraph. The linearization problem for the QSPP…
Grammar compression is, next to Lempel-Ziv (LZ77) and run-length Burrows-Wheeler transform (RLBWT), one of the most flexible approaches to representing and processing highly compressible strings. The main idea is to represent a text as a…
The advent of massive datasets (and the consequent design of high-performing distributed storage systems) have reignited the interest of the scientific and engineering community towards the design of lossless data compressors which achieve…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
Algorithms which compute the coarsest simulation preorder are generally designed on Kripke structures. Only in a second time they are extended to labelled transition systems. By doing this, the size of the alphabet appears in general as a…
Linear-probing hash tables have been classically believed to support insertions in time $\Theta(x^2)$, where $1 - 1/x$ is the load factor of the hash table. Recent work by Bender, Kuszmaul, and Kuszmaul (FOCS'21), however, has added a new…
Unlike the matrix case, computing low-rank approximations of tensors is NP-hard and numerically ill-posed in general. Even the best rank-1 approximation of a tensor is NP-hard. In this paper, we use convex optimization to develop…
The notion of the cover is a generalization of a period of a string, and there are linear time algorithms for finding the shortest cover. The seed is a more complicated generalization of periodicity, it is a cover of a superstring of a…
Compressed indexing enables powerful queries over massive and repetitive textual datasets using space proportional to the compressed input. While theoretical advances have led to highly efficient index structures, their practical…
We show how to obtain a fast component-by-component construction algorithm for higher order polynomial lattice rules. Such rules are useful for multivariate quadrature of high-dimensional smooth functions over the unit cube as they achieve…
Indexing very large collections of strings, such as those produced by the widespread next generation sequencing technologies, heavily relies on multistring generalization of the Burrows-Wheeler Transform (BWT): large requirements of…
In this paper we consider the problem of computing the longest common abelian factor (LCAF) between two given strings. We present a simple $O(\sigma~ n^2)$ time algorithm, where $n$ is the length of the strings and $\sigma$ is the alphabet…
Lenstra's integer factorization algorithm is asymptotically one of the fastest known algorithms, and is ideally suited for parallel computation. We suggest a way in which the algorithm can be speeded up by the addition of a second phase.…
The Cartesian-tree pattern matching is a recently introduced scheme of pattern matching that detects fragments in a sequential data stream which have a similar structure as a query pattern. Formally, Cartesian-tree pattern matching seeks…