Related papers: On Dynamic Range Reporting in One Dimension
The two most common data-structures for genome indexing, FM-indices and hash-tables, exhibit a fundamental trade-off between memory footprint and performance. We present Ranger, a new indexing technique for nucleotide sequences that is both…
We propose a general framework for reconstructing and denoising single entries of incomplete and noisy entries. We describe: effective algorithms for deciding if and entry can be reconstructed and, if so, for reconstructing and denoising…
Let ${\cal{D}}$ = $\{d_1, d_2, d_3, ..., d_D\}$ be a given set of $D$ (string) documents of total length $n$. The top-$k$ document retrieval problem is to index $\cal{D}$ such that when a pattern $P$ of length $p$, and a parameter $k$ come…
Many signal processing problems can be solved by maximizing the fitness of a segmented model over all possible partitions of the data interval. This letter describes a simple but powerful algorithm that searches the exponentially large…
In the orthogonal range reporting problem we must pre-process a set $P$ of multi-dimensional points, so that for any axis-parallel query rectangle $q$ all points from $q\cap P$ can be reported efficiently. In this paper we study the query…
Understanding how the brain responds to sensory inputs is challenging: brain recordings are partial, noisy, and high dimensional; they vary across sessions and subjects and they capture highly nonlinear dynamics. These challenges have led…
Many learning algorithms are formulated in terms of finding model parameters which minimize a data-fitting loss function plus a regularizer. When the regularizer involves the l0 pseudo-norm, the resulting regularization path consists of a…
Decision Tree (DT) Learning is a fundamental problem in Interpretable Machine Learning, yet it poses a formidable optimisation challenge. Practical algorithms have recently emerged, primarily leveraging Dynamic Programming and Branch &…
We present a dynamic programming algorithm for selecting a representative subset of size $k$ from a given set with $n$ points such that the Riesz $s$-energy is near minimized. While NP-hard in general dimensions, the one-dimensional case…
As one popular modeling approach for end-to-end speech recognition, attention-based encoder-decoder models are known to suffer the length bias and corresponding beam problem. Different approaches have been applied in simple beam search to…
We introduce novel dynamical low-rank methods for solving large-scale matrix differential equations, motivated by algorithms from randomized numerical linear algebra. In terms of performance (cost and accuracy), our methods overperform…
In this paper we study the fundamental problem of maintaining a dynamic collection of strings under the following operations: concat - concatenates two strings, split - splits a string into two at a given position, compare - finds the…
We present a general technique, based on parametric search with some twist, for solving a variety of optimization problems on a set of semi-algebraic geometric objects of constant complexity. The common feature of these problems is that…
In this paper we revisit the classical regular expression matching problem, namely, given a regular expression $R$ and a string $Q$, decide if $Q$ matches one of the strings specified by $R$. Let $m$ and $n$ be the length of $R$ and $Q$,…
In this paper, we describe a new type of match between a pattern and a text that aren't necessarily maximal in the query, but still contain useful matching information: locally maximal exact matches (LEMs). There are usually a large amount…
We consider the multivariate response regression problem with a regression coefficient matrix of low, unknown rank. In this setting, we analyze a new criterion for selecting the optimal reduced rank. This criterion differs notably from the…
Simultaneous Localization and Mapping (SLAM) is considered an ever-evolving problem due to its usage in many applications. Evaluation of SLAM is done typically using publicly available datasets which are increasing in number and the level…
We study the problem of clustering networks whose nodes have imputed or physical positions in a single dimension, for example prestige hierarchies or the similarity dimension of hyperbolic embeddings. Existing algorithms, such as the…
We propose a general framework for end-to-end learning of data structures. Our framework adapts to the underlying data distribution and provides fine-grained control over query and space complexity. Crucially, the data structure is learned…
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…