Related papers: A Limit Theorem for Radix Sort and Tries with Mark…
Tries are among the most versatile and widely used data structures on words. They are pertinent to the (internal) structure of (stored) words and several splitting procedures used in diverse contexts ranging from document taxonomy to IP…
A fundamental algorithm for selecting ranks from a finite subset of an ordered set is Radix Selection. This algorithm requires the data to be given as strings of symbols over an ordered alphabet, e.g., binary expansions of real numbers. Its…
Efficiently word storing and searching is an important task in computer science. An application space complexity, time complexity, and overall performance depend on this string data. Many word searching data structures and algorithms exist…
The trie-based radix sort algorithm stores pairwise different infinite binary strings in the leaves of a binary tree in a way that the Ulam-Harris coding of each leaf equals a prefix (that is, an initial segment) of the corresponding…
The complexity of the algorithm Radix Selection is considered for independent data generated from a Markov source. The complexity is measured by the number of bucket operations required and studied as a stochastic process indexed by the…
In many branches of engineering, Banach contraction mapping theorem is employed to establish the convergence of certain deterministic algorithms. Randomized versions of these algorithms have been developed that have proved useful in…
A radix sort tree arises when storing distinct infinite binary words in the leaves of a binary tree such that for any two words their common prefixes coincide with the common prefixes of the corresponding two leaves. If one deletes the…
Methods for proving functional limit laws are developed for sequences of stochastic processes which allow a recursive distributional decomposition either in time or space. Our approach is an extension of the so-called contraction method to…
Tries are popular data structures for storing a set of strings, where common prefixes are represented by common root-to-node paths. Over fifty years of usage have produced many variants and implementations to overcome some of their…
Sorting is one of the most used and well investigated algorithmic problem [1]. Traditional postulation supposes the sorting data archived, and the elementary operation as comparisons of two numbers. In a view of appearance of new processors…
We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast…
Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic…
We study the problem of learning the Markov order in categorical sequences that represent paths in a network, i.e. sequences of variable lengths where transitions between states are constrained to a known graph. Such data pose challenges…
This paper presents NgramMarkov, a variant of the Markov constraints. It is dedicated to text generation in constraint programming (CP). It involves a set of n-grams (i.e., sequence of n words) associated with probabilities given by a large…
A class of random recursive sequences (Y_n) with slowly varying variances as arising for parameters of random trees or recursive algorithms leads after normalizations to degenerate limit equations of the form X\stackrel{L}{=}X. For…
Grammar-based compression is a popular and powerful approach to compressing repetitive texts but until recently its relatively poor time-space trade-offs during real-life construction made it impractical for truly massive datasets such as…
Graded posets frequently arise throughout combinatorics, where it is natural to try to count the number of elements of a fixed rank. These counting problems are often $\#\textbf{P}$-complete, so we consider approximation algorithms for…
String complexity is defined as the cardinality of a set of all distinct words (factors) of a given string. For two strings, we introduce the joint string complexity as the cardinality of a set of words that are common to both strings.…
We revisit the classical problem of computing the \emph{contour tree} of a scalar field $f:\mathbb{M} \to \mathbb{R}$, where $\mathbb{M}$ is a triangulated simplicial mesh in $\mathbb{R}^d$. The contour tree is a fundamental topological…
Iterative algorithms are ubiquitous in the field of data mining. Widely known examples of such algorithms are the least mean square algorithm, backpropagation algorithm of neural networks. Our contribution in this paper is an improvement…