Related papers: On Compressing Permutations and Adaptive Sorting

The problem of storing a set of strings --- a string dictionary --- in compact form appears naturally in many cases. While classically it has represented a small part of the whole data to be processed (e.g., for Natural Language processing…

Adaptive filters exploiting sparsity have been a very active research field, among which the algorithms that follow the "proportional-update principle", the so-called proportionate-type algorithms, are very popular. Indeed, there are…

The simple permutations in two permutation classes --- the 321-avoiding permutations and the skew-merged permutations --- are enumerated using a uniform method. In both cases, these enumerations were known implicitly, by working backwards…

For text retrieval systems, the assumption that all data structures reside in main memory is increasingly common. In this context, we present a novel incremental inverted indexing algorithm for web-scale collections that directly constructs…

Data compression techniques are characterized by four key performance indices which are (i) associated accuracy, (ii) compression ratio, (iii) computational work, and (iv) degree of freedom. The method of data compression developed in this…

We present an easily defined countable family of permutations of the natural numbers for which explicit rearrangements (i.e., the sums induced by the permutations) can be computed. The digamma function proves to be the key tool for the…

In prefix coding over an infinite alphabet, methods that consider specific distributions generally consider those that decline more quickly than a power law (e.g., Golomb coding). Particular power-law distributions, however, model many…

This work describes the principled design of a theoretical framework leading to fast and accurate algorithmic information measures on finite multisets of finite strings by means of compression. One distinctive feature of our approach is to…

The goal of this thesis is to study the compression problems arising in distributed computing systematically. In the first part of the thesis, we study gradient compression for distributed first-order optimization. We begin by establishing…

Sorting and searching are large parts of database query processing, e.g., in the forms of index creation, index maintenance, and index lookup; and comparing pairs of keys is a substantial part of the effort in sorting and searching. We have…

We consider the effect on the mixing properties of a piecewise smooth interval map $f$ when its domain is divided into $N$ equal subintervals and $f$ is composed with a permutation of these. The case of the stretch-and-fold map $f(x)=mx…

The problem of answering rank/select queries over a bitmap is of utmost importance for many succinct data structures. When the bitmap does not change, many solutions exist in the theoretical and practical side. In this work we consider the…

This paper studies the subspace clustering problem in which data points collected from high-dimensional ambient space lie in a union of linear subspaces. Subspace clustering becomes challenging when the dimension of intersection between…

Dimension reduction is widely regarded as an effective way for decreasing the computation, storage and communication loads of data-driven intelligent systems, leading to a growing demand for statistical methods that allow analysis (e.g.,…

We consider sorting procedures for permutations making use of pop stacks with a bypass operation, and explore the combinatorial properties of the associated algorithms.

Graph-based representations underlie a wide range of scientific problems. Graph connectivity is typically represented as a sparse matrix in the Compressed Sparse Row format. Large-scale graphs rely on distributed storage, allocating…

Spaced seeds are important tools for similarity search in bioinformatics, and using several seeds together often significantly improves their performance. With existing approaches, however, for each seed we keep a separate linear-size data…

Real-world data typically contain repeated and periodic patterns. This suggests that they can be effectively represented and compressed using only a few coefficients of an appropriate basis (e.g., Fourier, Wavelets, etc.). However, distance…

Scientific computations or measurements may result in huge volumes of data. Often these can be thought of representing a real-valued function on a high-dimensional domain, and can be conceptually arranged in the format of a tensor of high…

The paper describes a general glance to the use of element exchange techniques for optimization over permutations. A multi-level description of problems is proposed which is a fundamental to understand nature and complexity of optimization…