Dynamic Relative Compression, Dynamic Partial Sums, and Substring Concatenation

Abstract

Given a static reference string R and a source string S, a relative compression of S with respect to R is an encoding of S as a sequence of references to substrings of R. Relative compression schemes are a classic model of compression and have recently proved very successful for compressing highly-repetitive massive data sets such as genomes and web-data. We initiate the study of relative compression in a dynamic setting where the compressed source string S is subject to edit operations. The goal is to maintain the compressed representation compactly, while supporting edits and allowing efficient random access to the (uncompressed) source string. We present new data structures that achieve optimal time for updates and queries while using space linear in the size of the optimal relative compression, for nearly all combinations of parameters. We also present solutions for restricted and extended sets of updates. To achieve these results, we revisit the dynamic partial sums problem and the substring concatenation problem. We present new optimal or near optimal bounds for these problems. Plugging in our new results we also immediately obtain new bounds for the string indexing for patterns with wildcards problem and the dynamic text and static pattern matching problem.

Practical trade‐offs for the prefix‐sum problem

“…Finally, several extensions to the problem exist, such as the so‐called searchable prefix‐sum problem , 5,6 where we are also asked to support the operation search( x ) which returns the smallest i such that sum( i ) ≥ x ; and the dynamic prefix‐sum problem with insertions/deletions of elements in/from A allowed 9 …”

“…It is an icon problem in data structure design and has been studied rather extensively from a theoretical point of view 1‐10 given its applicability to many areas of computing, such as coding, databases, parallel programming, dynamic data structures, and others 11 . For example, one of the most notable practical applications of this problem is for online analytical processing (OLAP) in databases.…”

Minimização do Consumo de Energia de Dispositivos Sem Fio em Ambientes Industriais

“…Finalmente, a sequênciaé enviada pela interface IEEE 802.11 / WiFi do dispositivo IIoT. É válido ressaltar que as técnicas mais modernas de compressão tornam-se inviáveis para cenários de IIoT e serem implementadas no HW usado, onde podemos destacar Partial Matching [Bille et al 2018], Golomb [Leon-Salas 2015 e Shannon-Fano [Mantoro et al 2017]. Estas técnicas são baseadas em análise probabilística e predição, as quais necessitam de uma maior capacidade computacional (memória e CPU) para calcular a ocorrência dos caracteres e gerar um resultadoótimo, elevando muito a complexidade e tempo de processamento (consequentemente consumo de energia).…”

Random Access in Persistent Strings and Segment Selection

“…The random access problem is to preprocess a data set into a compressed representation that supports fast retrieval of any part of the data without decompressing the entire data set. The random access problem is a well-studied problem for many types of data and compression schemes [1,3,5,8,9,19,31,35,41,48,53] and random access queries is a basic primitive in several algorithms and data structures on compressed data, see e.g., [7,9,23,24,25] In this paper, we consider the random access problem on collections of strings where each string is the result of an edit operation, i.e., inserting, delete, or replace a single character, from another string in the collection. Specifically, our collection is given by a rooted tree, called a version tree, where edges are labeled by an edit operation and a node represents the string obtained by applying the sequence of edit operation on the path from the root to the node (see Figure 1(a)).…”