Related papers: LZ-End Parsing in Compressed Space

One of the most fundamental method for comparing two given strings $A$ and $B$ is the longest common subsequence (LCS), where the task is to find (the length) of an LCS of $A$ and $B$. In this paper, we deal with the STR-IC-LCS problem…

Suppose we want to seek the longest common subsequences (LCSs) of two strings as informative patterns that explain the relationship between the strings. The dynamic programming algorithm gives us a table from which all LCSs can be extracted…

At the present scenario of the internet, there exist many optimization techniques to improve the Web speed but almost expensive in terms of bandwidth. So after a long investigation on different techniques to compress the data without any…

In this paper, we show that the LZ77 factorization of a text T {\in\Sigma^n} can be computed in O(R log n) bits of working space and O(n log R) time, R being the number of runs in the Burrows-Wheeler transform of T reversed. For extremely…

An initializable array is an array that supports the read and write operations for any element and the initialization of the entire array. This paper proposes a simple in-place algorithm to implement an initializable array of length $N$…

Let $T [1..n]$ be a text over an alphabet of size $\sigma \in \mathrm{polylog} (n)$, let $r^*$ be the sum of the numbers of runs in the Burrows-Wheeler Transforms of $T$ and its reverse, and let $z$ be the number of phrases in the LZ77…

We present an algorithm computing the longest periodic subsequence of a string of length $n$ in $O(n^7)$ time with $O(n^4)$ words of space. We obtain improvements when restricting the exponents or extending the search allowing the reported…

We consider the problem of {\em restructuring} compressed texts without explicit decompression. We present algorithms which allow conversions from compressed representations of a string $T$ produced by any grammar-based compression…

Converting a compressed format of a string into another compressed format without an explicit decompression is one of the central research topics in string processing. We discuss the problem of converting the run-length Burrows-Wheeler…

The random access problem for compressed strings is to build a data structure that efficiently supports accessing the character in position $i$ of a string given in compressed form. Given a grammar of size $n$ compressing a string of size…

Suppose that we are given a string $s$ of length $n$ over an alphabet $\{0,1,\ldots,n^{O(1)}\}$ and $\delta$ is the string complexity of $s$, a known compression measure. We describe an index on $s$ with $O(\delta\log\frac{n}{\delta})$…

Sublinear time quantum algorithms have been established for many fundamental problems on strings. This work demonstrates that new, faster quantum algorithms can be designed when the string is highly compressible. We focus on two popular and…

The Lempel-Ziv factorization (LZ77) and the Run-Length encoded Burrows-Wheeler Transform (RLBWT) are two important tools in text compression and indexing, being their sizes $z$ and $r$ closely related to the amount of text…

Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in $O(n \log n)$ time and space. Our goal in this paper is to reduce the space consumption while…

A family of Lempel-Ziv factorizations is a well-studied string structure. The LZ-End factorization is a member of the family that achieved faster extraction of any substrings (Kreft & Navarro, TCS 2013). One of the interests for LZ-End…

The unrestricted LZ78 universal data-compression algorithm (as well as the LZ77 and LZW versions) achieves asymptotically, as the block-length tends to infinity, the FS compressibility, namely the best compression-ratio that may be achieved…

We present a simple adaptation of the Lempel Ziv 78' (LZ78) compression scheme ({\em IEEE Transactions on Information Theory, 1978}) that supports efficient random access to the input string. Namely, given query access to the compressed…

We give algorithms that, given a straight-line program (SLP) with $g$ rules that generates (only) a text $T [1..n]$, builds within $O(g)$ space the Lempel-Ziv (LZ) parse of $T$ (of $z$ phrases) in time $O(n\log^2 n)$ or in time…

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…

We present a new on-line algorithm for computing the Lempel-Ziv factorization of a string that runs in $O(N\log N)$ time and uses only $O(N\log\sigma)$ bits of working space, where $N$ is the length of the string and $\sigma$ is the size of…