A Space-Saving Approximation Algorithm for Grammar-Based Compression

A Space-Saving Approximation Algorithm for Grammar-Based Compression

A space-efficient approximation algorithm for the grammar-based compression problem, which requests for a given string to find a smallest context-free grammar deriving the string, is presented. For the input length n and an optimum CFG size g, the algorithm consumes only O(g log g) space and O(n log∗n) time to achieve O((log∗n) logn) approximation ratio to the optimum compression, where log∗n i...

A Space-Saving Linear-Time Algorithm for Grammar-Based Compression

A space-efficient linear-time approximation algorithm for the grammar-based compression problem, which requests for a given string to find a smallest context-free grammar deriving the string, is presented. The algorithm consumes only O(g∗ log g∗) space and achieves the worstcase approximation ratio O(log g∗ log n), with the size n of an input and the optimum grammar size g∗. Experimental result...

A Fully Linear-Time Approximation Algorithm for Grammar-Based Compression

Approximation algorithms for grammar-based data compression

This thesis considers the smallest grammar problem: find the smallest context-free grammar that generates exactly one given string. We show that this problem is intractable, and so our objective is to find approximation algorithms. This simple question is connected to many areas of research. Most importantly, there is a link to data compression; instead of storing a long string, one can store a...

Approximation of Grammar-Based Compression via Recompression

In this paper we present a simple linear-time algorithm constructing a context-free grammar of size O(g log(N/g)) for the input string, where N is the size of the input string and g the size of the optimal grammar generating this string. The algorithm works for arbitrary size alphabets, but the running time is linear assuming that the alphabet Σ of the input string can be identified with number...