# LZRR: LZ77 Parsing with Right Reference

## TL;DR

This paper introduces LZRR, a novel bidirectional parsing method that guarantees fewer phrases than LZ77, achieving approximately 5% better compression on benchmark strings.

## Contribution

LZRR is the first practical bidirectional parsing method with theoretical guarantees of smaller phrase counts than LZ77.

## Key findings

- LZRR reduces phrase count by about 5% compared to LZ77.
- LZRR guarantees smaller phrase count theoretically.
- Experimental results confirm improved compression ratios.

## Abstract

Lossless data compression has been widely studied in computer science. One of the most widely used lossless data compressions is Lempel-Zip(LZ) 77 parsing, which achieves a high compression ratio. Bidirectional (a.k.a. macro) parsing is a lossless data compression and computes a sequence of phrases copied from another substring (target phrase) on either the left or the right position in an input string. Gagie et al.(LATIN 2018) recently showed that a large gap exists between the number of smallest bidirectional phrases of a given string and that of LZ77 phrases. In addition, finding the smallest bidirectional parse of a given text is NP-complete. Several variants of bidirectional parsing have been proposed thus far, but no prior work for bidirectional parsing has achieved high compression that is smaller than that of LZ77 phrasing for any string. In this paper, we present the first practical bidirectional parsing named LZ77 parsing with right reference (LZRR), in which the number of LZRR phrases is theoretically guaranteed to be smaller than the number of LZ77 phrases. Experimental results using benchmark strings show the number of LZRR phrases is approximately five percent smaller than that of LZ77 phrases.