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arXiv · 2106.01173

On the approximation ratio of LZ-End to LZ77

Takumi Ideue·Takuya Mieno·Mitsuru Funakoshi·Yuto Nakashima·Shunsuke Inenaga·Masayuki Takeda
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Abstract

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 factorizations is the possible difference between the size of LZ-End and LZ77 factorizations. They also showed families of strings where the approximation ratio of the number of LZ-End phrases to the number of LZ77 phrases asymptotically approaches 2. However, the alphabet size of these strings is unbounded. In this paper, we analyze the LZ-End factorization of the period-doubling sequence. We also show that the approximation ratio for the period-doubling sequence asymptotically approaches 2 for the binary alphabet.

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Takumi Ideue, Takuya Mieno, Mitsuru Funakoshi, Yuto Nakashima, Shunsuke Inenaga, Masayuki Takeda. 2021-06-02. On the approximation ratio of LZ-End to LZ77. https://arxiv.org/abs/2106.01173

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