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arXiv · 1211.5108

The Rightmost Equal-Cost Position Problem

Maxime Crochemore·Alessio Langiu·Filippo Mignosi
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Abstract

LZ77-based compression schemes compress the input text by replacing factors in the text with an encoded reference to a previous occurrence formed by the couple (length, offset). For a given factor, the smallest is the offset, the smallest is the resulting compression ratio. This is optimally achieved by using the rightmost occurrence of a factor in the previous text. Given a cost function, for instance the minimum number of bits used to represent an integer, we define the Rightmost Equal-Cost Position (REP) problem as the problem of finding one of the occurrences of a factor which cost is equal to the cost of the rightmost one. We present the Multi-Layer Suffix Tree data structure that, for a text of length n, at any time i, it provides REP(LPF) in constant time, where LPF is the longest previous factor, i.e. the greedy phrase, a reference to the list of REP({set of prefixes of LPF}) in constant time and REP(p) in time O(|p| log log n) for any given pattern p.

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Maxime Crochemore, Alessio Langiu, Filippo Mignosi. 2012-11-21. The Rightmost Equal-Cost Position Problem. https://arxiv.org/abs/1211.5108

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