Grammar-compressed Self-index with Lyndon Words

Kazuya Tsuruta; Dominik Köppl; Yuto Nakashima; Shunsuke Inenaga; Hideo Bannai; Masayuki Takeda

Grammar-compressed Self-index with Lyndon Words

Kazuya Tsuruta, Dominik Köppl, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda

Mathematical Informatics

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce a new class of straight-line programs (SLPs), named the Lyndon SLP, inspired by the Lyndon trees (Barcelo, 1990). Based on this SLP, we propose a self-index data structure of O(g) words of space that can be built from a string T in O(n lg n) expected time, retrieving the starting positions of all occurrences of a pattern P of length m in O(m + lg m lg n + occ lg g) time, where n is the length of T, g is the size of the Lyndon SLP for T, and occ is the number of occurrences of P in T.

Original language	English
Journal	Unknown Journal
Publication status	Published - Apr 11 2020

All Science Journal Classification (ASJC) codes

General

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title = "Grammar-compressed Self-index with Lyndon Words",

abstract = "We introduce a new class of straight-line programs (SLPs), named the Lyndon SLP, inspired by the Lyndon trees (Barcelo, 1990). Based on this SLP, we propose a self-index data structure of O(g) words of space that can be built from a string T in O(n lg n) expected time, retrieving the starting positions of all occurrences of a pattern P of length m in O(m + lg m lg n + occ lg g) time, where n is the length of T, g is the size of the Lyndon SLP for T, and occ is the number of occurrences of P in T.",

author = "Kazuya Tsuruta and Dominik K{\"o}ppl and Yuto Nakashima and Shunsuke Inenaga and Hideo Bannai and Masayuki Takeda",

year = "2020",

month = apr,

day = "11",

language = "English",

journal = "Quaternary International",

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T1 - Grammar-compressed Self-index with Lyndon Words

AU - Tsuruta, Kazuya

AU - Köppl, Dominik

AU - Nakashima, Yuto

AU - Inenaga, Shunsuke

AU - Bannai, Hideo

AU - Takeda, Masayuki

PY - 2020/4/11

Y1 - 2020/4/11

N2 - We introduce a new class of straight-line programs (SLPs), named the Lyndon SLP, inspired by the Lyndon trees (Barcelo, 1990). Based on this SLP, we propose a self-index data structure of O(g) words of space that can be built from a string T in O(n lg n) expected time, retrieving the starting positions of all occurrences of a pattern P of length m in O(m + lg m lg n + occ lg g) time, where n is the length of T, g is the size of the Lyndon SLP for T, and occ is the number of occurrences of P in T.

AB - We introduce a new class of straight-line programs (SLPs), named the Lyndon SLP, inspired by the Lyndon trees (Barcelo, 1990). Based on this SLP, we propose a self-index data structure of O(g) words of space that can be built from a string T in O(n lg n) expected time, retrieving the starting positions of all occurrences of a pattern P of length m in O(m + lg m lg n + occ lg g) time, where n is the length of T, g is the size of the Lyndon SLP for T, and occ is the number of occurrences of P in T.

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