Tighter bounds for the sum of irreducible LCP values

详细信息    查看全文

• 作者：Juha Kä ; rkkä ; inen^a ; ^{juha.karkkainen@cs.helsinki.fi} ; Dominik Kempa^a ; ^{dominik.kempa@cs.helsinki.fi} ; Marcin Pia̧tkowski^b ; ^{marcin.piatkowski@mat.umk.pl}
• 关键词：LCP array ; Irreducible LCP values ; Suffix array ; Burrows&ndash ; Wheeler transform
• 刊名：Theoretical Computer Science
• 出版年：2016
• 出版时间：20 December 2016
• 年：2016
• 卷：656
• 期：part_PB
• 页码：265-278
• 全文大小：418 K
• 卷排序：656

文摘

The suffix array is frequently augmented with the longest-common-prefix (LCP) array that stores the lengths of the longest common prefixes between lexicographically adjacent suffixes of a text. While the sum of the values in the LCP array can be Ω(n2)Ω(n2) for a text of length n  , the sum of so-called irreducible LCP values was shown to be O(nlg⁡n)O(nlg⁡n) a few years ago. In this paper, we improve the bound to O(nlg⁡r)O(nlg⁡r), where r≤nr≤n is the number of runs in the Burrows–Wheeler transform of the text. We also show that our bound is tight up to lower order terms (unlike the previous bound). Our results and the techniques used in proving them provide new insights into the combinatorics of text indexing and compression, and have immediate applications to LCP array construction algorithms.