1609.03000Sep 10, 201619 pages, 11 figures

Efficient computation of longest single-arm-gapped palindromes in a string

Shintaro Narisada, Diptarama Hendrian, Kazuyuki Narisawa, Shunsuke Inenaga, Ayumi Shinohara

Abstract

In this paper, we introduce new types of approximate palindromes called single-arm-gapped palindromes (shortly SAGPs). A SAGP contains a gap in either its left or right arm, which is in the form of either $wguc u^R w^R$ or $wuc u^Rgw^R$

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, where

w

and

u

are non-empty strings,

w^R

and

u^R

are respectively the reversed strings of

w

and

u

,

g

is a string called a gap, and

c

is either a single character or the empty string. Here we call

wu

and

u^R w^R

the arm of the SAGP, and

|uv|

the length of the arm. We classify SAGPs into two groups: those which have

ucu^R

as a maximal palindrome (type-1), and the others (type-2). We propose several algorithms to compute type-1 SAGPs with longest arms occurring in a given string, based on suffix arrays. Then, we propose a linear-time algorithm to compute all type-1 SAGPs with longest arms, based on suffix trees. Also, we show how to compute type-2 SAGPs with longest arms in linear time. We also perform some preliminary experiments to show practical performances of the proposed methods.