  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 $wuc
u^Rgw^R$, 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.
