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In this paper, we introduce new types of approximate palindromes calledsingle-arm-gapped palindromes (shortly SAGPs). A SAGP contains a gap in eitherits left or right arm, which is in the form of either $wguc u^R w^R$ or $wucu^Rgw^R$, where $w$ and $u$ are non-empty strings, $w^R$ and $u^R$ arerespectively 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 classifySAGPs into two groups: those which have $ucu^R$ as a maximal palindrome(type-1), and the others (type-2). We propose several algorithms to computetype-1 SAGPs with longest arms occurring in a given string, based on suffixarrays. Then, we propose a linear-time algorithm to compute all type-1 SAGPswith longest arms, based on suffix trees. Also, we show how to compute type-2SAGPs with longest arms in linear time. We also perform some preliminaryexperiments to show practical performances of the proposed methods.

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