Longest α-gapped repeat and palindrome

Abstract

We propose an efficient algorithm finding, for a word w and an integer α > 0, the longest word u such that w has a factor uvu, with |uv| ≤ α|u| (i. e., the longest α-gapped repeat of w). Our algorithm runs in O(αn) time. Moreover, it can be easily adapted to find the longest u such that w has a factor uRvu, with |uv| ≤ α|u| (i. e., the longest α-gapped palindrome), again in O(αn) time.