Longest Common Substring and Longest Palindromic Substring in $\tilde{\mathcal{O}}(\sqrt{n})$ Time

Abstract

The Longest Common Substring (LCS) and Longest Palindromic Substring (LPS) are classical problems in computer science, representing fundamental challenges in string processing. Both problems can be solved in linear time using a classical model of computation, by means of very similar algorithms, both relying on the use of suffix trees. Very recently, two sublinear algorithms for LCS and LPS in the quantum query model have been presented by Le Gall and Seddighin GallS23, requiring $\tilde{\mathcal{O}}(n^{5/6})$ and $\tilde{\mathcal{O}}(\sqrt{n})$