Palindrome Recognition In The Streaming Model

TL;DR

This paper introduces new streaming algorithms for palindrome detection and longest palindromic substring identification that operate efficiently with sublinear space and provide approximate or exact solutions.

Contribution

It presents the first one-pass randomized streaming algorithms for palindrome problems with additive and multiplicative errors, using minimal space.

Findings

One-pass randomized algorithm with $O(\sqrt{n})$ space for approximate palindrome detection.

Two-pass algorithm accurately finds all longest palindromes in streaming data.

One-pass algorithm with $O(\log n)$ space for exact longest palindromic substring detection.

Abstract

In the Palindrome Problem one tries to find all palindromes (palindromic substrings) in a given string. A palindrome is defined as a string which reads forwards the same as backwards, e.g., the string "racecar". A related problem is the Longest Palindromic Substring Problem in which finding an arbitrary one of the longest palindromes in the given string suffices. We regard the streaming version of both problems. In the streaming model the input arrives over time and at every point in time we are only allowed to use sublinear space. The main algorithms in this paper are the following: The first one is a one-pass randomized algorithm that solves the Palindrome Problem. It has an additive error and uses $O(\sqrt n$) space. The second algorithm is a two-pass algorithm which determines the exact locations of all longest palindromes. It uses the first algorithm as the first pass. The third algorithm is again a one-pass randomized algorithm, which solves the Longest Palindromic Substring Problem. It has a multiplicative error using only $O(\log(n))$ space. We also give two variants of the first algorithm which solve other related practical problems.