# Direct Linear Time Construction of Parameterized Suffix and LCP Arrays for Constant Alphabets

## TL;DR

This paper introduces the first worst-case linear time algorithm for directly constructing parameterized suffix and LCP arrays for constant alphabets, improving efficiency over previous methods that were slower or required additional structures.

## Contribution

It presents a novel linear time algorithm for directly computing parameterized suffix and LCP arrays for constant alphabets, eliminating the need for prior suffix tree construction.

## Key findings

- Algorithm runs in O(nπ) time and O(n) space.
- First worst-case linear time algorithm for this problem.
- Applicable to strings over static and parameterized alphabets.

## Abstract

We present the first worst-case linear time algorithm that directly computes the parameterized suffix and LCP arrays for constant sized alphabets. Previous algorithms either required quadratic time or the parameterized suffix tree to be built first. More formally, for a string over static alphabet $\Sigma$ and parameterized alphabet $\Pi$, our algorithm runs in $O(n\pi)$ time and $O(n)$ words of space, where $\pi$ is the number of distinct symbols of $\Pi$ in the string.