# Consensus Patterns parameterized by input string length is W[1]-hard

## TL;DR

This paper proves that the Consensus Patterns problem, which involves finding a common pattern in multiple strings with errors, is computationally hard (W[1]-hard) when parameterized by input string length.

## Contribution

It establishes the W[1]-hardness of the Consensus Patterns problem based on input string length, highlighting its computational complexity.

## Key findings

- Consensus Patterns problem is W[1]-hard when parameterized by string length.
- The hardness result applies to the problem with errors allowed in pattern matching.
- This work clarifies the computational limits of pattern extraction in strings.

## Abstract

We consider the Consensus Patterns problem, where, given a set of input strings, one is asked to extract a long-enough pattern which appears (with some errors) in all strings. We prove that this problem is W[1]-hard when parameterized by the maximum length of input strings.