The complexity of string partitioning

TL;DR

This paper proves that the string partition problem, which involves dividing strings into segments without collisions, is NP-complete even under restrictive conditions, highlighting its computational difficulty relevant to synthetic biology.

Contribution

The paper establishes the NP-completeness of the string partition problem for various collision definitions and restrictions, including binary alphabets, advancing understanding of its computational complexity.

Findings

String partition problem is NP-complete under multiple conditions.

Hardness persists even with binary alphabet restrictions.

Implications for oligo design in gene synthesis.

Abstract

Given a string $w$ over a finite alphabet $\Sigma$ and an integer $K$, can $w$ be partitioned into strings of length at most $K$, such that there are no \emph{collisions}? We refer to this question as the \emph{string partition} problem and show it is \NP-complete for various definitions of collision and for a number of interesting restrictions including $|\Sigma|=2$. This establishes the hardness of an important problem in contemporary synthetic biology, namely, oligo design for gene synthesis.