# A local search 2.917-approximation algorithm for duo-preservation string mapping

## TL;DR

This paper introduces an improved local search algorithm for the Max-Duo problem, achieving a 2.917-approximation ratio, which surpasses the previous best of 3.25, with detailed analysis and bounds on its performance.

## Contribution

It presents a novel local search algorithm with a better approximation ratio for Max-Duo, along with a comprehensive performance analysis and locality gap bounds.

## Key findings

- Achieved a 2.917-approximation ratio for Max-Duo.
- Improved upon the previous 3.25-approximation ratio.
- Provided lower bounds on the algorithm's locality gap.

## Abstract

We study the {\em maximum duo-preservation string mapping} ({\sc Max-Duo}) problem, which is the complement of the well studied {\em minimum common string partition} ({\sc MCSP}) problem. Both problems have applications in many fields including text compression and bioinformatics. Motivated by an earlier local search algorithm, we present an improved approximation and show that its performance ratio is no greater than ${35}/{12} < 2.917$. This beats the current best $3.25$-approximation for {\sc Max-Duo}. The performance analysis of our algorithm is done through a complex yet interesting amortization. Two lower bounds on the locality gap of our algorithm are also provided.