Parameterized Complexity of the Arc-Preserving Subsequence Problem

We study the Arc-Preserving Subsequence (APS) problem with unlimited annotations. Given two arc-annotated sequences P and T , this problem asks if it is possible to delete characters from T to obtain P . Since even the unary version of APS is NP-hard, we used the framework of parameterized complexity, focusing on a parameterization of this problem where the parameter is the number of deletions we can make. We present a linear-time FPT algorithm for a generalization of APS, applying techniques originally designed to give an FPT algorithm for Induced Subgraph Isomorphism on interval graphs [12].