Chain minors are FPT

Abstract

Given two finite posets P and Q, P is a chain minor of Q if there exists a partial function f from the elements of Q to the elements of P such that for every chain in P there is a chain CQ in Q with the property that f restricted to CQ is an isomorphism of chains. We give an algorithm to decide whether a poset P is a chain minor of a poset Q that runs in time O(|Q|log|Q|) for every fixed poset P. This solves an open problem from the monograph by Downey and Fellows [Parameterized Complexity, 1999] who asked whether the problem was fixed parameter tractable. © 2013 Springer International Publishing.