Chain minors are FPT
Data Structures and Algorithms
2013-04-23 v1 Discrete Mathematics
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 C_Q in Q with the property that f restricted to C_Q is an isomorphism of chains. We give an algorithm to decide whether a poset P is a chain minor of o 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.
Cite
@article{arxiv.1304.5849,
title = {Chain minors are FPT},
author = {Jaroslaw Blasiok and Marcin Kaminski},
journal= {arXiv preprint arXiv:1304.5849},
year = {2013}
}