A Simpler Selfreduction Algorithm for Matroid Pathwidth
Abstract
Pathwidth of matroids naturally generalizes the better known parameter of pathwidth for graphs, and is NPhard by a reduction from the graph case. While the term matroid pathwidth was formally introduced by GeelenGerardsWhittle [JCTB 2006] in pure matroid theory, it was soon recognized by Kashyap [SIDMA 2008] that it is the same concept as longstudied so called trellis complexity in coding theory, later named trelliswidth, and hence it is an interesting notion also from the algorithmic perspective. It follows from a result of Hlineny [JCTB 2006] that the decision problem, whether a given matroid over a finite field has pathwidth at most t, is fixedparameter tractable (FPT) in t, but this result does not give any clue about constructing a pathdecomposition. The first constructive and rather complicated FPT algorithm for pathwidth of matroids over a finite field was given by JeongKimOum [SODA 2016]. Here we propose a simpler "selfreduction" FPT algorithm for a pathdecomposition. Precisely, we design an efficient routine that constructs an optimal pathdecomposition of a matroid by calling any subroutine for testing whether the pathwidth of a matroid is at most t (such as the aforementioned decision algorithm for matroid pathwidth).
 Publication:

arXiv eprints
 Pub Date:
 May 2016
 arXiv:
 arXiv:1605.09520
 Bibcode:
 2016arXiv160509520H
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Mathematics  Combinatorics;
 05B35;
 05C83;
 05C85;
 68R05