A Fast and Simple Subexponential Fixed Parameter Algorithm for One-Sided Crossing Minimization

A Fast and Simple Subexponential Fixed Parameter Algorithm for One-Sided Crossing Minimization

0.00 Avg rating0 Votes
Article ID: iaor201526358
Volume: 72
Issue: 3
Start Page Number: 778
End Page Number: 790
Publication Date: Jul 2015
Journal: Algorithmica
Authors: ,
Keywords: graphs, programming: dynamic, programming: linear
Abstract:

We give a subexponential fixed parameter algorithm for one‐sided crossing minimization. It runs in O ( k 2 2 k + n ) equ1 time, where n is the number of vertices of the given graph and parameter k is the number of crossings. The exponent of O ( k ) equ2 in this bound is asymptotically optimal assuming the Exponential Time Hypothesis and the previously best known algorithm runs in 2 O ( k log k ) + n O ( 1 ) equ3 time. We achieve this significant improvement by the use of a certain interval graph naturally associated with the problem instance and a simple dynamic program on this interval graph. The linear dependency on n is also achieved through the use of this interval graph.

Reviews

Required fields are marked *. Your email address will not be published.