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

We give a subexponential fixed parameter algorithm for one-sided crossing minimization. It runs in time, where n is the number of vertices of the given graph and parameter k is the number of crossings. The exponent of in this bound is asymptotically optimal assuming the Exponential Time Hypothesis a...

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Bibliographic Details
Published in:	Algorithmica Vol. 72; no. 3; pp. 778 - 790
Main Authors:	Kobayashi, Yasuaki, Tamaki, Hisao
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.07.2015
Subjects:	Algorithm Analysis and Problem Complexity Algorithms Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Mathematics of Computing Theory of Computation Subexponential time Graph drawing Fixed parameter algorithm
ISSN:	0178-4617, 1432-0541
Online Access:	Get full text
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Summary:	We give a subexponential fixed parameter algorithm for one-sided crossing minimization. It runs in time, where n is the number of vertices of the given graph and parameter k is the number of crossings. The exponent of in this bound is asymptotically optimal assuming the Exponential Time Hypothesis and the previously best known algorithm runs in 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.
ISSN:	0178-4617 1432-0541
DOI:	10.1007/s00453-014-9872-x