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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Vydáno v:Algorithmica Ročník 72; číslo 3; s. 778 - 790
Hlavní autoři: Kobayashi, Yasuaki, Tamaki, Hisao
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.07.2015
Témata:
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
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Popis
Shrnutí: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