The book crossing number of a graph

SOFSEM 2005: Theory and Practice of Computer Science

et al. 2005

• his is onferene pperF he definitive version is ville fromX httpXGGspringerlinkFmetpressFomGontentGIHSTQQGcsortorderas8poaUIW Abstract. An outerplanar (also called circular, convex, one-page) drawing of an n-vertex graph G is a drawing in which the vertices are placed on a circle and each edge is drawn using one straight-line segment. We derive exact results for the minimal number of crossings in any outerplanar drawings of the following classes of graphs: 3-row meshes, Halin graphs and complete p−partite graphs with equal size partite sets.

Section: Introductionmentioning

confidence: 69%

Outerplanar Crossing Numbers of 3-Row Meshes, Halin Graphs and Complete p-Partite Graphs

Fulek

SOFSEM 2005: Theory and Practice of Computer Science

et al. 2005

“…The first upper bound follows from our paper [11] (Corollary 3.2) and a simple observation that a drawing of a graph G in 2k pages gives a drawing of the graph G in k planes. The second upper bound follows by iteration from the inequality cr 2 (G) ≤ 3 8 cr(G), proved in [5].…”

Section: Proofmentioning

confidence: 99%

Bounds and Methods for k-Planar Crossing Numbers

Shahrokhi

Lecture Notes in Computer Science

Székely

et al. 2004

Self Cite

“…Edge crossing minimisation is the main goal in the linear VLSI design, since smaller number of crossings means cheaper design. The minimal number of edge crossings over all book drawings of a graph is called the book crossing number (29).…”

Section: Introductionmentioning

confidence: 99%

Parallelisation of genetic algorithms for the 2-page crossing number problem

Journal of Parallel and Distributed Computing

Sălăgean

et al. 2007

Citation: HE et al, 2007. Parallelisation of genetic algorithms for the 2-page crossing number problem. Journal of parallel and distributed computing, 66 (2) AbstractGenetic algorithms have been applied to solve the 2-page crossing number problem successfully, but since they work with one global population, the search time and space are limited. Parallelisation provides an attractive prospect to improve the efficiency and solution quality of genetic algorithms. This paper investigates the complexity of parallel genetic algorithms (PGAs) based on two evaluation measures: Computation-time to Communication-time and Population-size to Chromosomesize. Moreover, the paper unifies the framework of PGA models with the function P GA(subpopulation size, cluster size, migration period, topology), and explores the performance of PGAs for the 2-page crossing number problem.