The book embedding of ordered sets

A large number of important problems in different areas can be expressed as graph layout problems whose objective is to determine a linear layout in such way that a certain objective cost is optimized. In a book embedding for an ordered set, the elements are embedded on the spine of the book to form a linear extension. The pagenumber is the minimum number of pages needed to draw the edges as simple curves such that edges drawn in the same page do not intersect. The book (stack) layout can be applied to several areas of computer science and engineering disciplines including ordered sets, interconnection networks, fault tolerant VLSI design, circuit designs, sorting permutations, complexity theory, and graph drawing. In this thesis we investigate the book (stack) layout problem of ordered sets. The pagenumber problem is known to be NP-complete, even if the order of the elements on the spine is fixed. As a result, the pagenumber problem has been studied only for some restricted classes of ordered sets. A literature review on the pagenumber problem for graphs and ordered sets is presented. We also provide the first efficient algorithm for drawing the bipartite interval orders in the minimum number of pages needed. We also give an upper bound for the pagenumber of bipartite ordered sets and the pagenumber of the complete multipartite ordered sets with length 4 and 5.

Grantor dc:publisher

University of Ottawa (Canada)

Year dc:date

2013

Author dc:creator

• Alhashem, Mustafa

• Computer Science.

Language dc:language

en

Identifier

Source: Masters Abstracts International, Volume: 44-04, page: 1874.
http://dx.doi.org/10.20381/ruor-9813

OAI identifier oai:identifier

oai:ruor.uottawa.ca:10393/26835