Orthogonal axial line placement in hole free collections of rectangles

Authors:
Hein Kruger;Ian Sanders
Affiliations:
University of the Witwatersrand;University of the Witwatersrand
Venue:
SAICSIT '05 Proceedings of the 2005 annual research conference of the South African institute of computer scientists and information technologists on IT research in developing countries
Year:
2005

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The axial line placement problem

The axial line placement problem
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)

Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)

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Abstract

Previous research showed that the problem of finding the smallest set of orthogonal axial lines needed to cross all adjacencies between rectangles in a collection of orthogonal rectangles (ALP-OLOR) is NP-Complete. There are, however, some cases where the problem can be solved in polynomial time by mapping adjacencies to intervals on a line and finding a clique cover of the resulting interval graph. In this paper we extend that result and show that ALP-OLOR can be solved in polynomial time for all hole free collections of rectangles as well as for some collections of rectangles with holes.