The straight-line RAC drawing problem is NP-hard

Authors:
Evmorfia N. Argyriou;Michael A. Bekos;Antonios Symvonis
Affiliations:
School of Applied Mathematical & Physical Sciences, National Technical University of Athens, Greece;School of Applied Mathematical & Physical Sciences, National Technical University of Athens, Greece;School of Applied Mathematical & Physical Sciences, National Technical University of Athens, Greece
Venue:
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Year:
2011

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Abstract

Recent cognitive experiments have shown that the negative impact of an edge crossing on the human understanding of a graph drawing, tends to be eliminated in the case where the crossing angles are greater than 70 degrees. This motivated the study of RAC drawings, in which every pair of crossing edges intersects at right angle. In this work, we demonstrate a class of graphs with unique RAC combinatorial embedding and we employ members of this class in order to show that it is NP-hard to decide whether a graph admits a straight-line RAC drawing.