An interesting class of orthogonal representations consists of the so-called turn-regular ones, i.e., those that do not contain any pair of reflex corners that “point to each other” inside a face. For such a representation H it is possible to compute in linear time a minimum-area drawing, i.e., a drawing of minimum area over all possible assignments of vertex and bend coordinates of H. In contrast, finding a minimum-area drawing of H is NP-hard if H is non-turn-regular. This scenario naturally motivates the study of which graphs admit turn-regular orthogonal representations. In this paper we identify notable classes of biconnected planar graphs that always admit such repre-sentations, which can be computed in linear time. We also describe a linear-time testing algorithm for trees and provide a polynomial-time algorithm that tests whether a bi-connected plane graph with “small” faces has a turn-regular orthogonal representation without bends.

On Turn-Regular Orthogonal Representations

Binucci C.;Didimo W.;
2022

Abstract

An interesting class of orthogonal representations consists of the so-called turn-regular ones, i.e., those that do not contain any pair of reflex corners that “point to each other” inside a face. For such a representation H it is possible to compute in linear time a minimum-area drawing, i.e., a drawing of minimum area over all possible assignments of vertex and bend coordinates of H. In contrast, finding a minimum-area drawing of H is NP-hard if H is non-turn-regular. This scenario naturally motivates the study of which graphs admit turn-regular orthogonal representations. In this paper we identify notable classes of biconnected planar graphs that always admit such repre-sentations, which can be computed in linear time. We also describe a linear-time testing algorithm for trees and provide a polynomial-time algorithm that tests whether a bi-connected plane graph with “small” faces has a turn-regular orthogonal representation without bends.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11391/1531273
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