Computing Bend-Minimum Orthogonal Drawings of Plane Series–Parallel Graphs in Linear Time

A planar orthogonal drawing of a planar 4-graph G (i.e., a planar graph with vertex-degree at most four) is a crossing-free drawing that maps each vertex of G to a distinct point of the plane and each edge of G to a polygonal chain consisting of horizontal and vertical segments. A longstanding open...

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Vydáno v:Algorithmica Ročník 85; číslo 9; s. 2605 - 2666
Hlavní autoři: Didimo, Walter, Kaufmann, Michael, Liotta, Giuseppe, Ortali, Giacomo
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.09.2023
Springer Nature B.V
Témata:
Algorithm Analysis and Problem Complexity
Algorithms
Bends
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Graphs
Mathematics of Computing
Questions
Theory of Computation
Plane graphs
Bend minimization
Series–parallel graphs
Linear-time algorithms
Orthogonal drawings
ISSN:0178-4617, 1432-0541
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Shrnutí:A planar orthogonal drawing of a planar 4-graph G (i.e., a planar graph with vertex-degree at most four) is a crossing-free drawing that maps each vertex of G to a distinct point of the plane and each edge of G to a polygonal chain consisting of horizontal and vertical segments. A longstanding open question in Graph Drawing, dating back over 30 years, is whether there exists a linear-time algorithm to compute an orthogonal drawing of a plane 4-graph with the minimum number of bends. The term “plane” indicates that the input graph comes together with a planar embedding, which must be preserved by the drawing (i.e., the drawing must have the same set of faces as the input graph). In this paper we positively answer the question above for the widely-studied class of series–parallel graphs. Our linear-time algorithm is based on a characterization of the planar series–parallel graphs that admit an orthogonal drawing without bends. This characterization is given in terms of the orthogonal spirality that each type of triconnected component of the graph can take; the orthogonal spirality of a component measures how much that component is “rolled-up” in an orthogonal drawing of the graph.
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-023-01110-6