TY - GEN
T1 - Monotone drawings of graphs with fixed embedding
AU - Angelini, Patrizio
AU - Didimo, Walter
AU - Kobourov, Stephen
AU - McHedlidze, Tamara
AU - Roselli, Vincenzo
AU - Symvonis, Antonios
AU - Wismath, Stephen
N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.
PY - 2012
Y1 - 2012
N2 - A drawing of a graph is a monotone drawing if for every pair of vertices u and v, there is a path drawn from u to v that is monotone in some direction. In this paper we investigate planar monotone drawings in the fixed embedding setting, i.e., a planar embedding of the graph is given as part of the input that must be preserved by the drawing algorithm. In this setting we prove that every planar graph on n vertices admits a planar monotone drawing with at most two bends per edge and with at most 4n - 10 bends in total; such a drawing can be computed in linear time and requires polynomial area. We also show that two bends per edge are sometimes necessary on a linear number of edges of the graph. Furthermore, we investigate subclasses of planar graphs that can be realized as embedding-preserving monotone drawings with straight-line edges, and we show that biconnected embedded planar graphs and outerplane graphs always admit such drawings, which can be computed in linear time.
AB - A drawing of a graph is a monotone drawing if for every pair of vertices u and v, there is a path drawn from u to v that is monotone in some direction. In this paper we investigate planar monotone drawings in the fixed embedding setting, i.e., a planar embedding of the graph is given as part of the input that must be preserved by the drawing algorithm. In this setting we prove that every planar graph on n vertices admits a planar monotone drawing with at most two bends per edge and with at most 4n - 10 bends in total; such a drawing can be computed in linear time and requires polynomial area. We also show that two bends per edge are sometimes necessary on a linear number of edges of the graph. Furthermore, we investigate subclasses of planar graphs that can be realized as embedding-preserving monotone drawings with straight-line edges, and we show that biconnected embedded planar graphs and outerplane graphs always admit such drawings, which can be computed in linear time.
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U2 - 10.1007/978-3-642-25878-7_36
DO - 10.1007/978-3-642-25878-7_36
M3 - Conference contribution
AN - SCOPUS:84455209585
SN - 9783642258770
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 379
EP - 390
BT - Graph Drawing - 19th International Symposium, GD 2011, Revised Selected Papers
T2 - 19th International Symposium on Graph Drawing, GD 2011
Y2 - 21 September 2011 through 23 September 2011
ER -