TY - GEN

T1 - Orthogonal layout with optimal face complexity

AU - Alam, M. Jawaherul

AU - Kobourov, Stephen G.

AU - Mondal, Debajyoti

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2016.

PY - 2016

Y1 - 2016

N2 - We study a problem motivated by rectilinear schematization of geographic maps. Given a biconnected plane graph G and an integer k ≥ 0, does G have a strict-orthogonal drawing with at most k reflex angles per face? For k = 0 the problem is equivalent to realizing each face as a rectangle. The problem can be reduced to a max-flow problem in some linear-size nonplanar network, but the best solutions require Ω(n1.5 log n log k) time. We describe a graph matching approach that can decide strict-orthogonal drawability for arbitrary reflex complexity k in O((nk)1.5) time, which is faster for constant values of k. In contrast, if the embedding is not fixed, we prove that it is NP-complete to decide whether a planar graph admits a strict-orthogonal drawing with reflex face complexity 4.

AB - We study a problem motivated by rectilinear schematization of geographic maps. Given a biconnected plane graph G and an integer k ≥ 0, does G have a strict-orthogonal drawing with at most k reflex angles per face? For k = 0 the problem is equivalent to realizing each face as a rectangle. The problem can be reduced to a max-flow problem in some linear-size nonplanar network, but the best solutions require Ω(n1.5 log n log k) time. We describe a graph matching approach that can decide strict-orthogonal drawability for arbitrary reflex complexity k in O((nk)1.5) time, which is faster for constant values of k. In contrast, if the embedding is not fixed, we prove that it is NP-complete to decide whether a planar graph admits a strict-orthogonal drawing with reflex face complexity 4.

UR - http://www.scopus.com/inward/record.url?scp=84956698256&partnerID=8YFLogxK

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U2 - 10.1007/978-3-662-49192-8_10

DO - 10.1007/978-3-662-49192-8_10

M3 - Conference contribution

AN - SCOPUS:84956698256

SN - 9783662491911

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 121

EP - 133

BT - SOFSEM 2016

A2 - Freivalds, Rūsiņš Mārtiņš

A2 - Engels, Gregor

A2 - Catania, Barbara

PB - Springer-Verlag

T2 - 42nd International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2016

Y2 - 23 January 2016 through 28 January 2016

ER -