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Computing Orthogonal Drawings in a Variable Embedding Setting

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Algorithms and Computation (ISAAC 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1533))

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Abstract

This paper addresses the classical graph drawing problem of designing an algorithm that computes an orthogonal representation with the minimum number of bends, by considering all possible planar embeddings of the graph. While the general problem has been shown to be NP-complete [7], polynomial time algorithms have been devised for graphs whose vertex degree is at most three [5]. We show the first algorithm whose time complexity is exponential only in the number of vertices of degree four of the input graph. This settles a problem left as open in [5]. Our algorithm is further extended to handle graphs with vertices of degree higher than four. The analysis of the algorithm is supported by several experiments on the structure of a large set of input graphs.

Research supported in part by the ESPRIT LTR Project no. 20244 - ALCOM-IT and by the CNR Project “Geometria Computazionale Robusta con Applicazioni alla Grafica ed al CAD.”

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica e Automazione, Università di Roma Tre, via della Vasca Navale 79, 00146, Roma, Italy

    Walter Didimo

  2. Dipartimento di Informatica e Sistemistica, Università di Roma ‘La Sapienza’, via Salaria 113, I-00198, Rome, Italy

    Giuseppe Liotta

Authors
  1. Walter Didimo
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  2. Giuseppe Liotta
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Korea Advanced Institute of Science and Technology, 373-1, Kusong-dong, Yusong-gu, Taejon, 305-701, Korea

    Kyung-Yong Chwa

  2. Department of Computer Science, University of California, Santa Barbara, CA, 93106, USA

    Oscar H. Ibarra

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© 1998 Springer-Verlag Berlin Heidelberg

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Didimo, W., Liotta, G. (1998). Computing Orthogonal Drawings in a Variable Embedding Setting. In: Chwa, KY., Ibarra, O.H. (eds) Algorithms and Computation. ISAAC 1998. Lecture Notes in Computer Science, vol 1533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49381-6_10

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  • DOI: https://doi.org/10.1007/3-540-49381-6_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65385-1

  • Online ISBN: 978-3-540-49381-5

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