Algorithmica

, Volume 32, Issue 3, pp 474–506 | Cite as

Quasi-Upward Planarity

  • Bertolazzi
  • Di Battista
  • Didimo
Article

Abstract

An upward planar drawing of a directed graph (digraph) is a planar drawing such that all the edges are represented by curves monotonically increasing in the vertical direction. In this paper we introduce and study the concept of quasi-upward planarity. Quasi-upward planarity allows us to extend the upward planarity theory to a large class of digraphs including digraphs that also have directed cycles. First, we characterize the digraphs that have a quasi-upward planar drawing. Second, we give a polynomial time algorithm for computing ``optimal'' quasi-upward planar drawings within a given planar embedding. Further, we apply branch and bound techniques to the problem of computing optimal quasi-upward planar drawings, considering all possible planar embeddings. The paper also contains experimental results about the proposed techniques.

Key words. Planarity, Upward, Flow techniques, Branch and bound. 

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Copyright information

© Springer-Verlag New York Inc. 2001

Authors and Affiliations

  • Bertolazzi
    • 1
  • Di Battista
    • 2
  • Didimo
    • 2
  1. 1.IASI, CNR, viale Manzoni 30, 00185 Roma, Italy. bertola@iasi.rm.cnr.it.IT
  2. 2.Dipartimento di Informatica e Automazione, Università Roma Tre, via della Vasca Navale 79, 00146 Roma, Italy.gdb@dia.uniroma3.it,didimo@dia.uniroma3.it.IT

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