View in EDS PDF Full Text

The Price of Upwardness.

Saved in:
Bibliographic Details
Title: The Price of Upwardness.
Authors: Angelini, Patrizio1, Biedl, Therese2, Chimani, Markus3, Cornelsen, Sabine4, Da Lozzo, Giordano5, Hong, Seok-Hee6, Liotta, Giuseppe7, Patrignani, Maurizio5, Pupyrev, Sergey8, Rutter, Ignaz9, Wolff, Alexander10
Source: Discrete Mathematics & Theoretical Computer Science (DMTCS). 2025, Vol. 27 Issue 3, p1-30. 30p.
Subjects: Directed acyclic graphs, NP-complete problems
Abstract: Not every directed acyclic graph (DAG) whose underlying undirected graph is planar admits an upward planar drawing. We are interested in pushing the notion of upward drawings beyond planarity by considering upward k-planar drawings of DAGs in which the edges are monotonically increasing in a common direction and every edge is crossed at most k times for some integer k ≥ 1. We show that the number of crossings per edge in a monotone drawing is in general unbounded for the class of bipartite outerplanar, cubic, or bounded pathwidth DAGs. However, it is at most two for outerpaths and it is at most quadratic in the bandwidth in general. From the computational point of view, we prove that testing upward k-planarity is NP-complete already for k = 1 and even for restricted instances for which upward planarity testing is polynomial. On the positive side, we can decide in linear time whether a single-source DAG admits an upward 1-planar drawing in which all vertices are incident to the outer face. [ABSTRACT FROM AUTHOR]
Copyright of Discrete Mathematics & Theoretical Computer Science (DMTCS) is the property of Discrete Mathematics & Theoretical Computer Science DMTCS and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
FullText Links:
  – Type: pdflink
Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 188966922
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: The Price of Upwardness.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Angelini%2C+Patrizio%22">Angelini, Patrizio</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Biedl%2C+Therese%22">Biedl, Therese</searchLink><relatesTo>2</relatesTo><br /><searchLink fieldCode="AR" term="%22Chimani%2C+Markus%22">Chimani, Markus</searchLink><relatesTo>3</relatesTo><br /><searchLink fieldCode="AR" term="%22Cornelsen%2C+Sabine%22">Cornelsen, Sabine</searchLink><relatesTo>4</relatesTo><br /><searchLink fieldCode="AR" term="%22Da+Lozzo%2C+Giordano%22">Da Lozzo, Giordano</searchLink><relatesTo>5</relatesTo><br /><searchLink fieldCode="AR" term="%22Hong%2C+Seok-Hee%22">Hong, Seok-Hee</searchLink><relatesTo>6</relatesTo><br /><searchLink fieldCode="AR" term="%22Liotta%2C+Giuseppe%22">Liotta, Giuseppe</searchLink><relatesTo>7</relatesTo><br /><searchLink fieldCode="AR" term="%22Patrignani%2C+Maurizio%22">Patrignani, Maurizio</searchLink><relatesTo>5</relatesTo><br /><searchLink fieldCode="AR" term="%22Pupyrev%2C+Sergey%22">Pupyrev, Sergey</searchLink><relatesTo>8</relatesTo><br /><searchLink fieldCode="AR" term="%22Rutter%2C+Ignaz%22">Rutter, Ignaz</searchLink><relatesTo>9</relatesTo><br /><searchLink fieldCode="AR" term="%22Wolff%2C+Alexander%22">Wolff, Alexander</searchLink><relatesTo>10</relatesTo>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Discrete+Mathematics+%26+Theoretical+Computer+Science+%28DMTCS%29%22">Discrete Mathematics & Theoretical Computer Science (DMTCS)</searchLink>. 2025, Vol. 27 Issue 3, p1-30. 30p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Directed+acyclic+graphs%22">Directed acyclic graphs</searchLink><br /><searchLink fieldCode="DE" term="%22NP-complete+problems%22">NP-complete problems</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Not every directed acyclic graph (DAG) whose underlying undirected graph is planar admits an upward planar drawing. We are interested in pushing the notion of upward drawings beyond planarity by considering upward k-planar drawings of DAGs in which the edges are monotonically increasing in a common direction and every edge is crossed at most k times for some integer k ≥ 1. We show that the number of crossings per edge in a monotone drawing is in general unbounded for the class of bipartite outerplanar, cubic, or bounded pathwidth DAGs. However, it is at most two for outerpaths and it is at most quadratic in the bandwidth in general. From the computational point of view, we prove that testing upward k-planarity is NP-complete already for k = 1 and even for restricted instances for which upward planarity testing is polynomial. On the positive side, we can decide in linear time whether a single-source DAG admits an upward 1-planar drawing in which all vertices are incident to the outer face. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Discrete Mathematics & Theoretical Computer Science (DMTCS) is the property of Discrete Mathematics & Theoretical Computer Science DMTCS and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=188966922
RecordInfo BibRecord:
  BibEntity:
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 30
        StartPage: 1
    Subjects:
      – SubjectFull: Directed acyclic graphs
        Type: general
      – SubjectFull: NP-complete problems
        Type: general
    Titles:
      – TitleFull: The Price of Upwardness.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Angelini, Patrizio
      – PersonEntity:
          Name:
            NameFull: Biedl, Therese
      – PersonEntity:
          Name:
            NameFull: Chimani, Markus
      – PersonEntity:
          Name:
            NameFull: Cornelsen, Sabine
      – PersonEntity:
          Name:
            NameFull: Da Lozzo, Giordano
      – PersonEntity:
          Name:
            NameFull: Hong, Seok-Hee
      – PersonEntity:
          Name:
            NameFull: Liotta, Giuseppe
      – PersonEntity:
          Name:
            NameFull: Patrignani, Maurizio
      – PersonEntity:
          Name:
            NameFull: Pupyrev, Sergey
      – PersonEntity:
          Name:
            NameFull: Rutter, Ignaz
      – PersonEntity:
          Name:
            NameFull: Wolff, Alexander
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 09
              Text: 2025
              Type: published
              Y: 2025
          Identifiers:
            – Type: issn-print
              Value: 13658050
          Numbering:
            – Type: volume
              Value: 27
            – Type: issue
              Value: 3
          Titles:
            – TitleFull: Discrete Mathematics & Theoretical Computer Science (DMTCS)
              Type: main
ResultId 1