Optimal Upward Planarity Testing of Single-Source Digraphs

Bertolazzi, Paola; Battista, Giuseppe Di; Mannino, Carlo; Tamassia, Roberto

doi:10.1137/s0097539794279626

Cited by 98 publications

(77 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Fernau et al also make the simple observation that the edges of the tanglegram can be directed from one root to the other. Thus the existence of a crossing-free tanglegram can be verified using a linear-time upward-planarity test for single-source directed acyclic graphs [3]. Later, apparently not being aware of the above mentioned results, Lozano et al [20] give a quadratic-time algorithm for the same special case, to which they refer as planar tanglegram layout.…”

Section: Related Problemsmentioning

confidence: 99%

Drawing (Complete) Binary Tanglegrams

Buchin

Byrka

et al. 2009

Lecture Notes in Computer Science

View full text Add to dashboard Cite

A binary tanglegram is a drawing of a pair of rooted binary trees whose leaf sets are in one-to-one correspondence; matching leaves are connected by intertree edges. For applications, for example, in phylogenetics, it is essential that both trees are drawn without edge crossings and that the inter-tree edges have as few crossings as possible. It is known that finding a tanglegram with the minimum number of crossings is NP-hard and that the problem is fixed-parameter tractable with respect to that number.We prove that under the Unique Games Conjecture there is no constant-factor approximation for binary trees. We show that the problem is NP-hard even if both trees are complete binary trees. For this case we give an O(n 3 )-time 2-approximation and a new, simple fixed-parameter algorithm. We show that the maximization version of the dual problem for binary trees can be reduced to a version of MAXCUT for which the algorithm of Goemans and Williamson yields a 0.878-approximation.

show abstract

Section: Related Problemsmentioning

confidence: 99%

Drawing (Complete) Binary Tanglegrams

Buchin

Byrka

et al. 2009

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…a planar DAG with one source and one sink, both on the outer face [7]. Testing upward planarity is NP-complete [15] but for DAGs with a single source or a single sink it may be tested efficiently [4,21]. However, many DAGs (even planar DAGs such as the one in Figure 2) are not upward planar.…”

Section: Introductionmentioning

confidence: 99%

Confluent Hasse Diagrams

Eppstein¹,

Simons²

2013

JGAA

View full text Add to dashboard Cite

We show that a transitively reduced digraph has a confluent upward drawing if and only if its reachability relation has order dimension at most two. In this case, we construct a confluent upward drawing with O(n 2 ) features, in an O(n) × O(n) grid in O(n 2 ) time. For the digraphs representing series-parallel partial orders we show how to construct a drawing with O(n) features in an O(n) × O(n) grid in O(n) time from a series-parallel decomposition of the partial order. Our drawings are optimal in the number of confluent junctions they use.

show abstract

“…A digraph G is upward planar if it has a planar drawing with all edges pointing monotonically upward [6]. It is NP-hard to test if a digraph G is upward planar [9], hence upward planarity testing is either done for a fixed embedding [3,7], or for special classes of digraphs like single-source digraphs [10,4], series-parallel digraphs [8], and outer planar digraphs [11].…”

Section: Introductionmentioning

confidence: 99%

A Fully Dynamic Algorithm to Test the Upward Planarity of Single-Source Embedded Digraphs

Rextin

Healy

2009

Graph Drawing

View full text Add to dashboard Cite

Abstract. In this paper, we present a dynamic algorithm that checks if a singlesource embedded digraph is upward planar in the presence of edge insertions and edge deletions. Let G φ be an upward planar single-source embedded digraph and let G φ be a single-source embedded digraph obtained by updating G φ . We show that the upward planarity of G φ can be checked in O(log n) amortized time when the external face is fixed.

show abstract

Optimal Upward Planarity Testing of Single-Source Digraphs

Cited by 98 publications

References 26 publications

Drawing (Complete) Binary Tanglegrams

Drawing (Complete) Binary Tanglegrams

Confluent Hasse Diagrams

A Fully Dynamic Algorithm to Test the Upward Planarity of Single-Source Embedded Digraphs

Contact Info

Product

Resources

About