1. UPWARD SPIRALITY AND UPWARD PLANARITY TESTING.
- Author
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Didimo, Walter, Giordano, Francesco, and Liotta, Giuseppe
- Subjects
ALGORITHMS ,GRAPH theory ,GRAPHIC methods ,MATHEMATICAL analysis ,PLANE geometry ,NUMBER theory - Abstract
A digraph is upward planar if it admits a planar drawing where all edges are monotone in the upward direction. It is known that the problem of testing a digraph for upward planarity is NP-complete in general. This paper describes an O(n
4 )-time upward planarity testing algorithm for all digraphs that have a series-parallel structure, where n is the number of vertices of the input. This significantly enlarges the family of digraphs for which a polynomial-time testing algorithm is known. Furthermore, the study is extended to general digraphs, and a fixed parameter tractable algorithm for upward planarity testing is described, whose time complexity is O(dt · t · n3 + d · t2 · n + d2 · n2 ) where t is the number of triconnected components of the digraph and d is an upper bound on the diameter of any split component of the digraph. Our results use the new notion of upward spirality that, informally speaking, is a measure of the "level of winding" that a triconnected component of a digraph G can have in an upward planar drawing of G. [ABSTRACT FROM AUTHOR]- Published
- 2009
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