On the Complexity of Clustered-Level Planarity and T-Level Planarity
Patrizio Angelini, Giordano Da Lozzo, Giuseppe Di Battista and, Fabrizio Frati, Vincenzo Roselli
TL;DR
This paper investigates the computational complexity of T-Level Planarity and Clustered-Level Planarity problems, establishing NP-completeness in general and polynomial-time solvability for proper instances.
Contribution
It proves NP-completeness of both problems in general and provides polynomial algorithms for proper instances, advancing understanding of level graph drawing complexities.
Findings
NP-complete in general case
Polynomial-time solvable for proper instances
Clarifies complexity boundaries for level graph problems
Abstract
In this paper we study two problems related to the drawing of level graphs, that is, T-LEVEL PLANARITY and CLUSTERED-LEVEL PLANARITY. We show that both problems are NP-complete in the general case and that they become polynomial-time solvable when restricted to proper instances.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Digital Image Processing Techniques · Advanced Graph Theory Research