Maximum upward planar subgraphs of embedded planar digraphs

Authors:
Carla Binucci;Walter Didimo;Francesco Giordano
Affiliations:
Dipartimento di Ingegneria Elettronica e dell'Informazione, Università degli Studi di Perugia, Italy;Dipartimento di Ingegneria Elettronica e dell'Informazione, Università degli Studi di Perugia, Italy;Dipartimento di Ingegneria Elettronica e dell'Informazione, Università degli Studi di Perugia, Italy
Venue:
Computational Geometry: Theory and Applications
Year:
2008

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Abstract

Let G be an embedded planar digraph. A maximum upward planar subgraph of G is an embedding preserving subgraph that is upward planar and, among those, has the maximum number of edges. This paper presents an extensive study on the problem of computing maximum upward planar subgraphs of embedded planar digraphs: Complexity results, algorithms, and experiments are presented. Namely: (i) we prove that the addressed problem is NP-Hard; (ii) a fast heuristic and an exponential-time exact algorithm are described; (iii) a wide experimental analysis is performed to show the effectiveness of our techniques.