A Polyhedral Approach to Planar Augmentation and Related Problems (1995)
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BibTeX
@MISC{Mutzel95apolyhedral,
author = {Petra Mutzel},
title = {A Polyhedral Approach to Planar Augmentation and Related Problems},
year = {1995}
}
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Abstract
. Given a planar graph G, the planar (biconnectivity) augmentation problem is to add the minimum number of edges to G such that the resulting graph is still planar and biconnected. Given a nonplanar and biconnected graph, the maximum planar biconnected subgraph problem consists of removing the minimum number of edges so that planarity is achieved and biconnectivity is maintained. Both problems are important in Automatic Graph Drawing. In [JM95], the minimum planarizing k- augmentation problem has been introduced, that links the planarization step and the augmentation step together. Here, we are given a graph which is not necessarily planar and not necessarily k-connected, and we want to delete some set of edges D and to add some set of edges A such that jDj + jAj is minimized and the resulting graph is planar, k-connected and spanning. For all three problems, we have given a polyhedral formulation by defining three different linear objective functions over the same polytope, namely ...
