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Drawing Graphs Nicely (with Minimum Depth)
There are different ways of drawing a planar graph. This thesis is about a way to choose a specific drawing between others. This problem is one of the most intriguing of the graph drawing research area and known algorithms to produce nice drawings are so complex that are seldom implemented.
In a planar drawing of a graph the plane is partitioned into faces, connected regions surrounded by edges. One face of the is called the external face and is unbounded. All other faces have finite area and are called internal. One of the criteria that can be used measure the readability of a drawing is the fact that the internal faces should be "near" the external one. In fact, faces that share an edge are called adjacent. Two adjacent face are said to be at distance 1. The concept of distance between faces induces the following problem: is there a way to find a planar drawing such that the maximum distance between an internal face and the external one is minimized?
This problem was shown to be polynomial by Bienstock and Monma in the paper "On the complexity of embedding planar graphs to minimize certain distance measures" (Algorithmica 5, 93-109, 1990). The purpose of this thesis is to implement and test the algorithm introduced by these authors starting from a pseudo-code description of it.
The implementation should be in C++ and should be part of the GDToolkit Library.