Problem: Give a drawing of graph G which accurately reflects its structure.
Excerpt from The Algorithm Design Manual: Drawing graphs nicely is a problem that constantly arises in applications, such as displaying file directory trees or circuit schematic diagrams.Yet it is inherently ill-defined. What exactly does nicely mean? We seek an algorithm that shows off the structure of the graph so the viewer can best understand it. We also seek a drawing that looks aesthetically pleasing. Unfortunately, these are ``soft'' criteria for which it is impossible to design an optimization algorithm. Indeed, it is possible to come up with two or more radically different drawings of certain graphs and have each be most appropriate in certain contexts.
Several ``hard'' criteria can partially measure the quality of a drawing:
Unfortunately, these goals are mutually contradictory, and the problem of finding the best drawing under any nonempty subset of them will likely be NP-complete.
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