Automated Lattice Drawing

13 years 9 months ago

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Lattice diagrams, known as Hasse diagrams, have played an ever increasing role in lattice theory and ﬁelds that use lattices as a tool. Initially regarded with suspicion, they now play an important role in both pure lattice theory and in data representation. Now that lattices can be created by software, it is important to have software that can automatically draw them. This paper covers: – The role and history of the diagram. – What constitutes a good diagram. – Algorithms to produce good diagrams. Recent work on software incorporating these algorithms into a drawing program will also be covered. An ordered set P = (P, ≤) consists of a set P and a partial order relation ≤ on P. That is, the relation ≤ is reﬂexive (x ≤ x), transitive (x ≤ y and y ≤ z imply x ≤ z) and antisymmetric (x ≤ y and y ≤ x imply x = y). If P is ﬁnite there is a unique smallest relation , known as the cover or neighbor relation, whose transitive, reﬂexive closure is ≤. (Graph the...

Ralph Freese

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