On the structure and composition of forbidden sequences, with geometric applications

Forbidden substructure theorems have proved to be among of the most versatile tools in bounding the complexity of geometric objects and the running time of geometric algorithms. To apply them one typically transcribes an algorithm execution or geometric object as a sequence over some alphabet or a 0-1 matrix, proves that this object avoids some subsequence or submatrix σ, then uses an off the shelf bound on the maximum size of such a σ-free object. As a historical trend, expanding our library of forbidden substructure theorems has led to better bounds and simpler analyses of the complexity of geometric objects. We establish new and tight bounds on the maximum length of generalized Davenport-Schinzel sequences, which are those whose subsequences are not isomorphic to some fixed sequence σ. (The standard Davenport-Schinzel sequences restrict σ to be of the form abab · · · .)

• Type: Journal
• Year: 2011
• Where: COMPGEOM
• Authors: Seth Pettie
• Keywords: COMPGEOM 2011, Discrete Geometry, Geometric Algorithms, Geometric Object, Geometric Objects