Log In Sign Up

Dynamic Schnyder Woods

by   Sujoy Bhore, et al.

A realizer, commonly known as Schnyder woods, of a triangulation is a partition of its interior edges into three oriented rooted trees. A flip in a realizer is a local operation that transforms one realizer into another. Two types of flips in a realizer have been introduced: colored flips and cycle flips. A corresponding flip graph is defined for each of these two types of flips. The vertex sets are the realizers, and two realizers are adjacent if they can be transformed into each other by one flip. In this paper we study the relation between these two types of flips and their corresponding flip graphs. We show that a cycle flip can be obtained from linearly many colored flips. We also prove an upper bound of O(n^2) on the diameter of the flip graph of realizers defined by colored flips. In addition, a data structure is given to dynamically maintain a realizer over a sequence of colored flips which supports queries, including getting a node's barycentric coordinates, in O(log n) time per flip or query.


page 1

page 2

page 3

page 4


Cycle Intersection Graphs and Minimum Decycling Sets of Even Graphs

We introduce the cycle intersection graph of a graph, an adaptation of t...

Random 2-cell embeddings of multistars

By using permutation representations of maps, one obtains a bijection be...

Bounds on the Diameter of Graph Associahedra

Graph associahedra are generalized permutohedra arising as special cases...

Dynamic Planar Point Location in External Memory

In this paper we describe a fully-dynamic data structure for the planar ...

Treedepth vs circumference

The circumference of a graph G is the length of a longest cycle in G, or...

An Upper Bound for Sorting R_n with LRE

A permutation π over alphabet Σ = 1,2,3,...,n, is a sequence where every...

Folding and Unfolding on Metagraphs

Typed metagraphs are defined as hypergraphs with types assigned to hyper...