Resolutions modeled on ternary trees

On an Optimality Property of Ternary Trees

In the book of Knuth (1972) an extensive discussion can be found on some problems concerning rooted trees. Given a prescribed number of end-vertices, one may ask for the binary (or ternary) tree with minimal external path length (i.e. minimal sum of path lengths from the root to end-vertices), or minimal weighted external path length (here the end-vertices have given weights). In the first case...

A Note on Naturally Embedded Ternary Trees

In this note we consider ternary trees naturally embedded in the plane in a deterministic way such that the root has position zero, or in other words label zero, and the children of a node with position j have positions j− 1, j, and j + 1, for all j ∈ Z. We derive the generating function of ternary trees where all nodes have labels which are less or equal than j, with j ∈ N, which generalizes a...

On Embedding Ternary Trees into Boolean Hypercubes

Optimal Alphabetic Ternary Trees

We give a new algorithm to construct optimal alphabetic ternary trees, where every internal node has at most three children. This algorithm generalizes the classic Hu-Tucker algorithm, though the overall computational complexity has yet to be determined.

Clock-Modeled Ternary Spatial Relations for Visual Scene Analysis

The analysis and the description of complex visual scenes characterized by the presence of many objects of interests involve reasoning on spatial relations such as “above”, “below”,“before”, “after” and “between”. In this context, we have defined these semantic concepts in terms of ternary spatial relations and we have formalized them using the clock model which is based on the clock-face divis...