Embedding certain height-balanced trees and completepm-ary trees into hypercubes

On Embedding of m-Sequential k-ary Trees into Hypercubes

In this paper, we present an algorithm for embedding an m-sequential k-ary tree into its optimal hypercube with dilation at most 2 and prove its correctness.

Embedding complete ternary trees into hypercubes

We inductively describe an embedding of a complete ternary tree Th of height h into a hypercube Q of dimension at most d(1.6)he + 1 with load 1, dilation 2, node congestion 2 and edge congestion 2. This is an improvement over the known embedding of Th into Q. And it is very close to a conjectured embedding of Havel [3] which states that there exists an embedding of Th into its optimal hypercube...

On Embedding Binary Trees into Hypercubes

Hypercubes are known to be able to simulate other structures such as grids and binary trees. It has been shown that an arbitrary binary tree can be embedded into a hypercube with constant expansion and constant dilation. This paper presents a simple linear-time heuristic which embeds an arbitrary binary tree into a hypercube with expansion 1 and average dilation no more than 2. We also give som...

On Embedding Ternary Trees into Boolean Hypercubes

Embedding of Hypercubes into Complete Binary Trees

We estimate and characterize the edge congestion-sum measure for embeddings of hypercubes into complete binary trees. Our algorithms produce optimal values of sum of edge-congestions in linear time.