Dense sets and embedding binary trees into hypercubes

Authors:
Tomáš Dvořák
Affiliations:
Faculty of Mathematics and Physics, Charles University, Malostranské nám. 25, 11800 Praha, Czech Republic
Venue:
Discrete Applied Mathematics
Year:
2007

Citing 5
Cited 5

Embedding trees in a hypercube is NP-complete

SIAM Journal on Computing
Introduction to parallel algorithms and architectures: array, trees, hypercubes

Introduction to parallel algorithms and architectures: array, trees, hypercubes
A new efficient algorithm for embedding an arbitrary binary tree into its optimal hypercube

Journal of Algorithms
Optimal embeddings of odd ladders into a hypercube

Discrete Applied Mathematics
Hamiltonian cycles and paths with a prescribed set of edges in hypercubes and dense sets

Journal of Graph Theory

On embedding subclasses of height-balanced trees in hypercubes

Information Sciences: an International Journal
Panconnectivity and edge-pancyclicity of k-ary n-cubes with faulty elements

Discrete Applied Mathematics
Embedding hypercubes into cylinders, snakes and caterpillars for minimizing wirelength

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Embedding of hypercubes into necklace, windmill and snake graphs

Information Processing Letters
Wirelength of hypercubes into certain trees

Discrete Applied Mathematics

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Abstract

The purpose of this paper is to describe a method for embedding binary trees into hypercubes based on an iterative embedding into their subgraphs induced by dense sets. As a particular application, we present a class of binary trees, defined in terms of size of their subtrees, whose members allow a dilation two embedding into their optimal hypercubes. This provides a partial evidence in favor of a long-standing conjecture of Bhatt and Ipsen which claims that such an embedding exists for an arbitrary binary tree.