On Oriented Embedding of the Dichotomic Tree into the Hypercube
نویسنده
چکیده
We consider the oriented dichotomic tree and the oriented hypercube. The tree edges are oriented from the root to the leaves, while the orientation of the cube edges is induced by the direction from 0 to 1 in the coordinatewise form. The problem is to embed such a tree with l levels into the oriented n-cube as an oriented subgraph, for minimal possible n. A new approach to such problems is presented, which improves the known upper bound n/l ≤ 3/2 from [1] to n/l ≤ 4/3 + o(1) as l →∞.
منابع مشابه
Optimal Dynamic Edge-Disjoint Embeddings of Complete Binary Trees into Hypercubes
The double-rooted complete binary tree is a complete binary tree where the path (of length ) between the children of the root is replaced by a path of length . It is folklore that the double-rooted complete binary tree is a spanning tree of the hypercube of the same size. Unfortunately, the usual construction of an embedding of a double-rooted complete binary tree into the hypercube does not pr...
متن کاملEmbedding 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...
متن کاملEmbedding Graphs with Bounded Treewidth into Optimal Hypercubes
In this paper, we present a one-to-one embedding of a graph with bounded treewidth into its optimal hypercube. This is the first time that embeddings of graphs with a very irregular structure into hypercubes are investigated. The dilation of the presented embedding is bounded by , where denotes the treewidth of the graph and denotes the maximal degree of a vertex in the graph. The given embeddi...
متن کاملHierarchical Networks Into The Hypercube
The embedding of one interconnection network into another is a very important issue in the design and analysis of parallel algorithms. Through such embeddings the algorithms originally developed for one architecture can be directly mapped to another architecture. This paper describes novel methods for the embedding of hierarchical interconnection networks in the hypercube to minimize the dilati...
متن کاملEmbedding of Tree Machines into Hypercubes
In this paper, we present that a tree machine can be embedded into incomplete hypercube with expansion 1, load 1, dilation 2 and congestion 2. This result is better than the expansion (2+2)/(2+2-2) in [14]. Then we consider how to embed a large tree machine into a hypercube for considering load-balance. We have shown that a tree machine TMh (h1) can be embedded into a hypercube Hh+1 with dilat...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002