Dense sets and embedding binary trees into hypercubes

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

“…jF 2 j > 0, then we apply Lemma 2.7(5), if jF 2 j ! jF 1 j > 0, then we apply Lemma 2.7(6), and if F 1 ¼ ; or F 2 ¼ ;, then we apply Lemma 2.7(7) and (8). In each case we obtain PathðA; A; B; F Þ.…”

“…The key tool for a construction of optimal embeddings of caterpillars and ladders in [3], [6] and [7] is a construction of hamiltonian cycles and paths in subcubes or in dense sets with special properties (having a family of prescribed edges). An analogous technique was used by T. Dvořák in [8]. Continuing the theme of these articles, here we study an abstract version of the problem-a construction of hamiltonian paths and cycles in subcubes and dense sets with prescribed family of edges.…”

A Tight Bound for Congestion of an Embedding

“…An embedding with a large congestion faces many problems, such as long communication delay, circuit switching and the existence of different types of uncontrolled noise. Therefore, a minimum congestion is a most desirable feature in network embedding [3]. Congestion of an embedding has been well studied for a number of networks [4][5][6][7][8].…”

On embedding subclasses of height-balanced trees in hypercubes

“…They naturally arise in the design of parallel algorithms which require basic operations like merging, sorting and searching. Hence, there is a large literature on embeddings of various kinds of trees into the graphs of interconnection networks; see [4,[6][7][8][9][10][11][14][15][16]19,22,24,25]. In particular, embeddings of binary trees into hypercubes have received special attention since they naturally arise as the computational structures of algorithms that employ divide and conquer paradigm; see Knuth [17].…”