Congestion-free, dilation-2 embedding of complete binary trees into star graphs

Yu-Chee Tseng*, Yuh Shyan Chen, Tong Ying Juang, Chiou Jyu Chang

*Corresponding author for this work

Research output: Contribution to journalArticle

19 Scopus citations

Abstract

Trees are a common structure to represent the intertask communication pattern of a parallel algorithm. In this paper, we consider the embedding of a complete binary tree in a star graph with the objective of minimizing congestion and dilation. We develop two embeddings: (i) a congestion-free, dilation-2, load-1 embedding of a level-p binary tree, and (ii) a congestion-free, dilation-2, load-2k embedding of a level-(p + k) binary tree, into an n-dimensional star graph, where p = Σni-2 [log i] = Ω(n log n) and k is any positive integer. The first result offers a tree of size comparable or superior to existing results, but with less congestion and dilation. The second result provides more flexibility in the embeddable tree sizes compared to existing results.

Original languageEnglish
Pages (from-to)221-231
Number of pages11
JournalNetworks
Volume33
Issue number3
DOIs
StatePublished - 1 Jan 1999

Keywords

  • Complete binary tree
  • Graph embedding
  • Interconnection network
  • Parallel processing
  • Star graph

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