Embeddings in recursive combinatorial networks

  • Sajal K. Das
  • Aisheng Mao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 657)


This paper, evolved from an interplay between interconnection topology and combinatorics, is of interest to network designers and graph theorists. From combinatorial principles, we have recently designed a new family of labeled networks, called Recursive Combinatorial Networks (RCN's). These bipartite networks are recursive in nature with incrementability of one and succinctly representable. They have low diameter (equal to three), good fault-tolerance, and high degree of symmetry. In this paper we show that several standard interconnection topologies can be embedded in RCNs with dilation of one. For example, t-dimensional hypercube (Qt) is a subgraph of RCN of 2t vertices. Rings of even lengths are also embeddable. We provide an algorithm to systematically construct two isomorphic, embedded full binary trees (FBT's) in RCN's with expansion of two. A routing scheme is designed which resolves the root congestion problem in such binary trees. Finally, an m× m mesh is embedded in RCN's with dilation of one and expansion of 2km, where 2k−1 < m ≤ 2k for k ≥ 2.

Key words

Interconnection networks bipartite graphs combinatorial networks embedding hypercube full binary trees mesh congestion-free routing 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Sajal K. Das
    • 1
  • Aisheng Mao
    • 1
  1. 1.Department of Computer ScienceUniversity of North TexasDentonUSA

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