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A Rigorous Proof on Circular Wirelength for Hypercubes

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Abstract

We study embeddings of the n-dimensional hypercube into the circuit with 2n vertices. We prove that the circular wirelength attains a minimum by gray coding; that was called the CT conjecture by Chavez and Trapp (Discrete Applied Mathematics, 1998). This problem had claimed to be settled by Ching-Jung Guu in her doctoral dissertation “The circular wirelength problem for hypercubes” (University of California, Riverside, 1997). Many argue there are gaps in her proof. We eliminate the gaps in her dissertation.

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Authors and Affiliations

  1. School of Computer Science and Technology, Beijing Institute of Technology, Beijing, 100081, China

    Qinghui Liu  (刘庆晖) & Zhiyi Tang  (唐志毅)

Authors
  1. Qinghui Liu  (刘庆晖)
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  2. Zhiyi Tang  (唐志毅)
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Corresponding authors

Correspondence to Qinghui Liu  (刘庆晖) or Zhiyi Tang  (唐志毅).

Additional information

The first author was supported by the NSFC (11871098).

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Liu, Q., Tang, Z. A Rigorous Proof on Circular Wirelength for Hypercubes. Acta Math Sci 43, 919–941 (2023). https://doi.org/10.1007/s10473-023-0223-3

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  • DOI: https://doi.org/10.1007/s10473-023-0223-3

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