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Space-Stretch Tradeoff in Routing Revisited

Author Anatoliy Zinovyev

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Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Theory of computation → Data structures design and analysis
  • Mathematics of computing → Discrete mathematics
Keywords
  • Compact routing
  • labeled network routing
  • lower bounds

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Abstract

We present several new proofs of lower bounds for the space-stretch tradeoff in labeled network routing.
First, we give a new proof of an important result of Cyril Gavoille and Marc Gengler that any routing scheme with stretch < 3 must use Ω(n) bits of space at some node on some network with n vertices, even if port numbers can be changed. Compared to the original proof, our proof is significantly shorter and, we believe, conceptually and technically simpler. A small extension of the proof can show that, in fact, any constant fraction of the n nodes must use Ω(n) bits of space on some graph.
Our main contribution is a new result that if port numbers are chosen adversarially, then stretch < 2k+1 implies some node must use Ω(n^(1/k) log n) bits of space on some graph, assuming a girth conjecture by Erdős.
We conclude by showing that all known methods of proving a space lower bound in the labeled setting, in fact, require the girth conjecture.

Cite As Get BibTex

Anatoliy Zinovyev. Space-Stretch Tradeoff in Routing Revisited. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 37:1-37:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.DISC.2022.37

Author Details

Anatoliy Zinovyev
  • Boston University, MA, USA

References

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