eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-10-17
37:1
37:16
10.4230/LIPIcs.DISC.2022.37
article
Space-Stretch Tradeoff in Routing Revisited
Zinovyev, Anatoliy
1
Boston University, MA, USA
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol246-disc2022/LIPIcs.DISC.2022.37/LIPIcs.DISC.2022.37.pdf
Compact routing
labeled network routing
lower bounds