eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-02-01
20:1
20:22
10.4230/LIPIcs.ITCS.2023.20
article
Epic Fail: Emulators Can Tolerate Polynomially Many Edge Faults for Free
Bodwin, Greg
1
Dinitz, Michael
2
Nazari, Yasamin
3
University of Michigan, Ann Arbor, MI, USA
Johns Hopkins University, Baltimore, MD, USA
Universität Salzburg, Austria
A t-emulator of a graph G is a graph H that approximates its pairwise shortest path distances up to multiplicative t error. We study fault tolerant t-emulators, under the model recently introduced by Bodwin, Dinitz, and Nazari [ITCS 2022] for vertex failures. In this paper we consider the version for edge failures, and show that they exhibit surprisingly different behavior.
In particular, our main result is that, for (2k-1)-emulators with k odd, we can tolerate a polynomial number of edge faults for free. For example: for any n-node input graph, we construct a 5-emulator (k = 3) on O(n^{4/3}) edges that is robust to f = O(n^{2/9}) edge faults. It is well known that Ω(n^{4/3}) edges are necessary even if the 5-emulator does not need to tolerate any faults. Thus we pay no extra cost in the size to gain this fault tolerance. We leave open the precise range of free fault tolerance for odd k, and whether a similar phenomenon can be proved for even k.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol251-itcs2023/LIPIcs.ITCS.2023.20/LIPIcs.ITCS.2023.20.pdf
Emulators
Fault Tolerance
Girth Conjecture