Abstract
A k-fault-tolerant gossip graph is a (multiple) graph whose edges are linearly ordered such that for any ordered pair of vertices u and v, there are k + 1 edge-disjoint ascending paths from u to v. Let τ(n,k) denote the minimum number of edges in a k-fault-tolerant gossip graph with n vertices. In this paper, we present upper and lower bounds on τ(n,k) which improve the previously known bounds. In particular, from our upper bounds, it follows that \(\tau(n,k) \leq \frac{nk}{2} + O(n\log{n})\). Previously, it has been shown that this upper bound holds only for the case that n is a power of two.
This work was supported by JSPS KAKENHI 20500012, 21500017.
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Hasunuma, T., Nagamochi, H. (2011). Improved Bounds for Minimum Fault-Tolerant Gossip Graphs. In: Kolman, P., Kratochvíl, J. (eds) Graph-Theoretic Concepts in Computer Science. WG 2011. Lecture Notes in Computer Science, vol 6986. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25870-1_19
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DOI: https://doi.org/10.1007/978-3-642-25870-1_19
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