A Sample-Based Algorithm for Approximately Testing $r$-Robustness of a Digraph

25 Jul 2022  ·  Yuhao Yi, YuAn Wang, Xingkang He, Stacy Patterson, Karl H. Johansson ·

One of the intensely studied concepts of network robustness is $r$-robustness, which is a network topology property quantified by an integer $r$. It is required by mean subsequence reduced (MSR) algorithms and their variants to achieve resilient consensus. However, determining $r$-robustness is intractable for large networks. In this paper, we propose a sample-based algorithm to approximately test $r$-robustness of a digraph with $n$ vertices and $m$ edges. For a digraph with a moderate assumption on the minimum in-degree, and an error parameter $0<\epsilon\leq 1$, the proposed algorithm distinguishes $(r+\epsilon n)$-robust graphs from graphs which are not $r$-robust with probability $(1-\delta)$. Our algorithm runs in $\exp(O((\ln{\frac{1}{\epsilon\delta}})/\epsilon^2))\cdot m$ time. The running time is linear in the number of edges if $\epsilon$ is a constant.

PDF Abstract
No code implementations yet. Submit your code now

Tasks


Datasets


  Add Datasets introduced or used in this paper

Results from the Paper


  Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.

Methods