Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gracefully Degrading Consensus and $k$-Set Agreement in Directed Dynamic
  Networks   We study distributed agreement in synchronous directed dynamic networks,
where an omniscient message adversary controls the availability of
communication links. We prove that consensus is impossible under a message
adversary that guarantees weak connectivity only, and introduce vertex-stable
root components (VSRCs) as a means for circumventing this impossibility: A
VSRC(k, d) message adversary guarantees that, eventually, there is an interval
of $d$ consecutive rounds where every communication graph contains at most $k$
strongly (dynamic) connected components consisting of the same processes, which
have at most outgoing links to the remaining processes. We present a consensus
algorithm that works correctly under a VSRC(1, 4H + 2) message adversary, where
$H$ is the dynamic causal network diameter. On the other hand, we show that
consensus is impossible against a VSRC(1, H - 1) or a VSRC(2, $\infty$) message
adversary, revealing that there is not much hope to deal with stronger message
adversaries.
  However, we show that gracefully degrading consensus, which degrades to
general $k$-set agreement in case of unfavourable network conditions, is
feasible against stronger message adversaries: We provide a $k$-uniform $k$-set
agreement algorithm, where the number of system-wide decision values $k$ is not
encoded in the algorithm, but rather determined by the actual power of the
message adversary in a run: Our algorithm guarantees at most $k$ decision
values under a VSRC(n, d) + MAJINF(k) message adversary, which combines VSRC(n,
d) (for some small $d$, ensuring termination) with some information flow
guarantee MAJINF(k) between certain VSRCs (ensuring $k$-agreement). Our results
provide a significant step towards the exact solvability/impossibility border
of general $k$-set agreement in directed dynamic networks.

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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph