English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study distributed agreement in synchronous directed dynamic networks,where an omniscient message adversary controls the availability ofcommunication links. We prove that consensus is impossible under a messageadversary that guarantees weak connectivity only, and introduce vertex-stableroot components (VSRCs) as a means for circumventing this impossibility: AVSRC(k, d) message adversary guarantees that, eventually, there is an intervalof $d$ consecutive rounds where every communication graph contains at most $k$strongly (dynamic) connected components consisting of the same processes, whichhave at most outgoing links to the remaining processes. We present a consensusalgorithm 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 thatconsensus is impossible against a VSRC(1, H - 1) or a VSRC(2, $\infty$) messageadversary, revealing that there is not much hope to deal with stronger messageadversaries.  However, we show that gracefully degrading consensus, which degrades togeneral $k$-set agreement in case of unfavourable network conditions, isfeasible against stronger message adversaries: We provide a $k$-uniform $k$-setagreement algorithm, where the number of system-wide decision values $k$ is notencoded in the algorithm, but rather determined by the actual power of themessage adversary in a run: Our algorithm guarantees at most $k$ decisionvalues under a VSRC(n, d) + MAJINF(k) message adversary, which combines VSRC(n,d) (for some small $d$, ensuring termination) with some information flowguarantee MAJINF(k) between certain VSRCs (ensuring $k$-agreement). Our resultsprovide a significant step towards the exact solvability/impossibility borderof general $k$-set agreement in directed dynamic networks.

Gracefully Degrading Consensus and $k$-Set Agreement in Directed Dynamic Networks