1 research outputs found
Optimal Computation in Leaderless and Multi-Leader Disconnected Anonymous Dynamic Networks
We give a simple characterization of which functions can be computed
deterministically by anonymous processes in disconnected dynamic networks,
depending on the number of leaders in the network. In addition, we provide
efficient distributed algorithms for computing all such functions assuming
minimal or no knowledge about the network. Each of our algorithms comes in two
versions: one that terminates with the correct output and a faster one that
stabilizes on the correct output without explicit termination. Notably, these
are the first deterministic algorithms whose running times scale linearly with
both the number of processes and a parameter of the network which we call
"dynamic disconnectivity". We also provide matching lower bounds, showing that
all our algorithms are asymptotically optimal for any fixed number of leaders.
While most of the existing literature on anonymous dynamic networks relies on
classical mass-distribution techniques, our work makes use of a recently
introduced combinatorial structure called "history tree", also developing its
theory in new directions. Among other contributions, our results make
definitive progress on two popular fundamental problems for anonymous dynamic
networks: leaderless Average Consensus (i.e., computing the mean value of input
numbers distributed among the processes) and multi-leader Counting (i.e.,
determining the exact number of processes in the network). In fact, our
approach unifies and improves upon several independent lines of research on
anonymous networks, including Nedic et al., IEEE Trans. Automat. Contr. 2009;
Olshevsky, SIAM J. Control Optim. 2017; Kowalski-Mosteiro, ICALP 2019, SPAA
2021; Di Luna-Viglietta, FOCS 2022.Comment: 35 pages, 1 figure. arXiv admin note: text overlap with
arXiv:2204.0212