6,375 research outputs found
Non Trivial Computations in Anonymous Dynamic Networks
In this paper we consider a static set of anonymous processes, i.e., they do not have distinguished IDs, that communicate with neighbors using a local broadcast primitive. The communication graph changes at each computational round with the restriction of being always connected, i.e., the network topology guarantees 1-interval connectivity. In such setting non trivial computations, i.e., answering to a predicate like "there exists at least one process with initial input a?", are impossible. In a recent work, it has been conjectured that the impossibility holds even if a distinguished leader process is available within the computation. In this paper we prove that the conjecture is false. We show this result by implementing a deterministic leader-based terminating counting algorithm. In order to build our counting algorithm we first develop a counting technique that is time optimal on a family of dynamic graphs where each process has a fixed distance h from the leader and such distance does not change along rounds. Using this technique we build an algorithm that counts in anonymous 1-interval connected networks
A Faster Counting Protocol for Anonymous Dynamic Networks
We study the problem of counting the number of nodes in a slotted-time
communication network, under the challenging assumption that nodes do not have
identifiers and the network topology changes frequently. That is, for each time
slot links among nodes can change arbitrarily provided that the network is
always connected. Tolerating dynamic topologies is crucial in face of mobility
and unreliable communication whereas, even if identifiers are available, it
might be convenient to ignore them in massive networks with changing topology.
Counting is a fundamental task in distributed computing since knowing the size
of the system often facilitates the design of solutions for more complex
problems. Currently, the best upper bound proved on the running time to compute
the exact network size is double-exponential. However, only linear complexity
lower bounds are known, leaving open the question of whether efficient Counting
protocols for Anonymous Dynamic Networks exist or not. In this paper we make a
significant step towards answering this question by presenting a distributed
Counting protocol for Anonymous Dynamic Networks which has exponential time
complexity. Our algorithm ensures that eventually every node knows the exact
size of the system and stops executing the algorithm. Previous Counting
protocols have either double-exponential time complexity, or they are
exponential but do not terminate, or terminate but do not provide running-time
guarantees, or guarantee only an exponential upper bound on the network size.
Other protocols are heuristic and do not guarantee the correct count
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
Termination Detection of Local Computations
Contrary to the sequential world, the processes involved in a distributed
system do not necessarily know when a computation is globally finished. This
paper investigates the problem of the detection of the termination of local
computations. We define four types of termination detection: no detection,
detection of the local termination, detection by a distributed observer,
detection of the global termination. We give a complete characterisation
(except in the local termination detection case where a partial one is given)
for each of this termination detection and show that they define a strict
hierarchy. These results emphasise the difference between computability of a
distributed task and termination detection. Furthermore, these
characterisations encompass all standard criteria that are usually formulated :
topological restriction (tree, rings, or triangu- lated networks ...),
topological knowledge (size, diameter ...), and local knowledge to distinguish
nodes (identities, sense of direction). These results are now presented as
corollaries of generalising theorems. As a very special and important case, the
techniques are also applied to the election problem. Though given in the model
of local computations, these results can give qualitative insight for similar
results in other standard models. The necessary conditions involve graphs
covering and quasi-covering; the sufficient conditions (constructive local
computations) are based upon an enumeration algorithm of Mazurkiewicz and a
stable properties detection algorithm of Szymanski, Shi and Prywes
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