10,977 research outputs found
Investigating the Cost of Anonymity on Dynamic Networks
In this paper we study the difficulty of counting nodes in a synchronous
dynamic network where nodes share the same identifier, they communicate by
using a broadcast with unlimited bandwidth and, at each synchronous round,
network topology may change. To count in such setting, it has been shown that
the presence of a leader is necessary. We focus on a particularly interesting
subset of dynamic networks, namely \textit{Persistent Distance} - PD, in which each node has a fixed distance from the leader across
rounds and such distance is at most . In these networks the dynamic diameter
is at most . We prove the number of rounds for counting in PD is at least logarithmic with respect to the network size .
Thanks to this result, we show that counting on any dynamic anonymous network
with constant w.r.t. takes at least
rounds where represents the additional cost to be
payed for handling anonymity. At the best of our knowledge this is the fist non
trivial, i.e. different from , lower bounds on counting in anonymous
interval connected networks with broadcast and unlimited bandwith
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
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
Polynomial Counting in Anonymous Dynamic Networks with Applications to Anonymous Dynamic Algebraic Computations
Starting with Michail, Chatzigiannakis, and Spirakis work [Michail et al., 2013], the problem of Counting the number of nodes in {Anonymous Dynamic Networks} has attracted a lot of attention. The problem is challenging because nodes are indistinguishable (they lack identifiers and execute the same program) and the topology may change arbitrarily from round to round of communication, as long as the network is connected in each round. The problem is central in distributed computing as the number of participants is frequently needed to make important decisions, such as termination, agreement, synchronization, and many others. A variety of algorithms built on top of mass-distribution techniques have been presented, analyzed, and also experimentally evaluated; some of them assumed additional knowledge of network characteristics, such as bounded degree or given upper bound on the network size. However, the question of whether Counting can be solved deterministically in sub-exponential time remained open. In this work, we answer this question positively by presenting Methodical Counting, which runs in polynomial time and requires no knowledge of network characteristics. Moreover, we also show how to extend Methodical Counting to compute the sum of input values and more complex functions without extra cost. Our analysis leverages previous work on random walks in evolving graphs, combined with carefully chosen alarms in the algorithm that control the process and its parameters. To the best of our knowledge, our Counting algorithm and its extensions to other algebraic and Boolean functions are the first that can be implemented in practice with worst-case guarantees
Polynomial Anonymous Dynamic Distributed Computing Without a Unique Leader
Counting the number of nodes in {Anonymous Dynamic Networks} is enticing from an algorithmic perspective: an important computation in a restricted platform with promising applications. Starting with Michail, Chatzigiannakis, and Spirakis [Michail et al., 2013], a flurry of papers sped up the running time guarantees from doubly-exponential to polynomial [Dariusz R. Kowalski and Miguel A. Mosteiro, 2018]. There is a common theme across all those works: a distinguished node is assumed to be present, because Counting cannot be solved deterministically without at least one.
In the present work we study challenging questions that naturally follow: how to efficiently count with more than one distinguished node, or how to count without any distinguished node. More importantly, what is the minimal information needed about these distinguished nodes and what is the best we can aim for (count precision, stochastic guarantees, etc.) without any. We present negative and positive results to answer these questions. To the best of our knowledge, this is the first work that addresses them
On deterministic counting in anonymous dynamic networks
Nella tesi di dottorato si analizza il problema del counting in reti anonime dinamiche ed interval connesse. Vengono dimostrati lower bound non triviali sul tempo di conteggio in reti a diametro costante. Inoltre vengono sviluppati nuovi algoritmi di conteggio.Counting is a fundamental problem of every distributed system as it represents a basic building block to implement high level abstractions [2,4,6]. We focus on deterministic counting algorithms, that is we assume that no source of randomness is available to processes. We consider a dynamic system where processes do not leave the compu- tation while there is an adversary that continuously changes the communication graph connecting such processes. The adversary is only constrained to maintain at each round a connected topology, i.e. 1-interval connectivity G(1-IC) [3]. In such environment, it has been shown, [5], that counting cannot be solved without a leader. Therefore, we assume that all processes are anonymous but the distinguished leader.
In the thesis we will discuss bounds and algorithms for counting in the aforementioned framework. Our bounds are obtained investigating networks where the distance between the leader and an anonymous process is persistent across rounds and is at most h, we denote such networks as G(PD)h [1]. Interestingly we will show that counting in G(PD)2 requires Ω(log |V |) rounds even when the bandwidth is unlimited. This implies that counting in networks with constant dynamic diameter requires a number of rounds that is function of the network size. We will discuss other results concerning the accuracy of counting algorithms.
For the possibility side we will show an optimal counting algorithm for G(PD)h networks and a counting algorithm for G(1-IC) networks
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
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