5 research outputs found
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
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
Population stability: regulating size in the presence of an adversary
We introduce a new coordination problem in distributed computing that we call
the population stability problem. A system of agents each with limited memory
and communication, as well as the ability to replicate and self-destruct, is
subjected to attacks by a worst-case adversary that can at a bounded rate (1)
delete agents chosen arbitrarily and (2) insert additional agents with
arbitrary initial state into the system. The goal is perpetually to maintain a
population whose size is within a constant factor of the target size . The
problem is inspired by the ability of complex biological systems composed of a
multitude of memory-limited individual cells to maintain a stable population
size in an adverse environment. Such biological mechanisms allow organisms to
heal after trauma or to recover from excessive cell proliferation caused by
inflammation, disease, or normal development.
We present a population stability protocol in a communication model that is a
synchronous variant of the population model of Angluin et al. In each round,
pairs of agents selected at random meet and exchange messages, where at least a
constant fraction of agents is matched in each round. Our protocol uses
three-bit messages and states per agent. We emphasize that
our protocol can handle an adversary that can both insert and delete agents, a
setting in which existing approximate counting techniques do not seem to apply.
The protocol relies on a novel coloring strategy in which the population size
is encoded in the variance of the distribution of colors. Individual agents can
locally obtain a weak estimate of the population size by sampling from the
distribution, and make individual decisions that robustly maintain a stable
global population size