2,262 research outputs found
The Computational Power of Beeps
In this paper, we study the quantity of computational resources (state
machine states and/or probabilistic transition precision) needed to solve
specific problems in a single hop network where nodes communicate using only
beeps. We begin by focusing on randomized leader election. We prove a lower
bound on the states required to solve this problem with a given error bound,
probability precision, and (when relevant) network size lower bound. We then
show the bound tight with a matching upper bound. Noting that our optimal upper
bound is slow, we describe two faster algorithms that trade some state
optimality to gain efficiency. We then turn our attention to more general
classes of problems by proving that once you have enough states to solve leader
election with a given error bound, you have (within constant factors) enough
states to simulate correctly, with this same error bound, a logspace TM with a
constant number of unary input tapes: allowing you to solve a large and
expressive set of problems. These results identify a key simplicity threshold
beyond which useful distributed computation is possible in the beeping model.Comment: Extended abstract to appear in the Proceedings of the International
Symposium on Distributed Computing (DISC 2015
How to Elect a Leader Faster than a Tournament
The problem of electing a leader from among contenders is one of the
fundamental questions in distributed computing. In its simplest formulation,
the task is as follows: given processors, all participants must eventually
return a win or lose indication, such that a single contender may win. Despite
a considerable amount of work on leader election, the following question is
still open: can we elect a leader in an asynchronous fault-prone system faster
than just running a -time tournament, against a strong adaptive
adversary?
In this paper, we answer this question in the affirmative, improving on a
decades-old upper bound. We introduce two new algorithmic ideas to reduce the
time complexity of electing a leader to , using
point-to-point messages. A non-trivial application of our algorithm is a new
upper bound for the tight renaming problem, assigning items to the
participants in expected time and messages. We
complement our results with lower bound of messages for solving
these two problems, closing the question of their message complexity
Convergence of some leader election algorithms
We start with a set of n players. With some probability P(n,k), we kill n-k
players; the other ones stay alive, and we repeat with them. What is the
distribution of the number X_n of phases (or rounds) before getting only one
player? We present a probabilistic analysis of this algorithm under some
conditions on the probability distributions P(n,k), including stochastic
monotonicity and the assumption that roughly a fixed proportion alpha of the
players survive in each round.
We prove a kind of convergence in distribution for X_n-log_a n, where the
basis a=1/alpha; as in many other similar problems there are oscillations and
no true limit distribution, but suitable subsequences converge, and there is an
absolutely continuous random variable Z such that the distribution of X_n can
be approximated by Z+log_a n rounded to the nearest larger integer.
Applications of the general result include the leader election algorithm
where players are eliminated by independent coin tosses and a variation of the
leader election algorithm proposed by W.R. Franklin. We study the latter
algorithm further, including numerical results.Comment: 27 pages, 13 figures, 5 table
Improved Tradeoffs for Leader Election
We consider leader election in clique networks, where nodes are connected
by point-to-point communication links. For the synchronous clique under
simultaneous wake-up, i.e., where all nodes start executing the algorithm in
round , we show a tradeoff between the number of messages and the amount of
time. More specifically, we show that any deterministic algorithm with a
message complexity of requires rounds, for . Our result holds even if
the node IDs are chosen from a relatively small set of size ,
as we are able to avoid using Ramsey's theorem. We also give an upper bound
that improves over the previously-best tradeoff. Our second contribution for
the synchronous clique under simultaneous wake-up is to show that is in fact a lower bound on the message complexity that holds for any
deterministic algorithm with a termination time . We complement this
result by giving a simple deterministic algorithm that achieves leader election
in sublinear time while sending only messages, if the ID space is
of at most linear size. We also show that Las Vegas algorithms (that never
fail) require messages. For the synchronous clique under
adversarial wake-up, we show that is a tight lower bound for
randomized -round algorithms. Finally, we turn our attention to the
asynchronous clique: Assuming adversarial wake-up, we give a randomized
algorithm that achieves a message complexity of and an
asynchronous time complexity of . For simultaneous wake-up, we translate
the deterministic tradeoff algorithm of Afek and Gafni to the asynchronous
model, thus partially answering an open problem they pose
Blockchain moderated by empty blocks to reduce the energetic impact of crypto-moneys
While cryptocurrencies and blockchain applications continue to gain
popularity, their energy cost is evidently becoming unsustainable. In most
instances, the main cost comes from the required amount of energy for the
Proof-of-Work, and this cost is inherent to the design. In addition, useless
costs from discarded work (e.g., the so-called Forks) and lack of scalability
(in number of users and in rapid transactions) limit their practical
effectiveness.
In this paper, we present an innovative scheme which eliminates the nonce and
thus the burden of the Proof-of-Work which is the main cause of the energy
waste in cryptocurrencies such as Bitcoin. We prove that our scheme guarantees
a tunable and bounded average number of simultaneous mining whatever the size
of the population in competition, thus by making the use of nonce-based
techniques unnecessary, achieves scalability without the cost of consuming a
large volume of energy. The technique used in the proof of our scheme is based
on the analogy of the analysis of a green leader election. The additional
difference with Proof-of-Work schemes (beyond the suppression of the nonce
field that is triggering most of the waste), is the introduction of (what we
denote as) "empty blocks" which aim are to call regular blocks following a
staircase set of values. Our scheme reduces the risk of Forks and provides
tunable scalability for the number of users and the speed of block generation.
We also prove using game theoretical analysis that our scheme is resilient to
unfair competitive investments (e.g., "51 percent" attack) and block nursing.Comment: preliminary version appeared in CryBlock'2019, The IEEE 2nd Workshop
on Cryptocurrencies and Blockchains for Distributed Systems (co-located with
INFOCOM 2019), April 29th, 2019. Paris, France. Green Mining: toward a less
energetic impact of cryptocurrencies, P. Jacquet and B. Mans, IEEE Press, 6
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