340 research outputs found
Avatar: A Time- and Space-Efficient Self-Stabilizing Overlay Network
Overlay networks present an interesting challenge for fault-tolerant
computing. Many overlay networks operate in dynamic environments (e.g. the
Internet), where faults are frequent and widespread, and the number of
processes in a system may be quite large. Recently, self-stabilizing overlay
networks have been presented as a method for managing this complexity.
\emph{Self-stabilizing overlay networks} promise that, starting from any
weakly-connected configuration, a correct overlay network will eventually be
built. To date, this guarantee has come at a cost: nodes may either have high
degree during the algorithm's execution, or the algorithm may take a long time
to reach a legal configuration. In this paper, we present the first
self-stabilizing overlay network algorithm that does not incur this penalty.
Specifically, we (i) present a new locally-checkable overlay network based upon
a binary search tree, and (ii) provide a randomized algorithm for
self-stabilization that terminates in an expected polylogarithmic number of
rounds \emph{and} increases a node's degree by only a polylogarithmic factor in
expectation
Tight Bounds for MIS in Multichannel Radio Networks
Daum et al. [PODC'13] presented an algorithm that computes a maximal
independent set (MIS) within
rounds in an -node multichannel radio network with communication
channels. The paper uses a multichannel variant of the standard graph-based
radio network model without collision detection and it assumes that the network
graph is a polynomially bounded independence graph (BIG), a natural
combinatorial generalization of well-known geographic families. The upper bound
of that paper is known to be optimal up to a polyloglog factor.
In this paper, we adapt algorithm and analysis to improve the result in two
ways. Mainly, we get rid of the polyloglog factor in the runtime and we thus
obtain an asymptotically optimal multichannel radio network MIS algorithm. In
addition, our new analysis allows to generalize the class of graphs from those
with polynomially bounded local independence to graphs where the local
independence is bounded by an arbitrary function of the neighborhood radius.Comment: 37 pages, to be published in DISC 201
Fast and Compact Distributed Verification and Self-Stabilization of a DFS Tree
We present algorithms for distributed verification and silent-stabilization
of a DFS(Depth First Search) spanning tree of a connected network. Computing
and maintaining such a DFS tree is an important task, e.g., for constructing
efficient routing schemes. Our algorithm improves upon previous work in various
ways. Comparable previous work has space and time complexities of bits per node and respectively, where is the highest
degree of a node, is the number of nodes and is the diameter of the
network. In contrast, our algorithm has a space complexity of bits
per node, which is optimal for silent-stabilizing spanning trees and runs in
time. In addition, our solution is modular since it utilizes the
distributed verification algorithm as an independent subtask of the overall
solution. It is possible to use the verification algorithm as a stand alone
task or as a subtask in another algorithm. To demonstrate the simplicity of
constructing efficient DFS algorithms using the modular approach, We also
present a (non-sielnt) self-stabilizing DFS token circulation algorithm for
general networks based on our silent-stabilizing DFS tree. The complexities of
this token circulation algorithm are comparable to the known ones
An Improved Approximate Consensus Algorithm in the Presence of Mobile Faults
This paper explores the problem of reaching approximate consensus in
synchronous point-to-point networks, where each pair of nodes is able to
communicate with each other directly and reliably. We consider the mobile
Byzantine fault model proposed by Garay '94 -- in the model, an omniscient
adversary can corrupt up to nodes in each round, and at the beginning of
each round, faults may "move" in the system (i.e., different sets of nodes may
become faulty in different rounds). Recent work by Bonomi et al. '16 proposed a
simple iterative approximate consensus algorithm which requires at least
nodes. This paper proposes a novel technique of using "confession" (a mechanism
to allow others to ignore past behavior) and a variant of reliable broadcast to
improve the fault-tolerance level. In particular, we present an approximate
consensus algorithm that requires only nodes, an
improvement over the state-of-the-art algorithms.
Moreover, we also show that the proposed algorithm is optimal within a family
of round-based algorithms
Grover's Quantum Search Algorithm and Diophantine Approximation
In a fundamental paper [Phys. Rev. Lett. 78, 325 (1997)] Grover showed how a
quantum computer can find a single marked object in a database of size N by
using only O(N^{1/2}) queries of the oracle that identifies the object. His
result was generalized to the case of finding one object in a subset of marked
elements. We consider the following computational problem: A subset of marked
elements is given whose number of elements is either M or K, M<K, our task is
to determine which is the case. We show how to solve this problem with a high
probability of success using only iterations of Grover's basic step (and no
other algorithm). Let m be the required number of iterations; we prove that
under certain restrictions on the sizes of M and K the estimation m <
(2N^{1/2})/(K^{1/2}-M^{1/2}) obtains. This bound sharpens previous results and
is known to be optimal up to a constant factor. Our method involves
simultaneous Diophantine approximations, so that Grover's algorithm is
conceptualized as an orbit of an ergodic automorphism of the torus. We comment
on situations where the algorithm may be slow, and note the similarity between
these cases and the problem of small divisors in classical mechanics.Comment: 8 pages, revtex, Title change
Self-stabilizing virtual synchrony
Virtual synchrony (VS) is an important abstraction that is proven to be extremely useful when implemented over asynchronous, typically large, message-passing distributed systems. Fault tolerant design is critical for the success of such implementations since large distributed systems can be highly available as long as they do not depend on the full operational status of every system participant. Self-stabilizing systems can tolerate transient faults that drive the system to an arbitrary unpredictable configuration. Such systems automatically regain consistency from any such configuration, and then produce the desired system behavior ensuring it for practically infinite number of successive steps, e.g., 264 steps. We present a new multi-purpose self-stabilizing counter algorithm establishing an efficient practically unbounded counter, that can directly yield a self-stabilizing Multiple-Writer Multiple-Reader (MWMR) register emulation. We use our counter algorithm, together with a selfstabilizing group membership and a self-stabilizing multicast service to devise the first practically stabilizing VS algorithm and a self-stabilizing VS-based emulation of state machine replication (SMR). As we base the SMR implementation on VS, rather than consensus, the system progresses in more extreme asynchronous settings in relation to consensusbased SMR
Local Charge of the nu=5/2 Fractional Quantum Hall State
Electrons in two dimensions and strong magnetic fields effectively lose their
kinetic energy and display exotic behavior dominated by Coulomb forces. When
the ratio of electrons to magnetic flux quanta in the system is near 5/2, the
unique correlated phase that emerges is predicted to be gapped with
fractionally charged quasiparticles and a ground state degeneracy that grows
exponentially as these quasiparticles are introduced. Interestingly, the only
way to transform between the many ground states would be to braid the
fractional excitations around each other, a property with applications in
quantum information processing. Here we present the first observation of
localized quasiparticles at nu=5/2, confined to puddles by disorder. Using a
local electrometer to compare how quasiparticles at nu=5/2 and nu=7/3 charge
these puddles, we are able to extract the ratio of local charges for these
states. Averaged over several disorder configurations and samples, we find the
ratio to be 4/3, suggesting that the local charges are e/3 at seven thirds and
e/4 at five halves, in agreement with theoretical predictions. This
confirmation of localized e/4 quasiparticles is necessary for proposed
interferometry experiments to test statistics and computational ability of the
state at nu=5/2.Comment: 6 pages, 4 figures corrected titl
Peer-to-Peer Secure Multi-Party Numerical Computation Facing Malicious Adversaries
We propose an efficient framework for enabling secure multi-party numerical
computations in a Peer-to-Peer network. This problem arises in a range of
applications such as collaborative filtering, distributed computation of trust
and reputation, monitoring and other tasks, where the computing nodes is
expected to preserve the privacy of their inputs while performing a joint
computation of a certain function. Although there is a rich literature in the
field of distributed systems security concerning secure multi-party
computation, in practice it is hard to deploy those methods in very large scale
Peer-to-Peer networks. In this work, we try to bridge the gap between
theoretical algorithms in the security domain, and a practical Peer-to-Peer
deployment.
We consider two security models. The first is the semi-honest model where
peers correctly follow the protocol, but try to reveal private information. We
provide three possible schemes for secure multi-party numerical computation for
this model and identify a single light-weight scheme which outperforms the
others. Using extensive simulation results over real Internet topologies, we
demonstrate that our scheme is scalable to very large networks, with up to
millions of nodes. The second model we consider is the malicious peers model,
where peers can behave arbitrarily, deliberately trying to affect the results
of the computation as well as compromising the privacy of other peers. For this
model we provide a fourth scheme to defend the execution of the computation
against the malicious peers. The proposed scheme has a higher complexity
relative to the semi-honest model. Overall, we provide the Peer-to-Peer network
designer a set of tools to choose from, based on the desired level of security.Comment: Submitted to Peer-to-Peer Networking and Applications Journal (PPNA)
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