30 research outputs found
Lingering Issues in Distributed Scheduling
Recent advances have resulted in queue-based algorithms for medium access
control which operate in a distributed fashion, and yet achieve the optimal
throughput performance of centralized scheduling algorithms. However,
fundamental performance bounds reveal that the "cautious" activation rules
involved in establishing throughput optimality tend to produce extremely large
delays, typically growing exponentially in 1/(1-r), with r the load of the
system, in contrast to the usual linear growth.
Motivated by that issue, we explore to what extent more "aggressive" schemes
can improve the delay performance. Our main finding is that aggressive
activation rules induce a lingering effect, where individual nodes retain
possession of a shared resource for excessive lengths of time even while a
majority of other nodes idle. Using central limit theorem type arguments, we
prove that the idleness induced by the lingering effect may cause the delays to
grow with 1/(1-r) at a quadratic rate. To the best of our knowledge, these are
the first mathematical results illuminating the lingering effect and
quantifying the performance impact.
In addition extensive simulation experiments are conducted to illustrate and
validate the various analytical results
Delay Performance and Mixing Times in Random-Access Networks
We explore the achievable delay performance in wireless random-access
networks. While relatively simple and inherently distributed in nature,
suitably designed queue-based random-access schemes provide the striking
capability to match the optimal throughput performance of centralized
scheduling mechanisms in a wide range of scenarios. The specific type of
activation rules for which throughput optimality has been established, may
however yield excessive queues and delays.
Motivated by that issue, we examine whether the poor delay performance is
inherent to the basic operation of these schemes, or caused by the specific
kind of activation rules. We derive delay lower bounds for queue-based
activation rules, which offer fundamental insight in the cause of the excessive
delays. For fixed activation rates we obtain lower bounds indicating that
delays and mixing times can grow dramatically with the load in certain
topologies as well
A Multi-Scale Approach to Directional Field Estimation
This paper proposes a robust method for directional field estimation from fingerprint images that combines estimates at multiple scales. The method is able to provide accurate estimates in scratchy regions, while at the same time maintaining correct estimates around singular points. Compared to other methods, the penalty for detecting false singular points is much smaller, because this does not deteriorate the directional field estimate
Queues with random back-offs
We consider a broad class of queueing models with random state-dependent
vacation periods, which arise in the analysis of queue-based back-off
algorithms in wireless random-access networks. In contrast to conventional
models, the vacation periods may be initiated after each service completion,
and can be randomly terminated with certain probabilities that depend on the
queue length. We examine the scaled queue length and delay in a heavy-traffic
regime, and demonstrate a sharp trichotomy, depending on how the activation
rate and vacation probability behave as function of the queue length. In
particular, the effect of the vacation periods may either (i) completely vanish
in heavy-traffic conditions, (ii) contribute an additional term to the queue
lengths and delays of similar magnitude, or even (iii) give rise to an
order-of-magnitude increase. The heavy-traffic asymptotics are obtained by
combining stochastic lower and upper bounds with exact results for some
specific cases. The heavy-traffic trichotomy provides valuable insight in the
impact of the back-off algorithms on the delay performance in wireless
random-access networks
New Protocols for Secure Linear Algebra: Pivoting-Free Elimination and Fast Block-Recursive Matrix Decomposition
Cramer and Damg\aa{}rd were the first to propose a constant-rounds protocol for securely solving a linear system of unknown rank over a finite field in multiparty computation (MPC). For linear equations and unknowns, and for the case , the computational complexity of their protocol is . Follow-up work (by Cramer, Kiltz, and Padró) proposes another constant-rounds protocol for solving this problem, which has complexity . For certain applications, such asymptotic complexities might be prohibitive. In this work, we improve the asymptotic computational complexity of solving a linear system over a finite field, thereby sacrificing the constant-rounds property. We propose two protocols: (1) a protocol based on pivoting-free Gaussian elimination with computational complexity and linear round complexity, and (2) a protocol based on block-recursive matrix decomposition, having computational complexity (assuming ``cheap\u27\u27 secure inner products as in Shamir\u27s secret-sharing scheme) and (super-linear) round complexity