No abstract

Peer-to-peer (P2P) networks represent an effective way to share information, since there are no central points of failure or bottleneck. However, the flip side to the distributive nature of P2P networks is that it is not trivial to aggregate and broadcast global information efficiently. We believe that this aggregation/broadcast functionality is a fundamental service that should be layered over existing Distributed Hash Tables (DHTs), and in this work, we design a novel algorithm for this purpose. Specifically, we build an aggregation/broadcast tree in a bottom-up fashion by mapping nodes to their parents in the tree with a parent function. The particular parent function family we propose allows the efficient construction of multiple interior-node-disjoint trees, thus preventing single points of failure in tree structures. In this way, we provide DHTs with an ability to collect and disseminate information efficiently on a global scale. Simulation results demonstrate that our algorithm is efficient and robust.

Holistic aggregations are popular queries for users to obtain detailed summary information from Wireless Sensor Networks. An aggregation operation is holistic if there is no constant bound on the size of the storage needed to describe a sub-aggregation. Since holistic aggregation cannot be distributable, it requires that all the sensory data should be sent to the sink in order to obtain the exact holistic aggregation results, which costs lots of energy. However, in most applications, exact holistic aggregation results are not necessary; instead, approximate results are acceptable. To save energy as much as possible, we study the approximated holistic aggregation algorithms based on uniform sampling. In this article, four holistic aggregation operations, frequency, distinct-count, rank, and quantile, are investigated. The mathematical methods to construct their estimators and determine optional sample size are proposed, and the correctness of these methods are proved. Four corresponding distributed holistic algorithms to derive (ϵ, δ)-approximate aggregation results are given. The solid theoretical analysis and extensive simulation results show that all the proposed algorithms have high performance on the aspects of accuracy and energy consumption.

In our study, the dual time-stepping strategy of the gas-kinetic scheme is constructed and used for the simulation of unsteady flows. In comparison to the previous implicit gas-kinetic scheme, both the inviscid and viscous flux Jacobian are considered in our work, and the linear system of the pseudo-steady-state is solved by applying generalized minimal residual algorithm. The accuracy is validated by several numerical cases, the incompressible flow around blunt bodies (stationary circular cylinder and square cylinder), and the transonic buffet on the NACA0012 airfoil under hybrid mesh. The numerical cases also demonstrate that the present method is applicable to approach the fluid flows from laminar to turbulent and from incompressible to compressible. Finally, the case of acoustic pressure pulse is carried out to evaluate the effects of enlarged time step, and the side effect of enlarged time step is explained. Compared with the explicit gas-kinetic scheme, the proposed scheme can greatly accelerate the computation and reduce the computational costs for unsteady flow simulations.

For applications in computing, Bézier curves are pervasive and are defined by a piecewise linear curve L which is embedded in R 3 and yields a smooth polynomial curve C embedded in R 3 . It is of interest to understand when L and C have the same embeddings. One class of counterexamples is shown for L being unknotted, while C is knotted. Another class of counterexamples is created where L is equilateral and simple, while C is self-intersecting. These counterexamples were discovered using curve visualizing software and numerical algorithms that produce general procedures to create more examples. (a) Unknotted L with knotted C (b) Zoomed-in view of C * % The corresponding function values of S and F are given: Svalue = 1.0e − 03 * -0.3861 -0.0970 0.1462 Fvalue =2.2329e − 05 J. Li