Nearest-neighbor Communication Research Articles

Accelerating multivariate functional approximation computation with domain decomposition techniques

Modeling large datasets through Multivariate Functional Approximations (MFA) provide an elegant way to handle many visualization and scientific analysis workflows. The process necessitates scalable data partitioning methods to compute MFA representations efficiently without compromising the accuracy or continuity of the reconstructed solution. We propose a domain-decomposed method for computing the MFA with B-spline bases, which reduces the total work per task and uses a restricted Additive Schwarz (RAS) method to converge the control point data degrees-of-freedom along subdomain boundaries. We provide an in-depth analysis of the parallel approach with domain decomposition solvers, aiming to minimize local subdomain error residuals and recover high-order continuity at subdomain interfaces with appropriate choices of knot overlaps. The communication cost, determined by the overlap regions in the RAS implementation, is optimized to recover the numerical error profile of the single subdomain case. Our proposed method stands in contrast to previous methods, which typically only recover either C0 or at best C1 continuity for arbitrary B-spline degree expansions, or those that require post-processing to blend discontinuities in the reconstructed data. We demonstrate the effectiveness of our approach using analytical and real-world datasets in 1D, 2D, and 3D through both strong and weak scaling studies. The performance results indicate that the overall cost of computing the approximation is directly proportional to the underlying nearest-neighbor communication implementation, and is only weakly dependent on the overlap region size that determines the size of the messages. This finding underscores the efficiency and scalability of our proposed method, making it a promising solution for handling large datasets in scientific workflows.

Simulating magnetized neutron stars with discontinuous Galerkin methods

Discontinuous Galerkin methods are popular because they can achieve high order where the solution is smooth, because they can capture shocks while needing only nearest-neighbor communication, and because they are relatively easy to formulate on complex meshes. We perform a detailed comparison of various limiting strategies presented in the literature applied to the equations of general relativistic magnetohydrodynamics. We compare the standard minmod/$\Lambda\Pi^N$ limiter, the hierarchical limiter of Krivodonova, the simple WENO limiter, the HWENO limiter, and a discontinuous Galerkin-finite-difference hybrid method. The ultimate goal is to understand what limiting strategies are able to robustly simulate magnetized TOV stars without any fine-tuning of parameters. Among the limiters explored here, the only limiting strategy we can endorse is a discontinuous Galerkin-finite-difference hybrid method.

Research on time synchronization of linear pulse-coupled oscillators model with delay in nearest neighbor wireless multi-hop networks

Time synchronicity works as a popular requirement in wireless sensor networks. Pulse-coupled oscillators similar to firefly flashing and synchronization via discrete pulse coupling are widely used in wireless sensor networks. In this article, we have studied the time synchronization with communication delay in the nearest neighbor network of distributed sensors, based on the pulse-coupled oscillators model of synchronicity achieved by biological systems. First, we present a linear pulse-coupled oscillators model with coupling delay and the model is used to analyze the wireless sensor networks synchronization with communication delay. Second, we mathematically analyze the firing behaviors in the linear pulse-coupled oscillators network using the delayed excitatory coupling and track the synchronization process of the two and multi-oscillators and obtain the synchronization conditions from the regression mapping. Finally, through the proposed model implementation in the wireless sensor networks simulation framework, we demonstrate that the multi-oscillators system can be synchronized from a random starting stage distribution under linear phase responding functions and the nearest neighbor communication. The results show that our approach can achieve clock synchronization in wireless sensor networks with delayed nearest neighbor communication.

Gradient sensing via cell communication.

Experimental evidence lends support to the conjecture that cell-to-cell communication plays a role in the gradient sensing of chemical species by certain chains of cells. Models have been formulated to explore this idea. For cells with no identifiable sensing structure, Mugler etal. [Proc. Natl. Acad. Sci. (U.S.A.) 113, E689 (2016)10.1073/pnas.1509597112] have defined a particular local excitation, global inhibition (LEGI) model that pits nearest-neighbor communication against local reactions in a noisy environment to suggest how this sensing capability might arise in a physical system. In this study, we generalize the nearest-neighbor communication mechanism in the aforementioned LEGI model in order to explore the extent to which the gradient sensing characteristics depend on the parametrization of the communication itself, as well as on the cell size, the radius of influence of neighboring cells, and the influence of the background noise. Using our generalization and a collection of particular candidate communication models, we find that the precision of gradient sensing is indeed sensitive to the particular communication model, and we derive physical and analytic explanations for these results. The framework established and the associated results should prove useful in understanding the appropriateness of particular cell-to-cell communication models in gradient sensing studies.

Parallel Algorithms for Successive Convolution

The development of modern computing architectures with ever-increasing amounts of parallelism has allowed for the solution of previously intractable problems across a variety of scientific disciplines. Despite these advances, multiscale computing problems continue to pose an incredible challenge to modern architectures because they require resolving scales that often vary by orders of magnitude in both space and time. Such complications have led us to consider alternative discretizations for partial differential equations (PDEs) which use expansions involving integral operators to approximate spatial derivatives (Christlieb et al. in J Comput Phys 379:214–236, 2019; Christlieb et al. J Sci Comput 82:52(3):1–29, 2020; Christlieb et al. J Comput Phys 415:1–25, 2020). These constructions use explicit information within the integral terms, but treat boundary data implicitly, which contributes to the overall speed of the method. This approach is provably unconditionally stable for linear problems and stability has been demonstrated experimentally for nonlinear problems. Additionally, it is matrix-free in the sense that it is not necessary to invert linear systems and iteration is not required for nonlinear terms. Moreover, the scheme employs a fast summation algorithm that yields a method with a computational complexity of $${\mathcal {O}}(N)$$ , where N is the number of mesh points along a coordinate direction. While much work has been done to explore the theory behind these methods, their practicality in large scale computing environments is a largely unexplored topic. In this work, we explore the performance of these methods by developing a domain decomposition algorithm suitable for distributed memory systems along with shared memory algorithms. As a first pass, we derive an artificial Courant–Friedrichs–Lewy condition that enforces a nearest-neighbor (N-N) communication pattern and briefly discuss possible generalizations. We also analyze several approaches for implementing the parallel algorithms by optimizing predominant loop structures and maximizing data reuse. Using a hybrid design that employs MPI and Kokkos (Edwards and Trott in J Parallel Distrib Comput 74:3202–3216, 2014) for the distributed and shared memory components of the algorithms, respectively, we show that our methods are efficient and can sustain an update rate $$> 1\times 10^8$$ DOF/node/s. We provide results that demonstrate the scalability and versatility of our algorithms using several different PDE test problems, including a nonlinear example, which employs an adaptive time-stepping rule.

Distributed Control Design for Heterogeneous Interconnected Systems

This article presents scalable controller synthesis methods for heterogeneous and partially heterogeneous systems. First, heterogeneous systems composed of different subsystems that are interconnected over a directed graph are considered. Techniques from robust and gain-scheduled controller synthesis are employed, in particular, the full-block S-procedure, to deal with the decentralized system part in a nominal condition and with the interconnection part in a multiplier condition. Under some structural assumptions, we can decompose the synthesis conditions into conditions that are the size of the individual subsystems. To solve these decomposed synthesis conditions that are coupled only over neighboring subsystems, we propose a distributed method based on the alternating direction method of multipliers. It only requires nearest-neighbor communication and no central coordination is needed. Then, a new classification of systems is introduced that consists of groups of homogeneous subsystems with different interconnection types. This classification includes heterogeneous systems as the most general and homogeneous systems as the most specific case. Based on this classification, we show how the interconnected system model and the decomposed synthesis conditions can be formulated in a more compact way. The computational scalability of the presented methods with respect to a growing number of subsystems and interconnections is analyzed, and the results are demonstrated in numerical examples.

Implementation of the efficient communication layer for the highly parallel total FETI and hybrid total FETI solvers

This paper describes the implementation, performance, and scalability of our communication layer developed for Total FETI (TFETI) and Hybrid Total FETI (HTFETI) solvers. HTFETI is based on our variant of the Finite Element Tearing and Interconnecting (FETI) type domain decomposition method. In this approach a small number of neighboring subdomains is aggregated into clusters, which results in a smaller coarse problem. To solve the original problem TFETI method is applied twice: to the clusters and then to the subdomains in each cluster. The current implementation of the solver is focused on the performance optimization of the main CG iteration loop, including: implementation of communication hiding and avoiding techniques for global communications; optimization of the nearest neighbor communication - multiplication with a global gluing matrix; and optimization of the parallel CG algorithm to iterate over local Lagrange multipliers only. The performance is demonstrated on a linear elasticity 3D cube and real world benchmarks.

Secondary Frequency and Voltage Control of Islanded Microgrids via Distributed Averaging

In this work we present new distributed controllers for secondary frequency and voltage control in islanded microgrids. Inspired by techniques from cooperative control, the proposed controllers use localized information and nearest-neighbor communication to collectively perform secondary control actions. The frequency controller rapidly regulates the microgrid frequency to its nominal value while maintaining active power sharing among the distributed generators. Tuning of the voltage controller provides a simple and intuitive trade-off between the conflicting goals of voltage regulation and reactive power sharing. Our designs require no knowledge of the microgrid topology, impedances or loads. The distributed architecture allows for flexibility and redundancy, and eliminates the need for a central microgrid controller. We provide a voltage stability analysis and present extensive experimental results validating our designs, verifying robust performance under communication failure and during plug-and-play operation.

Coordinate-free formation stabilization based on relative position measurements

This paper presents a method to stabilize a group of agents moving in a two-dimensional space to a desired rigid geometric configuration. A common approach is to use information of relative interagent position vectors to carry out this specific control task. However, existing works in this vein either require the agents to express their measurements in a global coordinate reference, or generally fail to provide global stability guarantees. Our contribution is a globally convergent method that uses relative position information expressed in each agent’s local reference frame, and can be implemented in a distributed networked fashion. The proposed control strategy, which is shown to have exponential convergence properties, makes each agent move so as to minimize a cost function that encompasses all the agents in the team and captures the collective control objective. The coordinate-free nature of the method emerges through the introduction of a rotation matrix, computed by each agent, in the cost function. We consider that the agents form a nearest-neighbor communications network, and they obtain the required relative position information via multi-hop propagation, which is inherently affected by time-delays. We support the feasibility of such distributed networked implementation by obtaining global stability guarantees for the formation controller when these time-delays are incorporated in the analysis. The performance of our approach is illustrated with simulations.

A Scalable $O(N)$ Algorithm for Large-Scale Parallel First-Principles Molecular Dynamics Simulations

Traditional algorithms for first-principles molecular dynamics (FPMD) simulations only gain a modest capability increase from current petascale computers, due to their $O(N^3)$ complexity and their heavy use of global communications. To address this issue, we are developing a truly scalable $O(N)$ complexity FPMD algorithm, based on density functional theory (DFT), which avoids global communications. The computational model uses a general nonorthogonal orbital formulation for the DFT energy functional, which requires knowledge of selected elements of the inverse of the associated overlap matrix. We present a scalable algorithm for approximately computing selected entries of the inverse of the overlap matrix, based on an approximate inverse technique, by inverting local blocks corresponding to principal submatrices of the global overlap matrix. The new FPMD algorithm exploits sparsity and uses nearest neighbor communication to provide a computational scheme capable of extreme scalability. Accuracy is contr...

The Local Delay in Poisson Networks

Communication between two neighboring nodes is a very basic operation in wireless networks. Yet very little research has focused on the local delay in networks with randomly placed nodes, defined as the mean time it takes a node to connect to its nearest neighbor. We study this problem for Poisson networks, first considering interference only, then noise only, and finally and briefly, interference plus noise. In the noiseless case, we analyze four different types of nearest-neighbor communication and compare the extreme cases of high mobility, where a new Poisson process is drawn in each time slot, and no mobility, where only a single realization exists and nodes stay put forever. It turns out that the local delay behaves rather differently in the two cases. We also provide the low- and high-rate asymptotic behavior of the minimum achievable delay in each case. In the cases with noise, power control is essential to keep the delay finite, and randomized power control can drastically reduce the required (mean) power for finite local delay.

Delay-optimal Power Control Policies

The delay till success (DTS) is the mean number of transmissions needed, averaged over the fading, until a single packet is successfully received (decoded) over a wireless link. This paper shows that under a mean and a peak power constraint, random power control can significantly reduce the DTS. We derive the optimal power control policies that minimize the DTS at one link of given length. For most commonly used fading distributions, these optimal power control policies are random on-off policies, whose parameters depend on the fading statistics and the link distance. We present two applications of this result in the context of noise-limited wireless networks: minimizing the local delay (mean delay for successful nearest-neighbor communication) and minimizing the local anycast delay (mean delay for a transmission to any node).

Distributed Resource Sharing in Low-Latency Wireless Ad Hoc Networks

With the growing abundance of portable wireless communication devices, a challenging question that arises is whether one can efficiently harness the collective communication and computation power of these devices. In this paper, we investigate this question by studying a streaming application. Consider a network of N wireless nodes, each of power P, in which one or more nodes are interested in receiving a data stream from a fixed server node S. We ask whether distributed communication mechanisms exist to route media packets from S to the arbitrary but fixed receiver, such that 1) the average communication delay L is short, 2) the load is balanced, i.e., all nodes in the ensemble spend roughly the same amount of average power, and, more importantly, 3) power resources of all nodes are optimally shared, i.e., the lifetime of the network is comparable to an optimally designed network with L nodes whose total power is N ? P. We develop a theoretical framework for incorporation of random long range routes into wireless ad hoc networking protocols that can achieve such performance. Surprisingly, we show that wireless ad hoc routing algorithms, based on this framework, exist that can deliver this performance. The proposed solution is a randomized network structuring and packet routing framework whose communication latency is only L = O(log2 N) hops, on average, compared to O(?(N)) in nearest neighbor communications while distributing the power requirement almost equally over all nodes. Interestingly, all network formation and routing algorithms are completely decentralized, and the packets arriving at a node are routed randomly and independently, based only on the source and destination locations. The distributed nature of the algorithm allows it to be implemented within standard wireless ad hoc communication protocols and makes the proposed framework a compelling candidate for harnessing collective network resources in a truly large-scale wireless ad hoc networking environment.

High-Resolution Distributed Sampling of Bandlimited Fields With Low-Precision Sensors

The problem of sampling a discrete-time sequence of spatially bandlimited fields with a bounded dynamic range, in a distributed, communication-constrained, processing environment is addressed. A central unit, having access to the data gathered by a dense network of fixed-precision sensors, operating under stringent inter-node communication constraints, is required to reconstruct the field snapshots to maximum accuracy. Both deterministic and stochastic field models are considered. For stochastic fields, results are established in the almost-sure sense. The feasibility of having a flexible tradeoff between the oversampling rate (sensor density) and the analog-to-digital converter (ADC) precision, while achieving an exponential accuracy in the number of bits per Nyquist-interval per snapshot is demonstrated. This exposes an underlying ``conservation of bits'' principle: the bit-budget per Nyquist-interval per snapshot (the rate) can be distributed along the amplitude axis (sensor-precision) and space (sensor density) in an almost arbitrary discrete-valued manner, while retaining the same (exponential) distortion-rate characteristics. Achievable information scaling laws for field reconstruction over a bounded region are also derived: With N one-bit sensors per Nyquist-interval, $\Theta(\log N)$ Nyquist-intervals, and total network bitrate $R_{net} = \Theta((\log N)^2)$ (per-sensor bitrate $\Theta((\log N)/N)$), the maximum pointwise distortion goes to zero as $D = O((\log N)^2/N)$ or $D = O(R_{net} 2^{-\beta \sqrt{R_{net}}})$. This is shown to be possible with only nearest-neighbor communication, distributed coding, and appropriate interpolation algorithms. For a fixed, nonzero target distortion, the number of fixed-precision sensors and the network rate needed is always finite.

A Systolic FPGA Architecture of Two-Level Dynamic Programming for Connected Speech Recognition

In this paper, we present an efficient architecture for connected word recognition that can be implemented with field programmable gate array (FPGA). The architecture consists of newly derived two-level dynamic programming (TLDP) that use only bit addition and shift operations. The advantages of this architecture are the spatial efficiency to accommodate more words with limited space and the absence of multiplications to increase computational speed by reducing propagation delays. The architecture is highly regular, consisting of identical and simple processing elements with only nearest-neighbor communication, and external communication occurs with the end processing elements. In order to verify the proposed architecture, we have also designed and implemented it, prototyping with Xilinx FPGAs running at 33 MHz.

Threshold error penalty for fault-tolerant quantum computation with nearest neighbor communication

The error threshold for fault-tolerant quantum computation with concatenated encoding of qubits is penalized by internal communication overhead. Many quantum computation proposals rely on nearest neighbor communication, which requires excess gate operations. For a qubit stripe with a width of L+1 physical qubits implementing L levels of concatenation, we find that the error threshold of 2.1/spl times/10/sup -5/ without any communication burden is reduced to 1.2/spl times/10/sup -7/ when gate errors are the dominant source of error. This /spl sim/175/spl times/ penalty in error threshold translates to an /spl sim/13/spl times/ penalty in the amplitude and timing of gate operation control pulses.

A parallel two-sided contact algorithm in ALE3D

A scalable parallel algorithm for treating two-sided contact in a finite-element multi-physics code (ALE3D) is presented. This method assumes that proximity between the two sides changes continuously, and uses a local search to update proximity relations each cycle. The evolving communication pattern is treated entirely by local, nearest-neighbor communication; there is no global communication. Opening and closing voids, overlapping and intersecting contact surfaces, and a number of other special features are supported.

A scalable PC-based parallel computer for lattice QCD

A PC-based parallel computer for medium/large scale lattice QCD simulations is suggested. The Eo¨tvo¨s Univ., Inst. Theor. Phys. cluster consists of 137 Intel P4-1.7GHz nodes. Gigabit Ethernet cards are used for nearest neighbor communication in a two-dimensional mesh. The sustained performance for dynamical staggered (wilson) quarks on large lattices is around 70(110) GFlops. The exceptional price/performance ratio is below $1/Mflop.

Better than $l/Mflops sustained: a scalable PC-based parallel computer for lattice QCD

We study the feasibility of a PC-based parallel computer for medium to large scale lattice QCD simulations. The Eötvös Univ., Inst. Theor. Phys. cluster consists of 137 Intel P4-1.7GHz nodes with 512 MB RDRAM. The 32-bit, single precision sustained performance for dynamical QCD without communication is 1510 Mflops/node with Wilson and 970 Mflops/node with staggered fermions. This gives a total performance of 208 Gflops for Wilson and 133 Gflops for staggered QCD, respectively (for 64-bit applications the performance is approximately halved). The novel feature of our system is its communication architecture. In order to have a scalable, cost-effective machine we use Gigabit Ethernet cards for nearest-neighbor communications in a two-dimensional mesh. This type of communication is cost effective (only 30% of the hardware costs is spent on the communication). According to our benchmark measurements this type of communication results in around 40% communication time fraction for lattices upto 48 3·96 in full QCD simulations. The price/sustained-performance ratio for full QCD is better than $l/Mflops for Wilson (and around $1.5/Mflops for staggered) quarks for practically any lattice size, which can fit in our parallel computer. The communication software is freely available upon request for non-profit organizations.

QCDOC: A 10-teraflops scale computer for lattice QCD

The architecture of a new class of computers, optimized for lattice QCD calculations, is described. An individual node is based on a single integrated circuit containing a PowerPC 32-bit integer processor with a 1 Gflops 64-bit IEEE floating point unit, 4 Mbyte of memory, 8 Gbit/sec nearest-neighbor communications and additional control and diagnostic circuitry. The machine's name, QCDOC, derives from “QCD On a Chip”.