Smooth Trade-off Research Articles

Scheduling Storms and Streams in the Cloud

Motivated by emerging big streaming data processing paradigms (e.g., Twitter Storm, Streaming MapReduce), we investigate the problem of scheduling graphs over a large cluster of servers. Each graph is a job, where nodes represent compute tasks and edges indicate data-flows between these compute tasks. Jobs (graphs) arrive randomly over time, and upon completion, leave the system. When a job arrives, the scheduler needs to partition the graph and distribute it over the servers to satisfy load balancing and cost considerations. Specifically, neighboring compute tasks in the graph that are mapped to different servers incur load on the network; thus a mapping of the jobs among the servers incurs a cost that is proportional to the number of "broken edges''. We propose a low complexity randomized scheduling algorithm that, without service preemptions, stabilizes the system with graph arrivals/departures; more importantly, it allows a smooth trade-off between minimizing average partitioning cost and average queue lengths. Interestingly, to avoid service preemptions, our approach does not rely on a Gibbs sampler; instead, we show that the corresponding limiting invariant measure has an interpretation stemming from a loss system.

Cost-Effective Robustness in Clock Networks Using Near-Tree Structures

Clock trees are commonly used to deliver clock signals to sequential elements in circuits. However, by construction, tree structures are inherently prone to failure caused by variations. The robustness of a clock tree can be improved by inserting redundancy in the form of cross links or multilevel fusion trees. Such near-tree structures can provide robustness at low cost. In this paper, we establish that the locations of the inserted redundancy are crucial in providing cost-effective robustness. We present two methods to systematically insert redundancy. The redundancy is realized by either inserting cross links or performing local merges. Moreover, we present a vertex reduction method that reduces the amount of redundancy that needs to be inserted in our near-tree structures. Empirical results show that our structures are more robust to variations and have lower power consumption compared to the state-of-the-art clock networks. Furthermore, our near-tree structures provide smooth trade-offs between cost and robustness, reducing clock skews by 11%-39% at an expense of 3%-68% higher power consumption.

Monetary Policy with Diverse Private Expectations

We study the impact of diverse beliefs on conduct of monetary policy. Individual belief is modeled by a state variable that defines an individual’s perceived laws of motion. We use a New Keynesian Model that is solved with a quadratic approximation hence individual decisions are quadratic functions. Aggregation renders the belief distribution an aggregate state variable. Although the model has standard technology and policy shocks, diverse expectations change materially standard results about a smooth trade-off between inflation volatility and output volatility. Our main results are summed up as follows: (i) The policy space contains a curve of singularity which is a collection of policy parameters that divides the space into two sub-regions. Some trade-off between output and inflation volatilities exists within each region and some across regions. (ii) The singularity causes volatility of variables to be non monotone in policy parameters. Policymakers cannot assume a more aggressive policy will change outcomes in a predictable manner. (iii) When beliefs are diverse a central bank must also consider the volatility of individual consumption and the related volatility of financial markets. We show aggressive anti-inflation policy increases consumption volatility and aggressive output stabilization policy entails rising inflation volatility. Efficient central bank policy must therefore be moderate. (iv) High optimism about the future typically lowers aggregate output and increases inflation. This “stagflation” effect is stronger the stickier prices are. Policy response is muted since the effects of higher inflation and lower output on interest rates partially cancel each other. Effective policy requires targeting exuberance directly or its effects in asset markets. Central banks already do so with short term interventions. (v) The observed high serial correlation of 0.80 in policy shocks contributes greatly to market volatility and we show that a reduction in persistence of central bank’s deviations from a fixed rule will contribute to stability. (vi) Belief dispersion is measured by cross sectional standard deviation of individual beliefs. An increased belief diversity is found to make policy coordination harder and results in lower aggregate output and lower rate of inflation. Bank policy can lower belief dispersion by being more transparent.

Maximum Likelihood Sequence Detection Receivers for Nonlinear Optical Channels

The space-time whitened matched filter (ST-WMF) maximum likelihood sequence detection (MLSD) architecture has been recently proposed (Maggio et al., 2014). Its objective is reducing implementation complexity in transmissions over nonlinear dispersive channels. The ST-WMF-MLSD receiver (i) drastically reduces the number of states of the Viterbi decoder (VD) and (ii) offers a smooth trade-off between performance and complexity. In this work the ST-WMF-MLSD receiver is investigated in detail. We show that thespace compressionof the nonlinear channel is an instrumental property of the ST-WMF-MLSD which results in a major reduction of the implementation complexity in intensity modulation and direct detection (IM/DD) fiber optic systems. Moreover, we assess the performance of ST-WMF-MLSD in IM/DD optical systems with chromatic dispersion (CD) and polarization mode dispersion (PMD). Numerical results for a 10 Gb/s, 700 km, and IM/DD fiber-optic link with 50 ps differential group delay (DGD) show that the number of states of the VD in ST-WMF-MLSD can be reduced ~4 times compared to an oversampled MLSD. Finally, we analyze the impact of the imperfect channel estimation on the performance of the ST-WMF-MLSD. Our results show that the performance degradation caused by channel estimation inaccuracies is low and similar to that achieved by existing MLSD schemes (~0.2 dB).

IMPROVED POINTER MACHINE AND I/O LOWER BOUNDS FOR SIMPLEX RANGE REPORTING AND RELATED PROBLEMS

We investigate one of the fundamental areas in computational geometry: lower bounds for range reporting problems in the pointer machine and the external memory models. We develop new techniques that lead to new and improved lower bounds for simplex range reporting as well as some other geometric problems. Simplex range reporting is the problem of storing n points in the d-dimensional space in a data structure such that the k points that lie inside a query simplex can be found efficiently. This is one of the fundamental and extensively studied problems in computational geometry. Currently, the best data structures for the problem achieve Q(n) + O(k) query time using [Formula: see text] space in which the [Formula: see text] notation either hides a polylogarithmic or an nε factor for any constant ε > 0, (depending on the data structure and Q(n)). The best lower bound on this problem is due to Chazelle and Rosenberg who showed any pointer machine data structure that can answer queries in O(nγ + k) time must use Ω(nd-ε-dγ) space. Observe that this bound is a polynomial factor away from the best known data structures. In this article, we improve the space lower bound to [Formula: see text]. Not only this bridges the gap from polynomial to sub-polynomial, it also offers a smooth trade-off curve. For instance, for polylogarithmic values of Q(n), our space lower bound almost equals Ω((n/Q(n))d); the latter is generally believed to be the “right” bound. By a simple geometric transformation, we also improve the best lower bounds for the halfspace range reporting problem. Furthermore, we study the external memory model and offer a new simple framework for proving lower bounds in this model. We show that answering simplex range reporting queries with Q(n)+O(k/B) I/Os requires [Formula: see text]) space or [Formula: see text] blocks, in which B is the block size.

Fourier analysis of stochastic sampling strategies for assessing bias and variance in integration

Each pixel in a photorealistic, computer generated picture is calculated by approximately integrating all the light arriving at the pixel, from the virtual scene. A common strategy to calculate these high-dimensional integrals is to average the estimates at stochastically sampled locations. The strategy with which the sampled locations are chosen is of utmost importance in deciding the quality of the approximation, and hence rendered image. We derive connections between the spectral properties of stochastic sampling patterns and the first and second order statistics of estimates of integration using the samples. Our equations provide insight into the assessment of stochastic sampling strategies for integration. We show that the amplitude of the expected Fourier spectrum of sampling patterns is a useful indicator of the bias when used in numerical integration. We deduce that estimator variance is directly dependent on the variance of the sampling spectrum over multiple realizations of the sampling pattern. We then analyse Gaussian jittered sampling, a simple variant of jittered sampling, that allows a smooth trade-off of bias for variance in uniform (regular grid) sampling. We verify our predictions using spectral measurement, quantitative integration experiments and qualitative comparisons of rendered images.

Time–space trade-offs for longest common extensions

We revisit the longest common extension (LCE) problem, that is, preprocess a string T into a compact data structure that supports fast LCE queries. An LCE query takes a pair (i,j) of indices in T and returns the length of the longest common prefix of the suffixes of T starting at positions i and j. We study the time–space trade-offs for the problem, that is, the space used for the data structure vs. the worst-case time for answering an LCE query. Let n be the length of T. Given a parameter τ, 1⩽τ⩽n, we show how to achieve either O(n/τ) space and O(τ) query time, or O(n/τ) space and O(τlog(|LCE(i,j)|/τ)) query time, where |LCE(i,j)| denotes the length of the LCE returned by the query. These bounds provide the first smooth trade-offs for the LCE problem and almost match the previously known bounds at the extremes when τ=1 or τ=n. We apply the result to obtain improved bounds for several applications where the LCE problem is the computational bottleneck, including approximate string matching and computing palindromes. We also present an efficient technique to reduce LCE queries on two strings to one string. Finally, we give a lower bound on the time–space product for LCE data structures in the non-uniform cell probe model showing that our second trade-off is nearly optimal.

Improved Soundness for QMA with Multiple Provers

We present three contributions to the understanding of QMA with multiple provers: 1) We give a tight soundness analysis of the protocol of [Blier and Tapp, ICQNM '09], yielding a soundness gap Omega(1/N^2). Our improvement is achieved without the use of an instance with a constant soundness gap (i.e., without using a PCP). 2) We give a tight soundness analysis of the protocol of [Chen and Drucker, ArXiV '10], thereby improving their result from a monolithic protocol where Theta(sqrt(N)) provers are needed in order to have any soundness gap, to a protocol with a smooth trade-off between the number of provers k and a soundness gap Omega(k^2/N), as long as k>=Omega(log N). (And, when k=Theta(sqrt(N)), we recover the original parameters of Chen and Drucker.) 3) We make progress towards an open question of [Aaronson et al., ToC '09] about what kinds of NP-complete problems are amenable to sublinear multiple-prover QMA protocols, by observing that a large class of such examples can easily be derived from results already in the PCP literature - namely, at least the languages recognized by a non-deterministic RAMs in quasilinear time.

Compressed Transport of Baseband Signals in Radio Access Networks

In current wireless base station solutions it is becoming common to physically separate baseband units and radio subsystems. In many wireless technologies this architecture requires allocation of significant transport network resources. In this paper a low-latency baseband signal compression scheme is presented. The compression scheme significantly lowers the transport data rate while maintaining low levels of signal distortion, thus resulting in a lower-cost transport network. Considering the importance of packet-based networks, a number of additional novel compression schemes are proposed. They are optimized for transport networks that implement a quality-of-service (QoS) mechanism and/or multi-link transmission. The compression schemes are parameterized such that a smooth trade-off between the required signal quality and compression performance can be achieved through operator choice of the suitable parameter values. An attractive feature of these schemes is that they can be applied to different wireless technologies, with appropriate parameter settings, without disrupting the present architecture. The proposed solutions will lead to a cost-effective implementation of collocated and distributed network-centric baseband processing, coordinated multi-point (CoMP) and/or distributed antenna system (DAS) which are critical topics for the entire wireless telecommunications industry and infrastructure.

OPTICAL FLOW FOR GLACIER MOTION ESTIMATION

Abstract. Quantitative measurements of glacier flow over time are an important ingredient for glaciological research, for example to determine the mass balances and the evolution of glaciers. Measuring glacier flow in multi-temporal images involves the estimation of a dense set of corresponding points, which in turn define the flow vectors. Furthermore glaciers exhibit rather difficult radiometry, since their surface usually contains homogeneous areas as well as weak texture and contrast. To date glacier flow is usually observed by manually measuring a sparse set of correspondences, which is labor-intensive and often yields rather irregular point distributions, with the associated problems of interpolating over large areas. In the present work we propose to densely compute motion vectors at every pixel, by using recent robust methods for optic flow computation. Determining the optic flow, i.e. the dense deformation field between two images of a dynamic scene, has been a classic, long-standing research problem in computer vision and image processing. Sophisticated methods exist to optimally balance data fidelity with smoothness of the motion field. Depending on the strength of the local image gradients these methods yield a smooth trade-off between matching and interpolation, thereby avoiding the somewhat arbitrary decision which discrete anchor points to measure, while at the same time mitigating the problem of gross matching errors. We evaluate our method by comparing with manually measured point wise ground truth.

Smooth Trade-Offs between Throughput and Delay in Mobile Ad Hoc Networks

Throughput capacity in mobile ad hoc networks has been studied extensively under many different mobility models. However, most previous research assumes global mobility, and the results show that a constant per-node throughput can be achieved at the cost of very high delay. Thus, we are having a very big gap here, i.e., either low throughput and low delay in static networks or high throughput and high delay in mobile networks. In this paper, employing a practical restricted random mobility model, we try to fill this gap. Specifically, we assume that a network of unit area with n nodes is evenly divided into cells with an area of n^{-2\alpha }, each of which is further evenly divided into squares with an area of n^{-2\beta} (0 \le \alpha \le \beta \le {1\over 2} ). All nodes can only move inside the cell which they are initially distributed in, and at the beginning of each time slot, every node moves from its current square to a uniformly chosen point in a uniformly chosen adjacent square. By proposing a new multihop relay scheme, we present smooth trade-offs between throughput and delay by controlling nodes' mobility. We also consider a network of area n^\gamma (0\le \gamma \le 1) and find that network size does not affect the results obtained before.

Trading detection for resolution in active sonar receivers

This paper proposes an active sonar receivers that offers a smooth trade-off between detection and resolution. A matched filter is the optimal detector of known signals in white Gaussian noise but may fail to resolve the targets if the time separation of targets is less than the mainlobe width of the autocorrelation function of the transmitted signal. An inverse filter achieves optimal resolution performance for multiple targets in the absence of noise, but amplifies the noise outside the signal bandwidth in a manner that makes it impractical in many realistic scenarios. The proposed active sonar receiver, the variable resolution and detection receiver (VRDR) combines the matched and inverse filter properties to achieve a smooth trade-off between detection and resolution. Simulated receiver operating characteristics demonstrate that for a range of dipole sonar targets, the performance of the VRDR is superior to the matched and inverse filter, as well as another previously proposed bandlimited inverse filter.

MeshWorks: A Comprehensive Framework for Optimized Clock Mesh Network Synthesis

Clock mesh networks are well known for their variation tolerance. But their usage is limited to high-end designs due to the significantly high resource requirements compared to clock trees and the lack of automatic mesh synthesis tools. Most existing works on clock mesh networks either deal with semi-custom design or perform optimizations on a given clock mesh. However, the problem of obtaining a good initial clock mesh has not been addressed. Also, the problem of achieving a smooth tradeoff between variation tolerance and resource requirements has not been addressed adequately. In this paper, we present our MeshWorks framework, the first comprehensive automated framework for planning, synthesis, and optimization of clock mesh networks that addresses the above issues. Experimental results suggest that our algorithms can achieve an additional reduction of 31% in buffer area, 21% in wirelength, and 23% in power, compared to the best previous work, with similar worst case maximum frequency. We also demonstrate the effectiveness of our framework under several practical issues such as blockages, multiple clocks, uneven load distribution, and electromigration violations.

Randomized Self-Assembly for Exact Shapes

Working in Winfree's abstract tile assembly model, we show that a constant-sized tile assembly system can be programmed through relative tile concentrations to build an $n\times n$ square with high probability for any sufficiently large $n$. This answers an open question of Kao and Schweller [Automata, Languages and Programming, Lecture Notes in Comput. Sci. 5125, Springer, Berlin, 2008, pp. 370-384], who showed how to build an approximately $n\times n$ square using tile concentration programming and asked whether the approximation could be made exact with high probability. We show how this technique can be modified to answer another question of Kao and Schweller by showing that a constant-sized tile assembly system can be programmed through tile concentrations to assemble arbitrary finite scaled shapes, which are shapes modified by replacing each point with a $c\times c$ block of points for some integer $c$. Furthermore, we exhibit a smooth trade-off between specifying bits of $n$ via tile concentrations versus specifying them via hard-coded tile types, which allows tile concentration programming to be employed for specifying a fraction of the bits of “input” to a tile assembly system, under the constraint that concentrations can be specified to only a limited precision. Finally, to account for some unrealistic aspects of the tile concentration programming model, we show how to modify the construction to use only concentrations that are arbitrarily close to uniform.

Towards Unbiased End-to-End Network Diagnosis

Internet fault diagnosis is extremely important for end-users, overlay network service providers (like Akamai [), and even Internet service providers (ISPs). However, because link-level properties cannot be uniquely determined from end-to-end measurements, the accuracy of existing statistical diagnosis approaches is subject to uncertainty from statistical assumptions about the network. In this paper, we propose a novel least-biased end-to-end network diagnosis (in short, LEND) system for inferring link-level properties like loss rate. We define a minimal identifiable link sequence (MILS) as a link sequence of minimal length whose properties can be uniquely identified from end-to-end measurements. We also design efficient algorithms to find all the MILSs and infer their loss rates for diagnosis. Our LEND system works for any network topology and for both directed and undirected properties and incrementally adapts to network topology and property changes. It gives highly accurate estimates of the loss rates of MILSs, as indicated by both extensive simulations and Internet experiments. Furthermore, we demonstrate that such diagnosis can be achieved with fine granularity and in near real-time even for reasonably large overlay networks. Finally, LEND can supplement existing statistical inference approaches and provide smooth tradeoff between diagnosis accuracy and granularity.

ELIAS: An Accurate and Extensible Lithography Aerial Image Simulator With Improved Numerical Algorithms

Lithography simulators have been playing an indispensable role in process optimization and design for manufacturability (DFM). The ever smaller feature sizes demand higher numerical accuracy and faster runtime on these lithography simulators. Aerial image simulation is the first key step in lithography simulation, and the method using transmission cross coefficient (TCC), which is a two-dimensional integral, is the most commonly used technique for full-chip aerial image simulation. In this paper, we present a very accurate, yet efficient and extensible aerial image simulator, ELIAS. We find that the majority of the numerical error during the TCC computation is due to the discontinuous boundaries of the support of the TCC integrand. We reduce the error dramatically by using a recursive integration algorithm. Because TCC is usually computed on uniform grids, we further speed up the algorithm without increasing the errors. Given the same accuracy, our new algorithm can speed up the runtime by 100 times - 1000times. Our algorithm also provides smooth tradeoff between accuracy and runtime. It can be used to benchmark other lithography aerial simulators. In addition, ELIAS provides an open-source, flexible software framework to incorporate different lithography settings.

A generalized linear filtering approach for sonar receivers.

Active sonar systems operating in realistic environments face the challenge of simultaneously detecting and resolving multiple targets. Receiver signal‐to‐noise ratio gain and main‐lobe width of the receiver response to the transmitted signal limit the detection and resolution capability of an active sonar receiver, respectively. A matched filter is commonly used for target detection to exploit its optimal detection property. Theoretically, an inverse filter achieves optimal resolution and can be used to resolve targets. In practice, the inverse filter is difficult to implement and requires unrealistically high signal‐to‐noise ratio to perform well. For an active sonar receiver operating in a cluttered environment with closely spaced targets, a matched filter might not resolve some targets and an inverse filter could not detect some targets. For such environments, a generalized linear filtering approach is proposed. This new approach combines the matched and inverse filter properties in a controlled manner to achieve smooth trade off between detection and resolution. In simulation, the generalized linear filter output is compared with the matched and inverse filter outputs to demonstrate the advantages of the proposed filter. In addition, receiver operating characteristics of the filters confirm the improved performance of the generalized linear filter. [Work funded by ONR Code 321US.]

Archer: A History-Based Global Routing Algorithm

Global routing is an important step in the physical design process. In this paper, we propose a new global routing algorithm Archer, which resolves some of the most common problems with the state-of-the-art global routers. It is known that concurrent global routing algorithms are typically too expensive to be applied on today's large designs, which may contain up to a million nets. On the other hand, iterative rip-up and reroute (RNR)-based algorithms are susceptible to getting stuck in local optimal solutions. In this paper, we propose an RNR-based global routing algorithm that guides the routing iterations out of local optima through effective usage of congestion histories. We also focus on the problem of how to enable a smooth tradeoff between seemingly conflicting objectives of overflow and wirelength minimization. Furthermore, we propose a Lagrangian relaxation-based bounded-length min-cost topology improvement algorithm that enables Steiner trees to change dynamically for the purpose of congestion optimization. Our experiments on public benchmarks show the effectiveness of Archer compared to other state-of-the-art global routers.

Online Bicriteria Load Balancing Using Object Reallocation

We study the bicriteria load balancing problem on two independent parameters under the allowance of object reallocation. The scenario is a system of M distributed file servers located in a cluster, and we propose three online approximate algorithms for balancing their loads and required storage spaces during document placement. The first algorithm is for heterogeneous servers. Each server has its individual tradeoff of load and storage space under the same rule of selection. The other two algorithms are for homogeneous servers. The second algorithm combines the idea of the first one and the best existing solution for homogeneous servers. Using document reallocation, we obtain a smooth tradeoff curve of the upper bounds of load and storage space. The last one bounds the load and storage space of each server by less than three times of their trivial lower bounds, respectively; and more importantly, for each server, the value of at least one parameter is far from its worst case. The time complexities of these three algorithms are O(log M) plus the cost of document reallocation.

FAD and SPA: End-to-end link-level loss rate inference without infrastructure

It is highly desirable and important for end users, with no special privileges, to identify and pinpoint faults inside the network that degrade the performance of their applications. However, existing tools are inaccurate to infer the link-level loss rates and have large diagnosis granularity. To address these problems, we propose a suite of user-level diagnosis approaches in two categories: (1) the diagnosis tool needs to be deployed only at the source and (2) the tool has to be deployed at both source and destination. For the former, we propose two fragmentation aided diagnosis approaches (FAD), Algebraic FAD and Opportunistic FAD, which use IP fragmentation to enable accurate link-level loss rate inference. For the latter category, we propose Striped Probe Analysis (SPA) which significantly improves the diagnosis granularity over those of the source-only approaches. Internet experiments are applied to evaluate each individual scheme (including an improved version of the state-of-the-art tool, Tulip [R. Mahajan, N. Spring, D. Wetherall, T. Anderson, User-level internet path diagnosis, in: ACM SOSP, 2003]) and various hybrid approaches. The results indicate that our approaches dramatically outperform existing work (especially for diagnosis granularity). But more importantly, we show that combination of different individual approaches (e.g. OFAD+Tulip or OFAD+SPA) provide not only the best performance but also smooth tradeoff among deployment requirement, diagnosis accuracy and granularity.