Spectral Subspace Sparsification

We develop fast approximation algorithms for the minimum-cost version of the Bounded-Degree MST problem (BD-MST) and its generalization the Crossing Spanning Tree problem (Crossing-ST). We solve the underlying LP to within a $(1+\epsilon)$ approximation factor in near-linear time via the multiplicative weight update (MWU) technique. This yields, in particular, a near-linear time algorithm that outputs an estimate $B$ such that $B \le B^* \le \lceil (1+\epsilon)B \rceil +1$ where $B^*$ is the minimum-degree of a spanning tree of a given graph. To round the fractional solution, in our main technical contribution, we describe a fast near-linear time implementation of swap-rounding in the spanning tree polytope of a graph. The fractional solution can also be used to sparsify the input graph that can in turn be used to speed up existing combinatorial algorithms. Together, these ideas lead to significantly faster approximation algorithms than known before for the two problems of interest. In addition, a fast algorithm for swap rounding in the graphic matroid is a generic tool that has other applications, including to TSP and submodular function maximization.

RFID tags are being used in many diverse applications in increasingly large numbers. These capabilities of these tags span from very dumb passive tags to smart active tags, with the cost of these tags correspondingly ranging from a few pennies to many dollars. One of the common problems that arise in any RFID deployment is the problem of quick estimation of the number of tags in the field up to a desired level of accuracy. Prior work in this area has focused on the identification of tags, which needs more time, and is unsuitable for many situations, especially where the tag set is dense. We take a different, more practical approach, and provide very fast and reliable estimation mechanisms. In particular, we analyze our estimation schemes and show that the time needed to estimate the number of tags in the system for a given accuracy is much better than schemes presented in related work. We show that one can estimate the cardinality of tag-sets of any size in near-constant time, for a given accuracy of estimation.

Recently, neural network (NN) accelerators are gaining popularity as part of future heterogeneous multi-core architectures due to their broad application scope and excellent energy efficiency. Additionally, since neural networks can be retrained, they are inherently resillient to errors and noises. Prior work has utilized the error tolerance feature to design approximate neural network circuits or tolerate logical faults. However, besides high-level faults or noises, timing errors induced by delay faults, process variations, aging, etc. are dominating the reliability of NN accelerator under nanoscale manufacturing process. In this paper, we leverage the error resiliency of neural network to mitigate timing errors in NN accelerators. Specifically, when timing errors significantly affect the output results, we propose to retrain the accelerators to update their weights, thus circumventing critical timing errors. Experimental results show that timing errors in NN accelerators can be well tamed for different applications.

Recently, neural network (NN) accelerators are gaining popularity as part of future heterogeneous multi-core architectures due to their broad application scope and excellent energy efficiency. Additionally, since neural networks can be retrained, they are inherently resillient to errors and noises. Prior work has utilized the error tolerance feature to design approximate neural network circuits or tolerate logical faults. However, besides high-level faults or noises, timing errors induced by delay faults, process variations, aging, etc. are dominating the reliability of NN accelerator under nanoscale manufacturing process. In this paper, we leverage the error resiliency of neural network to mitigate timing errors in NN accelerators. Specifically, when timing errors significantly affect the output results, we propose to retrain the accelerators to update their weights, thus circumventing critical timing errors. Experimental results show that timing errors in NN accelerators can be well tamed for different applications.

We present a deterministic near-linear time algorithm that computes the edge-connectivity and finds a minimum cut for a simple undirected unweighted graph G with n vertices and m edges. This is the first o(mn) time deterministic algorithm for the problem. In near-linear time we can also construct the classic cactus representation of all minimum cuts.The previous fastest deterministic algorithm by Gabow from STOC'91 took O(m+λ2 n), where λ is the edge connectivity, but λ could be Ω(n).At STOC'96 Karger presented a randomized near linear time Monte Carlo algorithm for the minimum cut problem. As he points out, there is no better way of certifying the minimality of the returned cut than to use Gabow's slower deterministic algorithm and compare sizes.Our main technical contribution is a near-linear time algorithm that contracts vertex sets of a simple input graph G with minimum degree δ, producing a multigraph G with ~O(m/δ) edges which preserves all minimum cuts of G with at least two vertices on each side.In our deterministic near-linear time algorithm, we will decompose the problem via low-conductance cuts found using PageRank a la Brin and Page (1998), as analyzed by Andersson, Chung, and Lang at FOCS'06. Normally such algorithms for low-conductance cuts are randomized Monte Carlo algorithms, because they rely on guessing a good start vertex. However, in our case, we have so much structure that no guessing is needed.

The degree constrained minimum spanning tree problem is to determine a spanning tree of the minimum total edge cost and degree no more than a given value d (d-MST). A number of algorithms have been proposed for this problem. In [1] we introduced a new spanning tree called vertex subset degree preserving spanning tree, which was defined as a spanning tree T such that , v A-a non empty subset of the vertex set V of the graph G. This paper presents two algorithms to generate all degree constrained spanning trees and all vertex subset degree preserving spanning trees of a weighted graph in order of increasing cost. By generating spanning trees in order of increasing cost, it is possible to determine the second smallest or in general the k-th smallest spanning tree of a graph. Time complexity analyses are also given.

The surface code is a powerful quantum error correcting code that can be defined on a 2-D square lattice of qubits with only nearest neighbor interactions. Syndrome and data qubits form a checkerboard pattern. Information about errors is obtained by repeatedly measuring each syndrome qubit after appropriate interaction with its four nearest neighbor data qubits. Changes in the measurement value indicate the presence of chains of errors in space and time. The standard method of determining operations likely to return the code to its error-free state is to use the minimum weight matching algorithm to connect pairs of measurement changes with chains of corrections such that the minimum total number of corrections is used. Prior work has not taken into account the propagation of errors in space and time by the two-qubit interactions. We show that taking this into account leads to a quadratic improvement of the logical error rate.

Let $X_i, 1 \\leq i < \\infty$, denote independent random variables with values in $\\mathbb{R}^d, d \\geq 2$, and let $M_n$ denote the cost of a minimal spanning tree of a complete graph with vertex set $\\{X_1, X_2, \\ldots, X_n\\}$, where the cost of an edge $(X_i, X_j)$ is given by $\\psi(|X_i - X_j|)$. Here $|X_i - X_j|$ denotes the Euclidean distance between $X_i$ and $X_j$ and $\\psi$ is a monotone function. For bounded random variables and $0 < \\alpha < d$, it is proved that as $n\\rightarrow\\infty$ one has $M_n \\sim c(\\alpha, d)n^{(d - \\alpha)/d} \\int_{R^d} f(x)^{(d-\\alpha)/d} dx$ with probability 1, provided $\\psi(x) \\sim x^\\alpha$ as $x\\rightarrow 0$. Here $f(x)$ is the density of the absolutely continuous part of the distribution of the $\\{X_i\\}$.

Timing error tolerance is of great importance in nanometer technology integrated circuits. Two new flip-flop designs are presented for timing error tolerance, which are characterized by low silicon area overhead and power consumption compared to the state of the art Razor flip-flop. The first technique uses a new scan flip-flop, without any additional memory elements, to detect and correct timing errors at the minimum penalty of one clock cycle delay. The second technique is based on a new bit flipping flip-flop for local error detection and correction. In this topology, when a timing error is detected the output of the corresponding flip-flop is complemented for error correction. The proposed techniques and the well known Razor scheme were applied separately in the design of a 32-bit MIPS microprocessor core using a 90nm CMOS technology. Comparisons based on experimental results validate the efficiency of the new topologies with respect to Razor.

This paper presents a detailed study of fairness in cache sharing between threads in a chip multiprocessor (CMP) architecture. Prior work in CMP architectures has only studied throughput optimization techniques for a shared cache. The issue of fairness in cache sharing, and its relation to throughput, has not been studied. Fairness is a critical issue because the operating system (OS) thread scheduler's effectiveness depends on the hardware to provide fair cache sharing to co-scheduled threads. Without such hardware, serious problems, such as thread starvation and priority inversion, can arise and render the OS scheduler ineffective. This paper makes several contributions. First, it proposes and evaluates five cache fairness metrics that measure the degree of fairness in cache sharing, and shows that two of them correlate very strongly with the execution-time fairness. Execution-time fairness is defined as how uniform the execution times of co-scheduled threads are changed, where each change is relative to the execution time of the same thread running alone. Secondly, using the metrics, the paper proposes static and dynamic L2 cache partitioning algorithms that optimize fairness. The dynamic partitioning algorithm is easy to implement, requires little or no profiling, has low overhead, and does not restrict the cache replacement algorithm to LRU. The static algorithm, although requiring the cache to maintain LRU stack information, can help the OS thread scheduler to avoid cache thrashing. Finally, this paper studies the relationship between fairness and throughput in detail. We found that optimizing fairness usually increases throughput, while maximizing throughput does not necessarily improve fairness. Using a set of co-scheduled pairs of benchmarks, on average our algorithms improve fairness by a factor of 4/spl times/, while increasing the throughput by 15%, compared to a nonpartitioned shared cache.

Private record linkage (PRL) is the problem of identifying pairs of records that are similar as per an input matching rule from databases held by two parties that do not trust one another. We identify three key desiderata that a PRL solution must ensure: (1) perfect precision and high recall of matching pairs, (2) a proof of end-to-end privacy, and (3) communication and computational costs that scale subquadratically in the number of input records. We show that all of the existing solutions for PRL? including secure 2-party computation (S2PC), and their variants that use non-private or differentially private (DP) blocking to ensure subquadratic cost -- violate at least one of the three desiderata. In particular, S2PC techniques guarantee end-to-end privacy but have either low recall or quadratic cost. In contrast, no end-to-end privacy guarantee has been formalized for solutions that achieve subquadratic cost. This is true even for solutions that compose DP and S2PC: DP does not permit the release of any exact information about the databases, while S2PC algorithms for PRL allow the release of matching records. In light of this deficiency, we propose a novel privacy model, called output constrained differential privacy, that shares the strong privacy protection of DP, but allows for the truthful release of the output of a certain function applied to the data. We apply this to PRL, and show that protocols satisfying this privacy model permit the disclosure of the true matching records, but their execution is insensitive to the presence or absence of a single non-matching record. We find that prior work that combine DP and S2PC techniques even fail to satisfy this end-to-end privacy model. Hence, we develop novel protocols that provably achieve this end-to-end privacy guarantee, together with the other two desiderata of PRL. Our empirical evaluation also shows that our protocols obtain high recall, scale near linearly in the size of the input databases and the output set of matching pairs, and have communication and computational costs that are at least 2 orders of magnitude smaller than S2PC baselines.

Let P be a set of n points in d dimensions, each with an associated radius r_p > 0. The transmission graph G for P has vertex set P and an edge from p to q if and only if q lies in the ball with radius r_p around p. Let t > 1. A t-spanner H for G is a sparse subgraph of G such that for any two vertices p, q connected by a path of length l in G, there is a p-q-path of length at most tl in H. We show how to compute a t-spanner for G if d=2. The running time is O(n (log n + log Psi)), where Psi is the ratio of the largest and smallest radius of two points in P. We extend this construction to be independent of Psi at the expense of a polylogarithmic overhead in the running time. As a first application, we prove a property of the t-spanner that allows us to find a BFS tree in G for any given start vertex s of P in the same time. After that, we deal with reachability oracles for G. These are data structures that answer reachability queries: given two vertices, is there a directed path between them? The quality of a reachability oracle is measured by the space S(n), the query time Q(n), and the preproccesing time. For d=1, we show how to compute an oracle with Q(n) = O(1) and S(n) = O(n) in time O(n log n). For d=2, the radius ratio Psi again turns out to be an important measure for the complexity of the problem. We present three different data structures whose quality depends on Psi: (i) if Psi < sqrt(3), we achieve Q(n) = O(1) with S(n) = O(n) and preproccesing time O(n log n); (ii) if Psi >= sqrt(3), we get Q(n) = O(Psi^3 sqrt(n)) and S(n) = O(Psi^5 n^(3/2)); and (iii) if Psi is polynomially bounded in n, we use probabilistic methods to obtain an oracle with Q(n) = O(n^(2/3)log n) and S(n) = O(n^(5/3) log n) that answers queries correctly with high probability. We employ our t-spanner to achieve a fast preproccesing time of O(Psi^5 n^(3/2)) and O(n^(5/3) log^2 n) in case (ii) and (iii), respectively.

A full digital background method is proposed in this brief for timing mismatch calibrations of time-interleaved analog-to-digital converters (TIADCs) with wide sense stationary input signals. First, errors caused by timing mismatches are modeled as additive errors by applying the Taylor series approximation. Then, a mismatch estimation approach based on first-order statistics is proposed. In addition, computations are simplified significantly by using some valuable properties of the signals in TIADC channels. Further, a variable step-size iterative technique is presented to reduce steady-state errors. So the mismatch estimates are guaranteed to converge to actual values within three steps iterations. Theoretical analyses and experiments show that the proposed method has the advantages of low complexity and fast convergence over most other conventional methods. The proposed method is feasible for fast on-line timing mismatch calibrations of TIADCs.

Torsional vibrations experienced by drill strings can be detrimental to drilling operations. With a goal of understanding torsional vibrations experienced by drill strings and determining means to attenuate undesired vibrations, the authors have studied the effect of adding a sinusoidal modulation to a constant rotation speed of a drill string. A combination of modeling, analysis, and experiments is used to explore the influence of this rotation input modulation on the system response. The drill string is modeled as a modified Jeffcott rotor, which is described by a system with three degrees of freedom. Considering the case of forward whirling of a rotor in continuous contact with a stator, the equations of motion are reduced to a single degree-of-freedom nonlinear oscillator describing the torsional motions. In order to understand the fast time scale and slow time scale components of the motion, the method of direct partitions of motions is used to determine an approximate response to the nonlinear oscillator. The obtained results of the analysis illustrate that with the sinusoidal modulation of the rotor drive speed, the equivalent torsion stiffness can be enhanced and the character of the friction force at the contact can be made smooth. The analyses helps bring forth the stabilizing influence of the added sinusoidal input to the rotor drive speed. Over the considered parameter ranges, the numerical results obtained with the full three degree-of-freedom model and the reduced single degree-of-freedom model are found to be in agreement with each other. Furthermore, the results from these models are found to compare well with those obtained by using the method of direct partition of motions. Experiments with a laboratory scale drill-string arrangement are to be carried out to validate the analytical and numerical findings and further explore the effectiveness of the drive speed modulation on the rotor dynamics. Introduction Slender rotating structures are used in many engineering applications. Drill strings are long rotating slender structures, which are used in drilling operations. A schematic of a rotary drill rig is shown in Fig. 1 (e.g., Liao, Balachandran, Karkoub, and Abdel-Magid, 2011). Drill strings experience different types of vibrations (axial, torsional, and lateral vibrations) that may lead to detrimental failures of a drilling system. Drill-string vibrations have attracted the attention of many researchers, and many models have been developed to understand them. Since drill strings have a large length-to-diameter ratio, typically, the first torsional natural frequency and first lateral natural frequency are close to each other. This frequency proximity and the nature of the system allows for coupling and energy transfer between the associated vibration modes. Here, as a step towards developing further understanding, a drill string is modeled as an extended planar Jeffcott rotor with gravity acting normal to the rotor. Due to the planar motions, no gyroscopic effects are considered. The extended model, which was earlier considered in the work of Vlajic, Liu, Karki, and Balachandran (2014), is shown in Fig. 2. The model is described with three degrees of freedom (DOF), namely, x and y to account for lateral motions, and theta to account for torsional motion. A large number of research efforts have focused on controlling drill-string vibrations by using different feedback control algorithms, which need measurements along the drill string. In this work, the authors propose a different control approach to mitigate whirling motions during continuous rotor-stator contact. This can be compared to a situation of a drill string being in continuous contact with the borehole. The approach is open loop in implementation and this approach is based on adding a high frequency input to the drive speed of the drill string. Given the open-loop nature, the method does not depend on any measurements along the drill string or rotary table, which could be attractive for a practical stand point. Although the current focus is on motions of a rotor with continuous stator contact, it is planned to study stick-slip and non-contact cases in the future. System Modeling, Studies, and Results As previously mentioned, the drill string is modelled as a Jeffcott rotor with three DOF. Proceeding along the lines of the group's prior work (Vlajic, Liu, Karki, and Balachandran, 2014), after some approximations for the continuous rotor-stator contact case, the 3 DOF system is reduced to a single second-order nonlinear differential equation governing the torsional motion. In Fig. 3, for a representative case with a constant drive speed, the torsional state histories obtained for the full model and the reduced model are plotted. It is noted that the final state of the motion is captured quite well. To further analyze the response during forward whirling, the reduced-order model was nondimensionalized and an approximate solution was obtained by using the method of direct partitions. This method allows one to separate slow scale motions from fast scale motions. As discussed, in the group's prior work, this method can be useful to examine whirling motions. The results obtained by directly integrating the full model as well as the reduced-order model have been compared with that obtained by using the method of direct partitions of motions. It is seen that the perturbation analyses is able to provide an approximate solution that compares well with the numerical results obtained through direct integrations. Next, this analysis is used to examine the influence of the addition of secondary frequency component. It is seen that the addition of the secondary frequency, a high-frequency one, helps smooth out the friction coefficient variation with respect to the relative speed at contact. This is found to have a beneficial effect on the motion and helps suppress large-amplitude torsional motions. Stability analysis was also conducted to examine this effect. Concluding Remarks A study has been conducted to examine the influence of sinusoidal modulation of rotor drive speed in a system, wherein the rotor experiences continuous stator contact. A single degree of-freedom reduced model is developed to study the torsion response and it is found that the addition of a high frequency input can be beneficial in attenuating rotor motions. This is believed to be useful for developing open-loop control schemes for attenuating forward whirling motions of drill strings. Results obtained from a lab scale experimental arrangement will be used to examine the effect of this drive speed modulation further and they will be reported in the conference presentation. Future studies could build on the current effort to examine cases of backward whirling. Acknowledgment: The authors would like to gratefully acknowledge the support received from the Qatar National Research Fund for NPRP Project 7-083-2-041, to pursue this collaborative work between the University of Maryland, College Park, MD, USA and Qatar University, Doha, Qatar.

A new class of variable-length, and statistically-synchronisable codes is presented in conjunction with code-construction methods and some significant property theorems. A notable feature of the codes (augmented T-codes) is their ability to recover correct character synchronisation under normal decoding procedures, following timing or additive errors in a serial-message sequence. As a result of the code construction, the synchronisation delay is found to be largely independent of the source, with the expected delay typically fewer than three characters. A further class of associated fixed-length binary codes (the binary-depletion T-codes) is introduced, and shown to be important in systematic applications for code generation, encoding/decoding operations and determining synchronisation status in digital processors.