Repetitions detection on a linear array with reconfigurable pipelined bus system

We present two fast algorithms for sorting on a linear array with a reconfigurable pipelined bus system (LARPBS), one of the recently proposed parallel architectures based on optical buses. In our first algorithm, we sort N numbers in O(log N log log N) worst-case time using N processors. In our second algorithm, we sort N numbers in O((log log N)/sup 2/) worst-case time using N/sup 1+/spl epsi// processors, for any fixed /spl epsi/ such that 0 < /spl epsi/ < 1. Our algorithms are based on a novel deterministic sampling scheme for merging two sorted arrays of length N each in O(log log N) time on an LARPBS with N processors. To our knowledge, the previous best sorting algorithm on this architecture has a running time of O((log N)/sup 2/) using N processors.

We present a fast algorithm for sorting on a linear array with a reconfigurable pipelined bus system (LARPBS), one of the recently proposed parallel architectures based on optical buses. Our algorithm sorts N numbers in O(log N log logN) worst-case time using N processors. To our knowledge, the previous best sorting algorithm on this architecture has a running time of O(log2N).KeywordsLinear ArrayRecursive CallSorting AlgorithmMerging AlgorithmDestination ProcessorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In the channel routing problem, terminals between cells are interconnected completely while reducing channel routing area. The crossing number, the number of crossings between two wires in the channel, is related to the channel routing area. In this paper, we present a parallel algorithm finding a maximum crossing number, density, in the channel by using a LARPBS model (Linear Array with a Reconfigurable Pipelined Bus System), which is based on the advanced fiber optic technology. The maximum crossing number algorithm on the LARPBS model runs in O(n) time using O(n) number of processors, where n is the number of nets in a channel.

In this paper, we present deterministic and probabilistic methods for simulating PRAM computations on linear arrays with reconfigurable pipelined bus systems (LARPBS). The following results are established in this paper. (1) Each step of a p-processor PRAM with meO(p) shared memory cells can be simulated by a p-processors LARPBS in O(log p) time, where the constant in the big-O notation is small. (2) Each step of a p-processor PRAM with meΩ(p) shared memory cells can be simulated by a p-processors LARPBS in O(log m) time. (3) Each step of a p-processor PRAM can be simulated by a p-processor LARPBS in O(log p) time with probability larger than 1−1/p^c for all c>0. (4) As an interesting byproduct, we show that a p-processor LARPBS can sort p items in O(log p) time, with a small constant hidden in the big-O notation. Our results indicate that an LARPBS can simulate a PRAM very efficiently.

We present efficient parallel matrix multiplication algorithms for linear arrays with reconfigurable pipelined bus systems (LARPBS). Such systems are able to support a large volume of parallel communication of various patterns in constant time. An LARPBS can also be reconfigured into many independent subsystems and, thus, is able to support parallel implementations of divide-and-conquer computations like Strassen's algorithm. The main contributions of the paper are as follows. We develop five matrix multiplication algorithms with varying degrees of parallelism on the LARPBS computing model; namely, MM/sub 1/, MM/sub 2/, MM/sub 3/, and compound algorithms C/sub 1/(/spl epsiv/)and C/sub 2/(/spl delta/). Algorithm C/sub 1/(/spl epsiv/) has adjustable time complexity in sublinear level. Algorithm C/sub 2/(/spl delta/) implies that it is feasible to achieve sublogarithmic time using /spl sigma/(N/sup 3/) processors for matrix multiplication on a realistic system. Algorithms MM/sub 3/, C/sub 1/(/spl epsiv/), and C/sub 2/(/spl delta/) all have o(/spl Nscr//sup 3/) cost and, hence, are very processor efficient. Algorithms MM/sub 1/, MM/sub 3/, and C/sub 1/(/spl epsiv/) are general-purpose matrix multiplication algorithms, where the array elements are in any ring. Algorithms MM/sub 2/ and C/sub 2/(/spl delta/) are applicable to array elements that are integers of bounded magnitude, or floating-point values of bounded precision and magnitude, or Boolean values. Extension of algorithms MM/sub 2/ and C/sub 2/(/spl delta/) to unbounded integers and reals are also discussed.

In this paper, we present an efficient deterministic algorithm for sorting on the LARPBS (Linear Array with a Reconfigurable Pipelined Optical Bus System) model. Our sorting algorithm sorts n general keys in O(logn) time on a LARPBS of size nslogn. The previous best results can sort n items in O(lognloglogn) worst-case time using n processors or sort n items in O((log logn2)worst-case time using n1+ processors. Our algorithm is also scalable to certain extent. When the system size is reduced to nslogn/r for l≤r≤logn, the total computation time is O(rlogn).

Efficient and scalable quicksort on a linear array with a reconfigurable pipelined bus system

Almost all of the existing two-dimensional block-based medial axis transform (2D_BB_MAT) parallel algorithm are devised for solving the 2D_BB_MAT problem only and are very difficult to extend to a solution of the 3D_BB_MAT problem in parallel. In this paper, we propose efficient O(1) time algorithms for solving the hD_BB_MAT problems, where h is 2 or 3, on the linear array with a reconfigurable pipelined bus system (LARPBS) model. The proposed 2D_BB_MAT algorithm can easily extend to a solution of the 3D_BB_MAT problem in parallel by reducing the hD_BB_MAT problems to the forward chessboard distance transform problems. To the best of our knowledge, the proposed algorithms are the most efficient O(1) time algorithms compared with all the previously published algorithms known.

With the advent of optical fiber and other advanced technologies in solid state, pipelining signals at the wire (or transmission line) level has become possible. this has, in turn, made the slotted bus a potential candidate for interconnection networks (IN) for tightly coupled multiprocessor systems. However, a bus can provide only limited bandwidth. Though slotted bus can provide considerably more bandwidth in comparison to the traditional non-slotted bus, it is not enough for fine-grain parallel applications run on the shared-memory systems. One well known method to increase the effective bandwidth of a slotted bus in the LAN/MAN environment is to reuse the bandwidth by reusing slots. However, in a tightly coupled environment reusing slots is not a lucrative option because the significant buffering needs arising from slot reuse will introduce intolerable delay. In this paper we propose a methodology to reuse part of the bandwidth available from temporal and spectral bandwidth expansion with none or minimum buffering delay, resulting in significant performance improvement inboth the effective throughput and response time (communication latency). The proposed method entails the design and analysis of a re-configurable bus structure with both temporal and spectral bandwidth expansion and a polynomial time algorithm for optimal configurations for given traffic conditions. We have compared the performance of our reconfigured bus with that of the traditional slotted bus for uniform and localized traffic pattern and found that the reconfigured bus outperforms the traditional slotted bus substantially in many practical scenarios.

A constant time algorithm for finding maxima on reconfigurable bus systems using fewer processors

Total variation minimization (TVM) is a popular and useful method for accurate CT reconstruction from few-views and limited-angle data. However, the optimization procedure of previous TVM-based algorithms is very time-consuming. The purpose of this paper was to accelerate the high image quality CT reconstruction from few-views and limited-angle data. A new optimization algorithm based on the optimization transfer principle is proposed. The proposed algorithm uses TVM as the regularization term of the cost function that ensures the quality of the CT image reconstructed from few-views and limited-angle data. Additionally, half of the square of the difference between the original projection and the forward projection is used as the fidelity term. We then proved that the regularization term, i.e., 2-norm TV, is a convex function. Based on the convexity of the regularization and fidelity terms, a separable quadratic surrogate (SQS) function was proposed to substitute the regularization and fidelity terms. The solution of the cost function can be obtained by minimizing the SQS function and building the next SQS function at the minimum point. Both numerical simulations and simulations using real experimental data showed that the proposed algorithm reconstruct high-quality CT image from few-views and limited-angle data. The differences between the image reconstructed by the proposed algorithm and the images reconstructed by the previous algorithms are very small. However, the proposed algorithm required less than 1/10 time of the computational time of the previous algorithms. The image quality is not assessed in a rigorous way. The proposed algorithm can greatly accelerate the accurate CT reconstruction from few-views and limited-angle data relative to previous algorithms.

This paper deals with the problem of the Direction Of Arrival (DOA) estimation with nonuniform linear arrays. The proposed method is based on the Expectation Maximization method where ESPRIT is used in the maximization step. The key idea is to iteratively interpolate the data to a virtual uniform linear array in order to apply ESPRIT to estimate the DOA. The iterative approach allows one to improve the interpolation using the previously estimated DOA. One of this method’s novelties lies in its capacity of dealing with any nonuniform array geometry. This technique manifests significant performance and computational advantages over previous algorithms such as Spectral MUSIC, EM-IQML and the method based on manifold separation technique. EM-ESPRIT is shown to be more robust to additive noise. Furthermore, EM-ESPRIT fully exploits the advantages of using a nonuniform array over a uniform array: simulations show that for the same aperture and with a smaller number of sensors, the nonuniform array presents almost identical performance as the equivalent uniform array.

In the sensitive distance oracle problem, there are three phases. We first preprocess a given directed graph $G$ with $n$ nodes and integer weights from $[-W,W]$. Second, given a single batch of $f$ edge insertions and deletions, we update the data structure. Third, given a query pair of nodes $(u,v)$, return the distance from $u$ to $v$. In the easier problem called sensitive reachability oracle problem, we only ask if there exists a directed path from $u$ to $v$. Our first result is a sensitive distance oracle with $\tilde{O}(Wn^{\omega+(3-\omega)\mu})$ preprocessing time, $\tilde{O}(Wn^{2-\mu}f^{2}+Wnf^{\omega})$ update time, and $\tilde{O}(Wn^{2-\mu}f+Wnf^{2})$ query time where the parameter $\mu\in[0,1]$ can be chosen. The data-structure requires $O(Wn^{2+\mu} \log n)$ bits of memory. This is the first algorithm that can handle $f\ge\log n$ updates. Previous results (e.g. [Demetrescu et al. SICOMP'08; Bernstein and Karger SODA'08 and FOCS'09; Duan and Pettie SODA'09; Grandoni and Williams FOCS'12]) can handle at most 2 updates. When $3\le f\le\log n$, the only non-trivial algorithm was by [Weimann and Yuster FOCS'10]. When $W=\tilde{O}(1)$, our algorithm simultaneously improves their preprocessing time, update time, and query time. In particular, when $f=\omega(1)$, their update and query time is $\Omega(n^{2-o(1)})$, while our update and query time are truly subquadratic in $n$, i.e., ours is faster by a polynomial factor of $n$. To highlight the technique, ours is the first graph algorithm that exploits the kernel basis decomposition of polynomial matrices by [Jeannerod and Villard J.Comp'05; Zhou, Labahn and Storjohann J.Comp'15] developed in the symbolic computation community. [...]

The paper is concerned with the investigation of the detection and resolution capabilities inherent to the manifold of a linear (1-dimensional) array of omnidirectional sensors, not necessarily uniform. An initial discussion, associated with the shape of the manifold of a linear array, is presented by the application of differential geometry in complex space. The shape of the manifold, which for the case of linear arrays is a hyperhelix, can be fully characterised by its length and curvatures. In this paper it is shown that the array manifold may be locally approximated by a circular arc whose radius is the inverse of the manifold&apos;s first curvature. By using the above approximation, expressions for the thresholds of resolution and detection are derived as a function of the manifold length and first curvature even for sources of unequal powers. Two laws are established: the fourth-root law which is related to the resolution problem and the square-root law which is related to the detection problem. The overall conclusion is that the thresholds predicted via differential geometry concepts represent basic performance measures for assessing and comparing the performance of different linear array geometries irrespective of the algorithm used.

Order statistics on optically interconnected multiprocessor systems