(SoE) School of Engineering

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Shiv Nadar University

This paper’s main result is an O((√m lg m)(n lg n)+m lg n)-time algorithm for computing the kth smallest entry in each row of an m × n totally monotone array. (A two-dimensional array A = {a[i,j]} is totally monotone if for all i1 &lt; i2 and j1 &lt; j2, a[i1,j1] &lt; a[i1, j2] implies a[i2, j1] &lt; a[i2, j2].) For large values of k (in particular, for k = n/2'|), this algorithm is significantly faster than the O(k(m + n))-time algorithm for the same problem due to Kravets and Park (1991). An immediate consequence of this result is an O(n3/2 lg2 n)-time algorithm for computing the kth nearest neighbor of each vertex of a convex n-gon. In addition to the main result, we also give an O(n lg m)-time algorithm for computing an approximate median in each row of an m × n totally monotone array; this approximate median is an entry whose rank in its row lies between [n/4] and [3n/4]. © Springer-Verlag Berlin Heidelberg 1991.

World University root node

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Improved selection in totally monotone arrays

The DC motors used in robotics and other industrial applications are submitted to frequent environment changes. As a consequence the motor model has time-varying parameters resulting in a poor performance when nonadaptive linear controllers are used. In this paper, two adaptive schemes for the position control of DC servomotors have been studied. The first scheme is based on self-tuning technique which uses pole-assignment by linear state feedback as the control strategy The second scheme uses adaptive feedforward in addition to pole-assigning linear state feedback. Experimental results show that a simple self-tuning control scheme for DC servomotors is a better solution to low cost automation problems in robotics and other industrial applications. The results obtained show that the adaptive scheme proposed by Kelly seems to offer no great benefit, rather it seems to increase the amount of overshoot. Standard schemes such as self-tuning control provide cost-effective solution to the control problem. The paper is organized as follows: a DC motor model and linear state feedback controller are discussed in Section II. Section III deals with self-tuning regulator, whereas adaptive feed-forward with linear state feedback is dealt with in Section IV. Experimental results on the DC motor control are given in Section V and some conclusions are drawn in Section VI.

Electrical Engineering

IFAC Proceedings Series

Adaptive control schemes for DC servomotors

Given n elements from a totally ordered set we outline a method for choosing an element whose rank is γn for some 0 &lt;γ&lt;1 where γ is independent of n. The algorithm executes in constant time in a CRCW PRAM model using a linear number of processors and succeeds with probability 1 - n-c for any c&gt;0. © 1990.

Information Processing Letters

Finding an approximate median with high probability in constant parallel time

There are now a number of fundamental problems in computational geometry that have optimal algorithms on PRAM models. We present randomized parallel algorithms which execute on an n-processor butterfly inter-connection network in O(log n) time for the following problems of input size n: trapezoidal decomposition, visibility, triangulation and 2-D convex hull. These are based on some previous work of the authors on PRAM algorithms and a new algorithm for doing binary search on fixed connection network. Apart from a 2-D convex hull algorithm, these are the first non-trivial geometric algorithms which attain this performance on fixed connection networks. The techniques developed in this paper rely on random sampling methods to do load-balancing on fixed-connection networks; it seems likely that they will have wider applications.

Algorithms and Architectures

Randomized algorithms for binary search and load balancing on fixed connection networks with geometric applications

Two closed-loop hierarchical control strategies are examined for the control of a two-area hydro-thermal power system model. The control is obtained using the interaction prediction approach and structural perturbation method. The first approach has been developed to provide optimal feedback control using an off-line decentralized calculation procedure. The second method is based on obtaining local feedback controllers for each subsystem on the first level by ignoring the interactions, then a global controller at the second level provides corrective signals to neutralize the interaction effects. In addition, the dynamic behaviour of the power system under the effect of non-linearities is also investigated. Finally, a two-area hydro-thermal power system is used to illustrate the approaches. © 1989 Taylor & Francis Group, LLC.

International Journal of Systems Science

Multilevel optimization of a hydro-thermal interconnected power system

Shear-sort opened new avenues in the research of sorting techniques for meshconnected processor arrays. The algorithm is extremely simple and converges to a snake-like sorted sequence with a time complexity which is suboptimal by a logarithmic factor. The techniques used for analyzing shear-sort have been used to derive more efficient algorithms, which have important ramifications both from practical and theoretical viewpoints. Although the algorithms described apply to any general two-dimensional computational model, the focus of most discussions is on meshconnected computers which are now commercially available. In spite of a rich history of 0(n) sorting algorithms on an n × n SIMD mesh, the constants associated with the leading term (i.e., n) are fairly large. This had led researchers to speculate about the tightness of the lower bound. The work in this paper sheds some more light on this problem as a 4n-step algorithm is shown to exist for a model slightly more powerful than the conventional SIMD model. Moreover, this algorithm has a running time of 3n steps on the more powerful MIMD model, which is “truly” optimal for such a model. © 1989 IEEE

IEEE Transactions on Computers

Parallel Sorting in Two-Dimensional VLSI Models of Computation

The recently discovered Shear-sort algorithm requires log2n iterations of row and column sorts for ordering n2 elements on an n × n mesh-connected array of processors. Although the method is extremely simple and practical, it falls short by a factor of log2n of the well-known lower bound for sorting on a mesh-connected computer. Recursive application of Shear-sort in a square array leads to the first proposed O(n) algorithm. A slightly more complicated iterative algorithm, also executing in O(n) steps is presented next. Both algorithms are surprisingly simple and are the result of the adoption of an entirely new approach to two-dimensional sorting. © 1989.

Journal of Parallel and Distributed Computing

Two nearly optimal sorting algorithms for mesh-connected processor arrays using shear-sort

Industrial robots are multilink, highly nonlinear and coupled dynamic systems, where control is a difficult and challenging task. This paper presents a review of the basic problems involved and their existing control solutions. This review also attempts to give a broadbased classification of control strategies.

IETE Journal of Research

Control strategies for robot manipulators. A review

Randomization offers elegant solutions to some problems in parallel computing. In addition to improved efficiency it often leads to simpler and practical algorithms. In this paper we discuss some of the characteristics of randomized algorithms and also give applications in computational geometry where use of randomization gives us significant advantage over the best known deterministic parallel algorithms. © Springer-Verlag Berlin Heidelberg 1989.