An efficient parallel algorithm $({\text{RNC}}^2 )$ for the two-processor scheduling problem is presented. An interesting feature of this algorithm is that it finds a highest-level-first schedule; such a schedule defi...
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An efficient parallel algorithm $({\text{RNC}}^2 )$ for the two-processor scheduling problem is presented. An interesting feature of this algorithm is that it finds a highest-level-first schedule; such a schedule defines a lexicographically first solution to this problem in a natural way. A key ingredient of the algorithm is a generalization of a theorem of Tutte which establishes a one-to-one correspondence between the bases of the Tutte matrix of a graph and the sets of matched nodes in maximum matchings in the graph.
We consider the problem of estimating functions of distributed data using a distributed algorithm over a network. The extant literature on computing functions in distributed networks such as wired and wireless sensor ...
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We consider the problem of estimating functions of distributed data using a distributed algorithm over a network. The extant literature on computing functions in distributed networks such as wired and wireless sensor networks and peer-to-peer networks deals with computing linear functions of the distributed data when the alphabet size of the data values is small, O(1). We describe a distributed randomized algorithm to estimate a class of nonlinear functions of the distributed data which is over a large alphabet. We consider three types of networks: point-to-point networks with gossip based communication, random planar networks in the connectivity regime and random planar networks in the percolating regime both of which use the slotted Aloha communication protocol. For each network type, we estimate the scaled kth frequency moments, for k >= 2. Specifically, for every k >= 2, we give a distributed randomized algorithm that computes, with probability (1 - delta), an epsilon-approximation of the scaled kth frequency moment, F-k/N-k, using time O(M-1-1/k-1T) and O(M-1-1/k-1 log N log (delta(-1))/epsilon(2) bits of transmission per communication step. Here, N is the number of nodes in the network, T is the information spreading time and M = o(N) is the alphabet size.
We investigate the relative computational powers of a mesh with static buses and a mesh with half-duplex wrap-arounds. The latter model is like a torus, except that any wrap-around link of the architecture can only tr...
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We investigate the relative computational powers of a mesh with static buses and a mesh with half-duplex wrap-arounds. The latter model is like a torus, except that any wrap-around link of the architecture can only transmit data in one of the two directions at any clock tick. We show that the permutation routing problem can be solved as efficiently on a linear array augmented with a half-duplex wrap-around link, as on a linear array with an augmented broadcast bus. We also present a routing algorithm for a two-dimensional (2D) mesh with half-duplex wrap-around links whose run time is close to that of the best known algorithm for routing on a 2D mesh with broadcast buses in each dimension. In addition, we show that on an n×n 2D mesh with broadcast buses, randomized sorting of n 2 elements can be accomplished in time that is only o(n) more, with high probability, than the time needed for permutation routing.
This paper deals with the problem of different uncertainties in discrete time track following control of read/write head in hard disk drives (HDD). A multi-objective robust controller is designed which minimizes the w...
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This paper deals with the problem of different uncertainties in discrete time track following control of read/write head in hard disk drives (HDD). A multi-objective robust controller is designed which minimizes the worst case root mean square (RMS) value of the positioning error signal (PES) subject to the closed-loop stability in the presence of parametric and dynamic uncertainties. A sequential algorithm based on ellipsoid iteration is utilized to handle parametric uncertainty. Dynamic uncertainty is also represented as linear fractional transformation (LFT) and by the virtue of small gain theorem, the stability of closed-loop system is guaranteed. In this design, two sources of conservatism are avoided: embedding the original non-linear parametric uncertainty into affine structure (converting the original uncertain system into a polytopic uncertain system) and using a single Lyapunov matrix to test all the objectives. The resulting controller has much better track following performance compared to the classical robust approaches which tends to higher storage capacity of HDDs. Simulation as well as experimental results verify the effectiveness of the designed controller.
This work presents the concept of kernel mean embedding and kernel probabilistic programming in the context of stochastic systems. We propose formulations to represent, compare, and propagate uncertainties for fairly ...
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This work presents the concept of kernel mean embedding and kernel probabilistic programming in the context of stochastic systems. We propose formulations to represent, compare, and propagate uncertainties for fairly general stochastic dynamics in a distribution-free manner. The new tools enjoy sound theory rooted in functional analysis and wide applicability as demonstrated in distinct numerical examples. The implication of this new concept is a new mode of thinking about the statistical nature of uncertainty in dynamical systems.
This paper presents the development and evaluation of a novel three-phase global path planning framework that combines and modifies D* Lite, Rapidly Exploring Random Tree Star (RRT*), and local path optimization for n...
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This paper presents the development and evaluation of a novel three-phase global path planning framework that combines and modifies D* Lite, Rapidly Exploring Random Tree Star (RRT*), and local path optimization for nonholonomic autonomous off-road navigation on 3D terrains. This hierarchical algorithm inherits the advantage of D* Lite + RRT* algorithm proposed by Brunner in terms of sampling efficiency and incorporates the local path optimization used by Krüsi to further improve the path’s quality. To demonstrate the necessity for all three phases, a High Mobility Multipurpose Wheeled Vehicle (HMMWV) is simulated on 3D terrain and under various obstacle configurations, and the tracking performance of the proposed three-phase algorithm is compared with that of RRT* and D* Lite + RRT* as one-phase and two-phase benchmarks. The results show that the new framework offers a better path quality and higher success rate. Although the improvement comes at the expense of longer computation time, real-time performance is still ensured in the implementation.
Technology advances have enabled researchers to collect large amounts of data with lots of covariates. Because of the high volume (large n) and high variety (large p) properties, model estimation with such big data ha...
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Technology advances have enabled researchers to collect large amounts of data with lots of covariates. Because of the high volume (large n) and high variety (large p) properties, model estimation with such big data has posed great challenges for statisticians. In this paper, we focus on the algorithmic aspect of these challenges. We propose a numerical procedure for solving large scale regression estimation problems involving a structured l0-norm penalty function. This numerical procedure blends the ideas of randomization, blockwise coordinate descent algorithms, and a closed-form representation of the proximal operator of the structured l0-norm penalty function. In particular, it adopts an "attention" mechanism that exploits the iteration errors to build a sampling distribution for picking up regression coefficients for updates. Simulation study shows the proposed numerical procedure is competitive when comparing with other algorithms for sparse estimation in terms of runtime and statistical accuracy when both the sample size and the number of covariates become large.
We consider Lyapunov stability of switched linear systems whose switching signal is constrained to a subset of indices. We propose a switching rule that chooses the most stable subsystem among those belonging to the s...
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We consider Lyapunov stability of switched linear systems whose switching signal is constrained to a subset of indices. We propose a switching rule that chooses the most stable subsystem among those belonging to the subset. This rule is based on an ordering of the subsystems using a common Lyapunov function. We develop randomized algorithms for finding the ordering as well as for finding a subset of systems for which a common Lyapunov function exists. We show that the class of Las Vegas randomized algorithms is useful in the design.
In recent years, a great deal of attention has been devoted to iterative control as an efficient methodology for the design of highly-performing controllers. In this paper, we propose a new iterative scheme which expl...
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In recent years, a great deal of attention has been devoted to iterative control as an efficient methodology for the design of highly-performing controllers. In this paper, we propose a new iterative scheme which explicitly accounts for the presence of uncertainty. At each step, the designed controller is the best possible one relative to the existing level of uncertainty and uncertainty is reduced through steps. In this way, the achieved performance rapidly improves from one step to the next, while preserving the robust stability of the closed-loop system. The controller design is performed at a low computational effort thanks to the use of randomized algorithms.
In this note we obtain a new bound for the acyclic edge chromatic number a'(G) of a graph G with maximum degree Delta increment proving that a'(G) <= 3.569(Delta - 1). To get this result we revisit and slig...
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In this note we obtain a new bound for the acyclic edge chromatic number a'(G) of a graph G with maximum degree Delta increment proving that a'(G) <= 3.569(Delta - 1). To get this result we revisit and slightly modify the method described in Kirousis et al. (2017). (C) 2020 Elsevier B.V. All rights reserved.
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