We present a MATLAB toolbox that automatically computes tight worst-case performance guarantees for a broad class of first-order methods for convex optimization. The class of methods includes those performing explicit...
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ISBN:
(纸本)9781509028733
We present a MATLAB toolbox that automatically computes tight worst-case performance guarantees for a broad class of first-order methods for convex optimization. The class of methods includes those performing explicit, projected, proximal, conditional and inexact (sub) gradient steps. The toolbox relies on the performance estimation (PE) framework, which recently emerged through works of Drori and Teboulle and the authors. The PE approach is a very systematic manner of obtaining non-improvable worst-case guarantees for first-order numerical optimization schemes. However, using the PE methodology requires modelling efforts from the user, along with some knowledge of semidefinite programming. The goal of this work is to ease the use of the performance estimation methodology, by providing a toolbox that implicitly does the modelling job. In short, its aim is to (i) let the user write the algorithm in a natural way, as he/she would have implemented it, and (ii) let the computer perform the modelling and worst-case analysis parts automatically.
Limited wireless spectrum in future networks is an issue that millimeter-Wave (mmWave) frequencies can resolve. Beamforming is a challenging operation for mmWave systems. Both analogue and hybrid solutions have been p...
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ISBN:
(纸本)9781509059324
Limited wireless spectrum in future networks is an issue that millimeter-Wave (mmWave) frequencies can resolve. Beamforming is a challenging operation for mmWave systems. Both analogue and hybrid solutions have been proposed. Apart from Orthogonal Multiple Access (OMA) systems, the Non-Orthogonal Multiple Access (NOMA) scheme has been recently considered as an alternative and can outperform OMA in many cases. Our contribution is the application of NOMA to a hybrid precoder design in mmWave indoor scenarios with multiple users. Introducing to our system appropriate user grouping and scheduling schemes, we show that the NOMA outperforms, in terms of spectral efficiency, OMA by providing a 17.1% improvement for high SNR values. Finally, applying NOMA with fair power allocation improves the rate of users with weak channel conditions by around 1 bps/Hz for SNR > 5dB, without degrading the overall spectral efficiency in the cell.
Information technologies have allowed for the rapid growth of both data acquisition and data storage. With this growth comes the challenge of extracting useful information. One piece of information that is interesting...
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ISBN:
(纸本)9781538632505
Information technologies have allowed for the rapid growth of both data acquisition and data storage. With this growth comes the challenge of extracting useful information. One piece of information that is interesting to academics and industry is the relationships between items in a large data set. One approach is to find the relationships between items by calculating how frequently the items appear together in a subset. This is known as the frequent itemset mining problem. The problem goes as follows, given a database with sets of items, find the items that occur frequently together in a subset.
The scale of data used in graph analytics grows at an unprecedented rate. More than ever, domain experts require efficient and parallel algorithms for tasks in graph analytics. One such task is the truss decomposition...
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ISBN:
(纸本)9781538634721
The scale of data used in graph analytics grows at an unprecedented rate. More than ever, domain experts require efficient and parallel algorithms for tasks in graph analytics. One such task is the truss decomposition, which is a hierarchical decomposition of the edges of a graph and is closely related to the task of triangle enumeration. As evidenced by the recent GraphChallenge, existing algorithms and implementations for truss decomposition are insufficient for the scale of modern datasets. In this work, we propose a parallel algorithm for computing the truss decomposition of massive graphs on a shared-memory system. Our algorithm breaks a computation-efficient serial algorithm into several bulk-synchronous parallel steps which do not rely on atomics or other fine-grained synchronization. We evaluate our algorithm across a variety of synthetic and real-world datasets on a 56-core Intel Xeon system. Our serial implementation achieves over 1400x speedup over the provided GraphChallenge serial benchmark implementation and is up to 28x faster than the state-of-the-art shared-memory parallel algorithm.
Robotic behaviors are mainly described by differential equations. Those mathematical models are usually not precise enough because of inaccurately known parameters or model simplifications. Nevertheless, robots are of...
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ISBN:
(纸本)9781509067244
Robotic behaviors are mainly described by differential equations. Those mathematical models are usually not precise enough because of inaccurately known parameters or model simplifications. Nevertheless, robots are often used in critical contexts as medical or military fields. So, uncertainties in mathematical models have to be taken into account in order to produce reliable and safe analysis results. A framework based on interval analysis is proposed to safely verify and analyze robotic behaviors with bounded uncertainties. It follows an interval constraint programming approach, combined with validated numerical integration methods to deal with differential equations. A case study on robust path planning is presented to emphasize the efficiency of the complete framework.
We focus on inexact iteration of averaged operators with stochastic errors, and we give conditions for a sublinear O (1/K) convergence rate for this class of iteration. Then, we show that our general development gives...
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ISBN:
(纸本)9781538632666
We focus on inexact iteration of averaged operators with stochastic errors, and we give conditions for a sublinear O (1/K) convergence rate for this class of iteration. Then, we show that our general development gives convergence rate analysis for sampling-based algorithms for non-strongly convex stochastic optimization including minimization, saddle-point problems, and constrained optimization.
Routing and wavelength assignment(RWA) is one of the vital optical network issues of optical networks. With the tradeoff between the idle ratio and reliability of the candidate route, this paper resea
ISBN:
(纸本)9781467389808
Routing and wavelength assignment(RWA) is one of the vital optical network issues of optical networks. With the tradeoff between the idle ratio and reliability of the candidate route, this paper resea
There has been increasing interests in processing large-scale real-world graphs, and recently many graph systems have been proposed. Vertex-centric GAS (Gather-Apply-Scatter) and Edge-centric GAS are two graph computa...
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ISBN:
(纸本)9781509066117
There has been increasing interests in processing large-scale real-world graphs, and recently many graph systems have been proposed. Vertex-centric GAS (Gather-Apply-Scatter) and Edge-centric GAS are two graph computation models being widely adopted, and existing graph analytics systems commonly follow only one computation model, which is not the best choice for real-world graph processing. In fact, vertex degrees in real-world graphs often obey skewed power-law distributions: most vertices have relatively few neighbors while a few have many neighbors. We observe that vertex-centric GAS for high-degree vertices and edge-centric GAS for low-degree vertices is a much better choice for real-world graph processing. In this paper, we present Mermaid, a system for processing large-scale real-world graphs on a single machine. Mermaid skillfully integrates vertex-centric GAS with edge-centric GAS through a novel vertex-mapping mechanism, and supports streamlined graph processing. On a total of 6 practical natural graph processing tasks, we demonstrate that, on average, Mermaid achieves 1.83x better performance than the state-of-the-art graph system on a single machine.
Matchmaking is the process of grouping players together to set up game sessions in multiplayer online games. In this paper, we focus on the matchmaking for multiplayer cloud gaming (MCG). We formulate the MCG matchmak...
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ISBN:
(纸本)9781509050383
Matchmaking is the process of grouping players together to set up game sessions in multiplayer online games. In this paper, we focus on the matchmaking for multiplayer cloud gaming (MCG). We formulate the MCG matchmaking problem with the objectives of maximizing the number of game sessions formed and minimizing the cost of cloud servers rented to serve the sessions. We propose a two-step matchmaking framework and several heuristic algorithms to assign players to servers. Experimental evaluations are conducted with real Internet latency data.
Continuous Twisting algorithm (CTA) for systems of order n allows to compensate theoretically exactly Lipschitz time perturbations, generating a continuous control signal and ensuring finite-time convergence to a slid...
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ISBN:
(纸本)9781509028733
Continuous Twisting algorithm (CTA) for systems of order n allows to compensate theoretically exactly Lipschitz time perturbations, generating a continuous control signal and ensuring finite-time convergence to a sliding mode of order (n + 1). In this paper an idea of a recursive procedure for Lypaunov Function (LF) and gains design for n - th order CTA is proposed. The procedure consists in constructing a homogeneous LF for the n-th order CTA as a sum of three generalized homogeneous polynomials of the same degree: (i) a LF for the continuous state feedback controlled system of order n;(ii) a LF for CTA of order (n-1) and (iii) some extra cross terms. The two first terms can in turn be constructed in a recursive form. The proposed idea is illustrated with the design of a LF and gains for the second order CTA. Furthermore, the proposed procedure allows to select the control gains of the CTA for third order systems and to prove global finite-time stability.
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