Approximation Techniques for Average Completion Time Scheduling

We consider the problem of nonpreemptive scheduling to minimize average ( weighted) completion time, allowing for release dates, parallel machines, and precedence constraints. Recent work has led to constant-factor approximations for this problem based on solving a preemptive or linear programming relaxation and then using the solution to get an ordering on the jobs. We introduce several new techniques which generalize this basic paradigm. We use these ideas to obtain improved approximation algorithms for one-machine scheduling to minimize average completion time with release dates. In the process, we obtain an optimal randomized on-line algorithm for the same problem that beats a lower bound for deterministic on-line algorithms. We consider extensions to the case of parallel machine scheduling, and for this we introduce two new ideas: first, we show that a preemptive one-machine relaxation is a powerful tool for designing parallel machine scheduling algorithms that simultaneously produce good approximations and have small running times; second, we show that a nongreedy “rounding” of the relaxation yields better approximations than a greedy one. We also prove a general theore mrelating the value of one- machine relaxations to that of the schedules obtained for the original m-machine problems. This theorem applies even when there are precedence constraints on the jobs. We apply this result to obtain improved approximation ratios for precedence graphs such as in-trees, out-trees, and series-parallel graphs

of Digital Images

robust, watermarking, invisible This paper addresses the problem of watermarking a digital image, in order to detect or verify ownership. An invisible and resilient watermark is one that is not ordinarily visible and is robust in the face of common image manipulations such as lossy compression, scaling, cropping, rotation, reflection, and brightness/contrast adjustment. A watermarking scheme is non-invertible if a valid watermark cannot be subtracted from an image, within the framework of the scheme. We propose an invisible, resilient and noninvertibl

Robust Public Key Watermarking of Digital Images

This paper addresses the problem of watermarking a digital image, in order to detect or verify ownership. An invisible and resilient watermark is one that is not ordinarily visible and is robust in the face of common image manipulations such as lossy compression, scaling, cropping, rotation, reflection, and brightness/contrast adjustment. A watermarking scheme is non-invertible if a valid watermark cannot be subtracted from an image, within the framework of the scheme. We propose an invisible, resilient and non-invertible watermarking scheme that uses public key signatures, and is computationally inexpensive to create, detect and verify. 2 Introduction There are several ways of classifying watermarks for images. One classifications partitions them into visibile and invisible watermark. Another classification partitions them into resilient watermarks and integrity watermarks. Visible watermarks are created by simply blending the watermark image with the image to be protected. The wat..

LOSSY COMPRESSION OF IMAGES USING PIECEWISE-LINEAR APPROXIMATION

We explore the lossy compression of images using an optimal algorithm for the approximation of wav eforms by piecewise linear functions. We also present the hardware implementation of a modified version of the optimal algorithm. The modified algorithm is simpler and better suited for real-time applications. Furthermore, it retains all properties of the optimal algorithm, except that the compression ratios maybe at most twice the optimal number. Ratedistortion plots show that the proposed algorithms perform favorably in comparison with the JPEG standard. 1 1

On the design of morphing airfoils using spinal structures

In this paper the design of spinal structures for the control of morphing airfoils is examined. The aim is to find structures that, when suitably loaded, can alter the aerodynamic shape of a cladding that forms the airfoil. Morphing through different cambered airfoils to achieve aerodynamic properties for different maneuvers is then possible by exploiting a range of incremental non-linear structural solutions. Further, by using structures that are acting in the post-buckling regime, it is possible to obtain significant changes in shape with only modest changes in applied load. The structure also presents enhanced aeroelastic properties. Results are formulated in terms of the aerodynamic properties of the morphed airfoils using a shape optimized beam as the spinal structure with fixed aerodynamic cladding