R. N. Uma

Techniques for scheduling with rejection

We consider the general problem of scheduling a set of jobs where we may choose not to schedule certain jobs, and thereby incur a penalty for each rejected job. More specifically, we focus on choosing a set of jobs to reject and constructing a schedule for the remaining jobs so as to optimize the sum of the weighted completion times of the jobs scheduled plus the sum of the penalties of the jobs rejected. We give several techniques for designing scheduling algorithms under this criterion. Many of these techniques show how to reduce a problem with rejection to a (potentially more complex) scheduling problem without rejection. Some of the reductions are based on general properties of certain kinds of linear-programming relaxations of optimization problems, and therefore are applicable to problems outside of scheduling; we demonstrate this by giving an approximation algorithm for a variant of the facility-location problem.

Load-sharing in heterogeneous systems via weighted factoring

Jeanette Schmidt~ R. N. Uma

Battery power-aware encryption

Joel Wein~ We consider the problem of scheduling a parallel loop with independent iterations on a network of heterogeneous workstations, and demonstrate the effectiveness of a variant of fa.toring, a scheduling policy originating in the context of shared address-space homogeneous multiprocessors. In the new scheme, weighted factoring, processors are dynamically assigned decreasing size chunks of iterations in proportion to their processing speeds. Through experiments on a network of SUN Spare workstations we show that weighted factoring significantly outperforms variants of a work-stea!ing load-balancing algorithm and on certain applications dramatically outperforms factoring as well. We then study weighted work assignment analytically, giving upper and lower bounds on its performance under the assumption that the processor iteration execution times can be modeled as weighted random variables. *Department of Computer Science,Polytechmc Umverslty, Brooklyn, NY, 11201. Researchsupported by ARPA/USAF under Grant no F30602-95-1-OO08and the New York State Science and Technology Foundation through Its center for Advanced Technology in Telecommunications Joel Wein wassupported in part by NSF Grant CCR-9211494, and Jeanette Schmidt m part by NSF grant CCR9305873. thummelQmono poly edu (Contact Author) *JpsC!qmcs4 poly.edu

An Experimental Study of LP-Based Approximation Algorithms for Scheduling Problems

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On the Relationship Between Combinatorial and LP-Based Approaches to NP-Hard Scheduling Problems

Minimizing power consumption is crucial in battery power-limited secure wireless mobile networks. In this paper, we (a) introduce a hardware/software set-up to measure the battery power consumption of encryption algorithms through real-life experimentation, (b) based on the profiled data, propose mathematical models to capture the relationships between power consumption and security, and (c) formulate and solve security maximization subject to power constraints. Numerical results are presented to illustrate the gains that can be achieved in using solutions of the proposed security maximization problems subject to power constraints.

Optimal Joint Scheduling and Cloud Offloading for Mobile Applications

R there has been much progress on the design of approximation algorithms for a variety of scheduling problems in which the goal is to minimize the average weighted completion time of the jobs scheduled. Many of these approximation algorithms have been inspired by polyhedral formulations of the scheduling problems and their use in computing optimal solutions to small instances. In this paper we demonstrate that the progress in the design and analysis of approximation algorithms for these problems also yields techniques with improved computational efficacy. Specifically, we give a comprehensive experimental study of a number of these approximation algorithms for 1 rj ∑ wjCj , the problem of scheduling jobs with release dates on one machine so as to minimize the average weighted completion time of the jobs scheduled. We study both the quality of lower bounds given for this problem by different linearprogramming relaxations and combinatorial relaxations, and the quality of upper bounds delivered by a number of approximation algorithms based on them. The best algorithms, on almost all instances, come within a few percent of the optimal average weighted completion time. Furthermore, we show that this can usually be achieved with O n logn computation. In addition we observe that on most kinds of synthetic data used in experimental studies a simple greedy heuristic, used in successful combinatorial branch-and-bound algorithms for the problem, outperforms (on average) all of the LP-based heuristics. We identify, however, other classes of problems on which the LP-based heuristics are superior and report on experiments that give a qualitative sense of the range of dominance of each. We consider the impact of local improvement on the solutions as well. We also consider the performance of the algorithms for the average weighted flow-time criterion, which, although equivalent to average weighted completion time at optimality, is provably much harder to approximate. Nonetheless, we demonstrate that for most instances we consider that the algorithms give very good results for this criterion as well. Finally, we extend the techniques to a rather different and more complex problem that arises from an actual manufacturing application: resource-constrained project scheduling. In this setting as well, the techniques yield algorithms with improved performance; we give the best-known solutions for a set of instances provided by BASF AG, Germany.

Off-line admission control for general scheduling problems

Enumerative approaches, such as branch-and-bound, to solv- ing optimization problems require a subroutine that produces a lower bound on the value of the optimal solution. In the domain of scheduling problems the requisite lower bound has typically been derived from either the solution to a linear-programming relaxation of the problem or the solution of a combinatorial relaxation. In this paper we investigate, from both a theoretical and practical perspective, the relationship between several linear-programming based lower bounds and combinatorial lower bounds for two scheduling problems in which the goal is to minimize the average weighted completion time of the jobs scheduled.

MDC and path diversity in video streaming

Cloud offloading is an indispensable solution to supporting computationally demanding applications on resource constrained mobile devices. In this paper, we introduce the concept of wireless aware joint scheduling and computation offloading (JSCO) for multi-component applications, where an optimal decision is made on which components need to be offloaded as well as the scheduling order of these components. The JSCO approach allows for more degrees of freedom in the solution by moving away from a compiler pre-determined scheduling order for the components towards a more wireless aware scheduling order. For some component dependency graph structures, the proposed algorithm can shorten execution times by parallel processing appropriate components in the mobile and cloud. We define a net utility that trades-off the energy saved by the mobile, subject to constraints on the communication delay, overall application execution time, and component precedence ordering. The linear optimization problem is solved using real data measurements obtained from running multi-component applications on an HTC smartphone and the Amazon EC2, using WiFi for cloud offloading. The performance is further analyzed using various component dependency graph topologies and sizes. Results show that the energy saved increases with longer application runtime deadline, higher wireless rates, and smaller offload data sizes.

To transmit or not to transmit: an investigation using competitive analysis

We consider a class of scheduling problems which includes a variety of problems that are exceedingly diicult to approximate (unless P=NP). In the face of very strong hardness results, we consider a relaxed notion of approximability and show that under this notion the problems yield constant-factor approximation algorithms (of a kind). Speciically we give a pseudopolynomial-time algorithm that, given an n-job instance whose optimal schedule has optimality criterion of value OPT, schedules a constant fraction of the n jobs within a constant factor times OPT. In many cases this can be converted to a fully polynomial-time algorithm. We then study the experimental performance of this algorithm and some additional heuristics. Speciically, we consider a set of instances of a one-machine scheduling problem that we have studied previously in the context of traditional approximation algorithms, where the goal is to optimize average weighted ow time. We show that for the instances that were hardest empirically for previous traditional approximation algorithms, a large fraction of the set of jobs can be scheduled using these techniques, with good performance. Our results are based on the existence of approximation algorithms for the nonpreemptive scheduling of jobs with release dates and due dates on one machine so as to maximize the (weighted) number of on-time jobs. As an additional contribution, we generalize the state of the art for such problems, giving the rst constant-factor approximation algorithms for the problem of scheduling jobs with resource requirements and release and due dates so as to optimize the weighted number of on-time jobs. In turn, this result further broadens the class of problems to which we can apply our relaxed-approximation result.

On the use of genetic algorithms in database client clustering

Delivering multimedia content over the network pose several challenges that include higher bandwidth and sensitivity to packet losses resulting due to congestion and/or transmission errors. Multiple description coding (MDC) is one of the source coding approaches to alleviate the problems of packet loss in a network since MDC splits the source information into several descriptions which can then be transmitted over several paths in the network. Parallel delivery of descriptions over multiple paths should guarantee better quality of transmission. In this paper we investigate the performance of a generalized MDC scheme over multi-path and single path scenarios and compare its performance to a layered single description (SDC) scheme. In the multi-path case, multimedia content is delivered via k-shortest paths that are selected on the basis of the packet loss probability of overall links in that path. Our experimental results show that MDC scheme always outperforms the SDC scheme in terms of PSNR quality for both single and multi-path transmissions. The improvement varies from 7 dB at (5% packet loss) to 13 dB at (20% packet loss) for the single path and by 3 dB to 9 dB respectively for the multi-path transmission.