Sandy Irani

Algorithms for power savings

This paper examines two different mechanisms for saving power in battery-operated embedded systems. The first is that the system can be placed in a sleep state if it is idle. However, a fixed amount of energy is required to bring the system back into an active state in which it can resume work. The second way in which power savings can be achieved is by varying the speed at which jobs are run. We utilize a power consumption curve P(s). which indicates the power consumption level given a particular speed. We assume that P(s) and P(s)/s are convex. The problem is to schedule arriving jobs in a way that minimizes total energy use and so that each job is completed after its arrival time and before its deadline. Although each problem has been considered separately, this is the first theoretical analysis of systems which can use both mechanisms. We give an off line algorithm which is within a factor of three of the optimal algorithm. We also give an online algorithm with a constant competitive ratio.

Algorithmic problems in power management

We survey recent research that has appeared in the theoretical computer science literature on algorithmic problems related to power management. We will try to highlight some open problem that we feel are interesting. This survey places more concentration on lines of research of the authors: managing power using the techniques of speed scaling and power-down which are also currently the dominant techniques in practice.

Competitive paging with locality of reference

The Sleator-Tarjan competitive analysis of paging (Comm. ACM28 (1985), 202-208) gives us the ability to make strong theoretical statements about the performance of paging algorithms without making probabilistic assumptions on the input. Nevertheless practitioners voice reservations about the model, citing its inability to discern between LRU and FIFO (algorithms whose performances differ markedly in practice), and the fact that the theoretical comptitiveness of LRU is much larger than observed in practice, In addition, we would like to address the following important question: given some knowledge of a program?s reference pattern, can we use it to improve paging performance on that program? We address these concerns by introducing an important practical element that underlies the philosophy behind paging: locality of reference. We devise a graph-theoretical model, the access graph, for studying locality of reference. We use it to prove results that address the practical concerns mentioned above, In addition, we use our model to address the following questions: How well is LRU likely to perform on a given program? Is there a universal paging algorithm that achieves (nearly) the best possible paging performance on every program? We do so without compromising the benefits of the Sleator-Tarjan model, while bringing it closer to practice.

Page replacement with multi-size pages and applications to Web caching

We consider the paging problem where the pages have varying size This problem has applications to page replacement policies for caches containing World Wide Web documents We consider two models for the cost of an algorithm on a request sequence In the rst the Fault model the goal is to minimize the number of page faults In the second the Bit model the goal is to minimize the total number of bits that have to be read into the cache We show o ine algorithms for both cost models that obtain approximation factors of O log k where k is the ratio of the size of the cache to the size of the smallest page We show randomized online algorithms for both cost models that are O log k competitive In addition if the input sequence is generated by a known distribution we show an algorithm for the Fault model whose expected cost is within a factor of O log k of any other online algorithm

Efficient algorithms for optimum cycle mean and optimum cost to time ratio problems

The goal of this paper is to identify the most efficient algorithms for the optimum mean cycle and optimum cost to time ratio problems and compare them with the popular ones in the CAD community. These problems have numerous important applications in CAD, graph theory, discrete event system theory, and manufacturing systems. In particular, they are fundamental to the performance analysis of digital systems such as synchronous, asynchronous, dataflow, and embedded real-time systems. For instance, algorithms for these problems are used to compute the cycle period of any cyclic digital system. Without loss of generality, we discuss these algorithms in the context of the minimum mean cycle problem (MCMP). We performed a comprehensive experimental study of ten leading algorithms for MCMP. We programmed these algorithms uniformly and efficiently. We systematically compared them on a test suite composed of random graphs as well as benchmark circuits. Above all, our results provide important insight into the performance of these algorithms in practice. One of the most surprising results of this paper is that Howards algorithm, known primarily in the stochastic control community, is by far the fastest algorithm on our test suite although the only known bound on its running time is exponential. We provide two stronger bounds on its running time.

Randomized competitive algorithms for the list update problem

We prove upper and lower bounds on the competitiveness of randomized algorithms for the list update problem of Sleator and Tarjan. We give a simple and elegant randomized algorithm that is more competitive than the best previous randomized algorithm due to Irani. Our algorithm uses randomness only during an initialization phase, and from then on runs completely deterministically. It is the first randomized competitive algorithm with this property to beat the deterministic lower bound. We generalize our approach to a model in which access costs are fixed but update costs are scaled by an arbitrary constantd. We prove lower bounds for deterministic list update algorithms and for randomized algorithms against oblivious and adaptive on-line adversaries. In particular, we show that for this problem adaptive on-line and adaptive off-line adversaries are equally powerful.

Strongly Competitive Algorithms for Paging with Locality of Reference

What is the best paging algorithm if one has partial information about the possible sequences of page requests? We give a partial answer to this question, by presenting the analysis of strongly competitive paging algorithms in the access graph model. This model restricts page requests so that they conform to a notion of locality of reference, given by an arbitrary access graph. We first consider optimal algorithms for undirected access graphs. Borodin et al. [2] define an algorithm, called FAR, and proved that it is within a logarithmic factor of the optimal. We prove that FAR is in fact strongly competitive, i.e. within a constant factor of the optimum. For directed access graphs, we present an algorithm that is strongly competitive on all structured program graphs—graphs modeling the request sequences of structured programs.

Two results on the list update problem

Abstract In this paper we give a randomized on-line algorithm for the list update problem. Sleator and Tarjan show a deterministic algorithm, Move-to-Front, that achieves competitive ratio of ( 2L−1) L for lists of length L. Karp and Raghavan show that no deterministic algorithm can beat 2L (L+1) . We show that Move-to-Front in fact achieves an optimal competitive ratio of 2L (L+1) . We show a randomized algorithm that achieves a competitive ratio of (31L+1) 16(L+1) against an oblivious adversary. This is the first randomized strategy whose competitive factor beats a constant less than 2.

Optimal power-down strategies

We consider the problem of selecting threshold times to transition a device to low-power sleep states during an idle period. The two-state case in which there is a single active and a single sleep state is a continuous version of the ski-rental problem. We consider a generalized version in which there is more than one sleep state, each with its own power consumption rate and transition costs. We give an algorithm that, given a system, produces a deterministic strategy whose competitive ratio is arbitrarily close to optimal. We also give an algorithm to produce the optimal online strategy given a system and a probability distribution that generates the length of the idle period. We also give a simple algorithm that achieves a competitive ratio of 3 + 2/spl radic/2 /spl ap/ 5.828 for any system.

Combinatorial and experimental results for randomized point matching algorithms

Abstract The subject of this paper is the design and analysis of Monte Carlo algorithms for two basic matching techniques used in model-based recognition: alignment, and geometric hashing. We first give analyses of our Monte Carlo algorithms, showing that they are asymptotically faster than their deterministic counterparts while allowing failure probabilities that are provably very small. We then describe experimental results that bear out this speed-up, suggesting that randomization results in significant improvements in running time. Our theoretical analyses are not the best possible; as a step to remedying this we define a combinatorial measure of self-similarity for point sets, and give an example of its power.