We consider several well known nonclairvoyant scheduling problems, including the problem of minimizing the average response time, and best-effort firm real-time scheduling. It is known that there are no deterministic online algorithms for these problems with bounded (or even polylogarithmic in the number of jobs) competitive ratios. We show that moderately increasing the speed of the processor used by the nonclairvoyant scheduler effectively gives this scheduler the power of clairvoyance. Furthermore, we show that there exist online algorithms with bounded competitive ratios on all inputs that are not closely correlated with processor speed. 1 Introduction We consider several well known nonclairvoyant scheduling problems, including the problem of minimizing the average response time [13, 15], and besteffort firm real-time scheduling [1, 2, 3, 4, 8, 11, 12, 18]. (We postpone formally defining these problems until the next section.) In nonclairvoyant scheduling some relevant information...

The construction of disjoint paths in a network is a basic issue in combinatorial optimization: given a network, and specified pairs of nodes in it, we are interested in finding disjoint paths between as many of these pairs as possible. This leads to a variety of classical NP-complete problems for which very little is known from the point of view of approximation algorithms. It has recently been brought into focus in work on problems such as VLSI layout and routing in high-speed networks; in these settings, the current lack of understanding of the disjoint paths problem is often an obstacle to the design of practical heuristics.

The competitive analysis of online algorithms has been criticized as being too crude and unrealistic. We propose refinements of competitive analysis in two directions: The first restricts the power of the adversary by allowingonly certain input distributions, while the other allows for comparisons between information regimes for online decision-making. We illustrate the first with an application to the paging problem; as a byproduct we characterize completely the work functions of this important special case of the k-server problem. We use the second refinement to explore the power of lookahead in server and task systems.

We study scheduling problems in battery-operated computing devices, aiming at schedules with low total energy consumption. While most of the previous work has focused on finding feasible schedules in deadline-based settings, in this article we are interested in schedules that guarantee good response times. More specifically, our goal is to schedule a sequence of jobs on a variable-speed processor so as to minimize the total cost consisting of the energy consumption and the total flow time of all jobs. We first show that when the amount of work, for any job, may take an arbitrary value, then no online algorithm can achieve a constant competitive ratio. Therefore, most of the article is concerned with unit-size jobs. We devise a deterministic constant competitive online algorithm and show that

This paper is concerned with the time series search and one-way trading problems. In the (time series) search problem a player is searching for the maximum (or minimum) price in a sequence that unfolds sequentially, one price at a time. Once during this game the player can decide to accept the current price p in which case the game ends and the player's payoff is p.Intheone-way trading problem a trader is given the task of trading dollars to yen. Each day, a new exchange rate is announced and the trader must decide how many dollars to convert to yen according to the current rate. The game ends when the trader trades his entire dollar wealth to yen and his payoff is the number of yen acquired. The search and one-way trading are intimately related. Any (deterministic or randomized) one-way trading algorithm can be viewed as a randomized search algorithm. Using the competitive ratio as a performance measure we determine the optimal competitive performance for several variants of these problems. In particular, we show that a simple threat-based strategy is optimal and we determine its competitive ratio which yields, for realistic values of the problem parameters, surprisingly low competitive ratios. We also consider and analyze a one-way trading game played against an adversary called Nature where the online player knows the probability distribution of the maximum exchange rate and that distribution has been chosen by Nature. Finally, we consider some applications for a special case of portfolio selection called two-way trading in which the trader may trade back and forth between cash and one asset.

In the unidirectional conversion problem an on-line player is given the task of converting dollars to yen over some period of time. Each day, a new exchange rate is announced, and the player must decide how many dollars to convert. His goal is to minimize the competitive ratio, defined as sup E POPT (E) PX (E) , where E ranges over exchange rate sequences, POPT (E) is the number of yen obtained by an optimal off-line algorithm, and PX (E) is the number of yen obtained by the on-line algorithm X. We also consider a continuous version of the problem, in which the exchange rate varies over a continuous time interval. The on-line player's a priori information about the fluctuation of exchange rates distinguishes different variants of the problem. For three variants we show that a simple threat-based strategy is optimal for the on-line player and determine its competitive ratio. We also derive and analyze an optimal policy for the on-line player when he knows the probability distribution o...

Andrew Chou Jeremy Cooperstock y Ran El--Yaniv z Michael Klugerman x Tom Leighton -- November, 1993 Abstract The distributional approach and competitive analysis have traditionally been used for the design and analysis of on-line algorithms. The former assumes a specific distribution on inputs, while the latter assumes inputs are chosen by an unrestricted adversary. This paper employs the statistical adversary (recently proposed by Raghavan) to analyze and design on-line algorithms for two-way currency trading. The statistical adversary approach may be viewed as a hybrid of the distributional approach and competitive analysis. By statistical adversary, we mean an adversary that generates input sequences, where each sequence must satisfy certain general statistical properties. The on-line algorithms presented in this paper have some very attractive properties. For instance, the algorithms are money-making; they are guaranteed to be profitable when the optimal off-li...

There is an upsurge in interest in the Markov model and also more general stationary ergodic stochastic distributions in theoretical computer science community recently (e.g. see [Vitter,KrishnanSl], [Karlin,Philips,Raghavan92], [Raghavan9 for use of Markov models for on-line algorithms, e.g., cashing and prefetching). Their results used the fact that compressible sources are predictable (and vise versa), and showed that on-line algorithms can improve their performance by prediction. Actual page access sequences are in fact somewhat compressible, so their predictive methods can be of benefit. This paper investigates the interesting idea of decreasing computation by using learning in the opposite way, namely to determine the difficulty of prediction. That is, we will ap proximately learn the input distribution, and then improve the performance of the computation when the input is not too predictable, rather than the reverse. To our knowledge,

We deal with the problem of making capital investments in machines for manufacturing a product. Opportunities for investment occur over time, every such option consists of a capital cost for a new machine and a resulting productivity gain, i.e., a lower production cost for one unit of product. The goal is that of minimizing the total production costs and capital costs when future demand for the product being produced and investment opportunities are unknown. This can be viewed as a generalization of the ski-rental problem and related to the mortgage problem [3].

A novel algorithm for actively trading stocks is presented. While traditional universal algorithms (and technical trading heuristics) attempt to predict winners or trends, our approach relies on predictable statistical relations between all pairs of stocks in the market. Our empirical results on historical markets provide strong evidence that this type of technical trading can “beat the market ” and moreover, can beat the best stock in the market. In doing so we utilize a new idea for smoothing critical parameters in the context of expert learning. 1