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.

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

Discrete Optimization techniques have become a major and successful tool for modelling and solving many real world problems. In modelling real-time applications, we often have to face the inherent difficulty that an essential part of the data arrives sequentially in real-time, and that decision support is requested at the same time. Online and real-time algorithms are designed to handle such difficulties. We review some theoretical and practical aspects of online algorithms. Starting with theoretical concepts for performance evaluation, we survey typical results for classical optimization problems of discrete structure. Finally, we describe results on solving Discrete Optimization models for some real-time applications. Discrete Optimization has become a major and successful tool in modelling and solving real world problems arising in computer science, in economics, and in engineering. This success is based on two essential facts: computation times have decreased dramatically by the im...

. In this paper we examine problems motivated by on-line financial problems and stochastic games. In particular, we consider a sequence of entirely arbitrary distinct values arriving in random order, and must devise strategies for selecting low values followed by high values in such a way as to maximize the expected gain in rank from low values to high values. First, we consider a scenario in which only one low value and one high value may be selected. We give an optimal on-line algorithm for this scenario, and analyze it to show that, surprisingly, the expected gain is n \Gamma O(1), and so differs from the best possible off-line gain by only a constant additive term (which is, in fact, fairly small --- at most 15). In a second scenario, we allow multiple nonoverlapping low/high selections, where the total gain for our algorithm is the sum of the individual pair gains. We also give an optimal on-line algorithm for this problem, where the expected gain is n 2 =8 \Gamma \Theta(n log n). An analysis shows that the optimal expected off-line gain is n 2 =6 + \Theta(1), so the performance of our on-line algorithm is within a factor of 3=4 of the best off-line strategy. Key words. analysis of algorithms, on-line algorithms, financial games, secretary problem AMS subject classifications. 68Q20, 68Q25 PII. S0895480196307445 1.

Most on-line analysis assumes that, at each time step, all relevant information up to that time step is available and a decision has an immediate effect. In many on-line problems, however, the time relevant information is available and the time a decision has an effect may be decoupled. For example, when making an investment, one might not have completely up-to-date information on market prices. Similarly, a buy or sell order might only be executed some time later in the future. We introduce and explore natural delayed models for several well-known on-line problems. Our analyses demonstrate the importance of considering timeliness in determining the competitive ratio of an on-line algorithm. For many problems, we demonstrate that there exist algorithms with small competitive ratios even when large delays affect the timeliness of information and the effect of decisions.

this article, but rather a deep principle of on-line analysis known as Yao's minimax theorem [Yao, 1980]. This theorem is actually an adaptation of the famous minimax theorem of game theory [von Neumann and Morgenstern, 1947]. It states that the best ratio achievable by a deterministic algorithm against any distribution is exactly the same as the best ratio achievable by a randomized algorithm against a worst-case adversary. More formally, for a given on-line problem let F n denote the family of input instances of size at most n. Let D n denote the set of all probability distributions over the instances in F n . Let A n

. 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 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]. If all possible capital investments obey the rule that lower production costs require higher capital investments, then we present an algorithm with constant competitive ratio. If new opportunities may be strictly superior to previous ones (in terms of both capital cost and production cost), then we give an algorithm which is O(minflog C; log log P; log Mg) competitive, where C is the ratio between the highest and the ...

In this paper, we survey ideas and principles of modeling the investment decision process of economic agents. We start with the criteria of Markowitz of formulating return and risk as mean and variance, and also its extensions. We then look into other related criteria which are based on probability assumptions on future prices of securities. We also present methodologies which, instead of assuming probability distributions, rely on the best solution for the worst case scenario or in the average. A few multiple stage optimization models are discussed. Finally we give a few remarks on some interesting topics for further investigations.