Abstract: This paper revises and expands upon a paper presented by two of the present authors at AAAI 1986 [Vilain & Kautz 1986]. As with the original, this revised document considers computational aspects of intervalbased and point-based temporal representations. Computing the consequences of temporal assertions is shown to be computationally intractable in the interval-based representation, but not in the point-based one. However, a fragment of the interval language can be expressed using the point language and benefits from the tractability of the latter. The present paper departs from the original primarily in correcting claims made there about the point algebra, and in presenting some closely related results of van Beek [1989]. The representation of time has been a recurring concern of Artificial Intelligence researchers. Many representation schemes have been proposed for temporal reasoning; of these, one of the most attractive is James Allen's algebra of temporal intervals [Allen 1983]. This representation scheme is particularly appealing for its simplicity and for its ease of implementation with constraint propagation algorithms. Reasoners based on

. The Nash equilibria of a two-person, non-zero-sum game are the solutions of a certain linear complementarity problem (LCP). In order to use this for solving a game in extensive form, it is first necessary to convert the game to a strategic description such as the normal form. The classical normal form, however, is often exponentially large in the size of the game tree. In this paper we suggest an alternative approach, based on the sequence form of the game. For a game with perfect recall, the sequence form is a linear sized strategic description, which results in an LCP of linear size. For this LCP, we show that an equilibrium is found by Lemke's algorithm, a generalization of the Lemke-Howson method. Keywords. Equilibrium, extensive game, Lemke-Howson algorithm, linear complementarity, sequence form. Computer Science Division, University of California, Berkeley, CA 94720; and IBM Almaden Research Center, 650 Harry Road, San Jose, CA 95120 y IBM Almaden Research Center, 650 Harr...

This paper is a survey and exposition of linear methods for finding Nash equilibria. Above all, these apply to games with two players. In an equilibrium of a twoperson game, the mixed strategy probabilities of one player equalize the expected payoffs for the pure strategies used by the other player. This defines an optimization problem with linear constraints. We do not consider nonlinear methods like simplicial subdivision for approximating fixed points, or systems of inequalities for higher-degree polynomials as they arise for noncooperative games with more than two players. These are surveyed in McKelvey and McLennan (1996)

This paper is an invited contribution to the 50th anniversary issue of the journal Operations Research, published by the Institute of Operations Research and Management Science (INFORMS). It describes one persons perspective on the development of computational tools for linear programming. The paper begins with a short, personal history, followed by historical remarks covering the some 40 years of linear-programming developments that predate my own involvement in this subject. It concludes with a more detailed look at the evolution of computational linear programming since 1987. 2

Although ceteris paribus preference statements concisely represent one natural class of preferences over outcomes or goals, many applications of such preferences require numeric utility function representations to achieve computational efficiency. We provide algorithms, complete for finite universes of binary features, for converting a set of qualitative ceteris paribus preferences into quantitative utility functions.

. We propose the sequence form as a new strategic description for an extensive game with perfect recall. It is similar to the normal form but has linear instead of exponential complexity, and allows a direct representation and efficient computation of behavior strategies. Pure strategies and their mixed strategy probabilities are replaced by sequences of consecutive choices and their realization probabilities. A zero-sum game is solved by a corresponding linear program that has linear size in the size of the game tree. General two-person games are studied in the paper by Koller, Megiddo, and von Stengel in this journal issue. Journal of Economic Literature Classification Number: C72 Keywords. Behavior strategy, equilibrium, extensive game, linear programming, normal form, reduced normal form. 1. Introduction In applications, it is often convenient to describe a game in extensive form. The game tree, with its information sets, possible moves, chance probabilities and payoffs, gives a...

Sensor networks not only have the potential to change the way we use, interact with, and view computers, but also the way we use, interact with, and view the world around us. In order to maximize the effectiveness of sensor networks, one has to identify, examine, understand, and provide solutions for the fundamental problems related to wireless embedded sensor networks. We believe that one of such problems is to determine how well the sensor network monitors the instrumented area. These problems are usually classified as coverage problems. There already exist several methods that have been proposed to evaluate a sensor network's coverage. We start from

In many optimization and decision problems the objective function can be expressed as a linear combination of competing criteria, the weights of which specify the relative importance of the criteria for the user. We consider the problem of learning such a "subjective" function from preference judgments collected from traces of user interactions. We propose a new algorithm for that task based on the theory of Support Vector Machines. One advantage of the algorithm is that prior knowledge about the domain can easily be included to constrain the solution. We demonstrate the algorithm in a route recommendation system that adapts to the driver's route preferences. We present experimental results on real users that show that the algorithm performs well in practice. 1.

Goldfarb and Hao (1990) have proposed a pivot rule for the primal network simplex algorithm that will solve a maximum flow problem on an n-vertex, m-arc network in at most nm pivots and O(n²m) time. In this paper we describe how to extend the dynamic tree data structure of Sleator and Tarjan (1983, 1985) to reduce the running time of this algorithm to O(nm log n). This bound is less than a logarithmic factor larger than those of the fastest known algorithms for the problem. Our extension of dynamic trees is interesting in its own right and may well have additional applications.

. Programming by linear constraints makes it possible to express complex problems of operations research. However, real industrial problems cannot be solved in a reasonable amount of time if one insists on coding everything only in constraint programming languages. We have experienced this fact in the case of the Airline and bus Crew Scheduling problem. We propose a method based on constraint programming with a part of the implementation written in C. This allows us to solve more easily and also as efficiently as the best existing programs, difficult problems (300 flights and 500000 pairings). This program is currently used for a French airline company. 1 Introduction The crew scheduling problem is one which has been studied continuously for the past 40 years. The problem involves assigning crews to flights. The goal is to minimize crew costs while satisfying the many constraints imposed by governmental and labor work rules. Crew scheduling problems are now efficiently solved by opera...