The subgradient method is frequently used to optimize dual functions in Lagrangian relaxation for separable integer programming problems. In the method, all subproblems must be optimally solved to obtain a subgradient direction. In this paper, the "surrogate subgradient method" is developed, where a proper direction can be obtained without optimally solving all the subproblems. In fact, only approximate optimization of one subproblem is needed to get a proper "surrogate subgradient direction," and the directions are smooth for problems of large size. The convergence of the algorithm is proved. Compared with methods that take effort to find better directions, this method can obtain good directions with much less effort, and provides a new approach that is especially powerful for problems of very large size.

We thank the Island ECN for providing us with the data for this study, and are especially grateful for the help of Cameron Smith, Josh Levine, and Rob Newhouse. We also thank Tim McCormick and the NASD’s Economic Research for providing us with odd-lot data, and Lei Yu for her research assistance. For comments on an earlier draft we are indebted

This paper explores the competition between two trading venues, Electronic Communication Networks (ECNs) and Nasdaq market makers. ECNs o¡er the advantages of anonymity and speed of execution, which attract informed traders. Thus, trades are more likely to occur on ECNs when information asymmetry is greater and when trading volume and stock-return volatility are high. ECN trades have greater permanent price impacts and more private information is revealed through ECN trades than though market-maker trades. However, ECN trades have higher ex ante trading costs because market makers can preference or internalize the less informed trades and o¡er them better executions. TECHNOLOGICAL INNOVATIONS THAT ENABLE HIGH-SPEED, low-cost electronic trading systems are dramatically changing the structure of ¢nancial markets. Exchanges and markets around the world are merging or forming alliances to improve liquidity and reduce costs in the face of increased competition from each other and from these computerized trading systems.Trading volume on Electronic Communications Networks (ECNs) has grown rapidly over the past several years. ECNs are now involved in more than a third of Nasdaq trading volume and are attempting to increase their market share in NYSE-listed

Anew algorithm is introduced which computes the multivariate leading coefficients of polynomial factors from their univariate images. This algorithm is incorporated into a sparse Hensel lifting scheme and only requires the factorization of a single univariate image. The algorithm also provides the content of the input polynomial in the main variable as a by-product. We show how we can take advantage of this property when computing the GCD of multivariate polynomials by sparse Hensel lifting. 1.

In this paper we present a system which automatically corrects disfluencies such as repairs and restarts typically occurring in spontaneously spoken speech. The system is based on a noisy-channel model and its development requires no linguistic knowledge, but only annotated texts. Therefore, it has large potential for rapid deployment and the adaptation to new target languages. The experiments were conducted on spontaneously spoken dialogs from the English VERBMOBIL corpus where a recall of 77.2% and a precision of 90.2% was obtained. To demonstrate the feasibility of rapid adaptation additional experiments on the spontaneous Mandarin Chinese CallHome corpus were performed achieving 49.4% recall and 76.8% precision.

I propose a continuous-time model of price formation in a market where trading is conducted according to a limit-order book. Strategic liquidity traders arrive randomly in the market and dynamically choose between limit and market orders, trading off execution price with waiting costs. I prove the existence of a Markov equilibrium in which the bid and ask prices depend only on the numbers of buy and sell orders in the book, and which can be characterized in closed-form in several cases of interest. My model generates empirically verified implications for the shape of the limit-order book and the dynamics of prices and trades. In particular, I show that buy and sell orders can cluster away from the bid-ask spread, thus generating a hump-shaped limit-order book. Also, following a market buy order, both the ask and bid prices increase, with the ask increasing more than the bid—hence the spread widens.

We give an introduction to programming methods, software systems, and algorithms, suitable for parallelizing Computer Algebra on modern multiprocessor workstations. As concrete examples we present multi-threaded programming and its use in the PARSAC-2 system for parallel symbolic computation, and we present some examples of parallel algorithms useful for solving systems of polynomial equations.

Abstract not found

Three theorems are presented that establish polynomial straight-line complexity for certain operations on polynomials given by straight-line programs of unbounded input degree he first theorem shows how to compute a higher order partial derivative in a single variable. l The other two theorems impose the degree of the output polynomial as a parameter of the ength of the output program. First it is shown that if a straight-line program computes an l b arbitrary power of a multivariate polynomial, that polynomial also admits a polynomia ounded straight-line computation. Second, any factor of a multivariate polynomial given by e c a division-free straight-line program with relatively prime co-factor also admits a straight-lin omputation of length polynomial in the input length and the degree of the factor. This result t is based on a new Hensel lifting process, one where only one factor image is lifted back to he original factor. As an application we get that the greatest common divi...

The Heuristic Polynomial GCD procedure (GCDHEU) is used by the Maple computer algebra system, but no other. Because Maple has an especially efficient kernel that provides fast integer arithmetic, but a relatively slower interpreter for non-kernel code, the GCDHEU routine is especially effective in that it moves much of the computation into "bignum" arithmetic and hence executes primarily in the kernel. We speculated that in other computer algebra systems an implementation GCDHEU would not be advantageous. In particular, if all the system code is compiled to run at "full speed" in a (presumably more bulky) kernel that is entirely written in C or compiled Lisp, then there would seem to be no point in recasting the polynomial gcd problem into a bignum GCD problem. Manipulating polynomials that are vectors of coefficients would seem to be equivalent computationally to manipulating vectors of big digits. Yet our evidence suggests that one can take advantage of the GCDHEU in a Lisp system as...