Polynomial-time approximation algorithms with non-trivial performance guarantees are presented for the problems of (a) partitioning the vertices of a weighted graph into k blocks so as to maximise the weight of crossing edges, and (b) partitioning the vertices of a weighted graph into two blocks of equal cardinality, again so as to maximise the weight of crossing edges. The approach, pioneered by Goemans and Williamson, is via a semidefinite relaxation. 1 Introduction Goemans and Williamson [5] have significantly advanced the theory of approximation algorithms. Previous work on approximation algorithms was largely dependent on comparing heuristic solution values to that of a Linear Program (LP) relaxation, either implicitly or explicitly. This was recognised some time ago by Wolsey [11]. (One significant exception to this general rule has been the case of Bin Packing.) The main novelty of [5] is that it uses a Semi-Definite Program (SDP) as a relaxation. To be more precise let...

In this paper, we consider routing and wavelength assignment in wavelength-routed alloptical networks with circuit-switching. The conventional approaches to address this issue consider the two aspects of the problem sequentially by first finding a route from a predetermined set of candidate paths and then searching for an appropriate wavelength assignment. We adopt a more general approach in which we consider all paths between a source-destination pair and incorporate network state information into the routing decision. This approach performs routing and wavelength assignment jointly and adaptively, and outperforms fixed routing techniques. We present adaptive routing and wavelength assignment algorithms and evaluate their blocking performance. We obtain an algorithm to compute approximate blocking probabilities for networks employing fixed and alternate routing techniques. That algorithm can also accommodate networks with multiple fibers per link. The blocking performance of the propo...

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Although the capacity of multiple-input/multiple-output (MIMO) broadcast channels (BCs) can be achieved by dirty paper coding (DPC), it is difficult to implement in practical systems. This paper investigates if, for a large number of users, simpler schemes can achieve the same performance. Specifically, we show that a zero-forcing beamforming (ZFBF) strategy, while generally suboptimal, can achieve the same asymptotic sum capacity as that of DPC, as the number of users goes to infinity. In proving this asymptotic result, we provide an algorithm for determining which users should be active under ZFBF. These users are semiorthogonal to one another and can be grouped for simultaneous transmission to enhance the throughput of scheduling algorithms. Based on the user grouping, we propose and compare two fair scheduling schemes in round-robin ZFBF and proportional-fair ZFBF. We provide numerical results to confirm the optimality of ZFBF and to compare the performance of ZFBF and proposed fair scheduling schemes with that of various MIMO BC strategies.

Most performance debugging and tuning of parallel programs is based on the "measure-modify" approach, which is heavily dependent on detailed measurements of programs during execution. This approach is extremely time-consuming and does not lend itself to predicting performance under varying conditions. Analytic modeling and scalability analysis provide predictive power, but are not widely used inpractice, due primarily to their emphasis on asymptotic behavior and the difficulty of developing accurate models that work for real-world programs. In this paper we describe a set of tools for performance tuning of parallel programs that bridges this gap between measurement and modeling. Our approach is based on lost cycles analysis, which involves measurement and modeling of all sources of overhead in a parallel program. We first describe a tool for measuring overheads in parallel programs that we have incorporated into the runtime environment for Fortran programs on the Kendall Square KSR1. We then describe a tool that ts these overhead measurements to analytic forms. We illustrate the use of these tools by analyzing the performance tradeoffs among parallel implementations of 2D FFT. These examples show how our tools enable programmers to develop accurate performance models of parallel applications without requiring extensive performance modeling expertise.

Recent evidence suggests that some characteristics of computer and telecommunications systems may be well described using heavy tailed distributions — distributions whose tail declines like a power law, which means that the probability of extremely large observations is non-negligible. For example, such distributions have been found to describe the lengths of bursts in network traffic and the sizes of files in some systems. As a result, system designers are increasingly interested in employing heavy-tailed distributions in simulation workloads. Unfortunately, these distributions have properties considerably different from the kinds of distributions more commonly used in simulations; these properties make simulation stability hard to achieve. In this paper we explore the difficulty of achieving stability in such simulations, using tools from the theory of stable distributions. We show that such simulations exhibit two characteristics related to stability: slow convergence to steady state, and high variability at steady state. As a result, we argue that such simulations must be treated as effectively always in a transient condition. One way to address this problem is to introduce the notion of time scale as a parameter of the simulation, and we discuss methods for simulating such systems while explicitly incorporating time scale as a parameter. 1

Several researchers have experimentally shown that substantial improvements can be obtained in difficult pattern recognition problems by combining or integrating the outputs of multiple classifiers. This chapter provides an analytical framework to quantify the improvements in classification results due to combining. The results apply to both linear combiners and order statistics combiners. We first show that to a first order approximation, the error rate obtained over and above the Bayes error rate, is directly proportional to the variance of the actual decision boundaries around the Bayes optimum boundary. Combining classifiers in output space reduces this variance, and hence reduces the "added" error. If N unbiased classifiers are combined by simple averaging, the added error rate can be reduced by a factor of N if the individual errors in approximating the decision boundaries are uncorrelated. Expressions are then derived for linear combiners which are biased or correlated, and the effect of output correlations on ensemble performance is quantified. For order statistics based non-linear combiners, we derive expressions that indicate how much the median, the maximum and in general the ith order statistic can improve classifier performance. The analysis presented here facilitates the understanding of the relationships among error rates, classifier boundary distributions, and combining in output space. Experimental results on several public domain data sets are provided to illustrate the benefits of combining and to support the analytical results.

Blackbox optimization---optimization in presence of limited knowledge about the objective function---has recently enjoyed a large increase in interest because of the demand from the practitioners. This has triggered a race for new high performance algorithms for solving large, difficult problems. Simulated annealing, genetic algorithms, tabu search are some examples. Unfortunately, each of these algorithms is creating a separate field in itself and their use in practice is often guided by personal discretion rather than scientific reasons. The primary reason behind this confusing situation is the lack of any comprehensive understanding about blackbox search. This dissertation takes a step toward clearing some of the confusion. The main objectives of this dissertation are: 1. present SEARCH (Search Envisioned As Relation & Class Hierarchizing)---an alternate perspective of blackbox optimization and its quantitative analysis that lays the foundation essential for transcending the limits of random enumerative search; 2. design and testing of the fast messy genetic algorithm. SEARCH is a general framework for understanding blackbox optimization in terms of relations,

A number of recent papers have used nonparametric density estimation or nonparametric regression to study the instantaneous spot interest rate, and to test term structure models. However, little is known about the performance of these methods when applied to persistent time-series, such as U.S. interest rates. This paper uses the Vasicek [1977] model to study the performance of kernel density estimates of the ergodic distribution of the instantaneous spot rate. The model's tractability allows me to analyze the MISE of the kernel estimate as a function of persistence, variance of the ergodic distribution, span of the data, sampling frequency, and kernel bandwidth. Our principle result is that persistence has an important impact on optimal bandwidth selection and on nite sample performance. We also nd that sampling the data more frequently has little e ect on estimator quality. We also examine one of Ait-Sahalia's [1996a] new nonparametric tests of parametric continuous-time Markov models of the instantaneous spot interest rate. The test is based on the distance between parametric and nonparametric (kernel) estimates of the ergodic distribution of the interest rate process. Our principal result is that the test rejects too often when using asymptotic critical values and 22 years of data. The reason for the high rejection rate is probably because the asymptotic distribution of the test does not depend on persistence, but the nite sample performance of the estimator does. After critical values are adjusted for size, the test has low power in distinguishing between the Vasicek and Cox-Ingersoll-Ross models when compared with a conditional moment based speci cation test.

In high-speed networks it is desirable to interleave routing and resource (such as bandwidth) reservation. The PNNI standard for private ATM networks is a recent example for an algorithm that does this using a sequential crank-back mechanism. In this work, we suggest to do resource reservation along several routes in parallel. We present an analytical model that demonstrates that when there are several routes to the destination it pays to attempt reservation along more than a single route. Following this analytic observation, we present a family of algorithms that route and reserve resources along parallel subroutes. The algorithms of the family represent different trade-offs between the speed and the quality of the established route. The presented algorithms are simulated against several legacy algorithm, including PNNI crank-back, and exhibit higher network utilization and faster connection set-up time. 1 Introduction Broadband integrated services digital networks (BISDN) are aimed ...