The On-Line Multiprocessor Scheduling Problem with Known Sum of the Tasks

In this paper we investigate a semi on-line multiprocessor scheduling problem. The problem is the classical on-line multiprocessor problem where the total sum of the tasks is known in advance. We show an asymptotic lower bound on the performance ratio of any algorithm (as the number of processors gets large), and present an algorithm which has performance ratio at most for any number of processors. When compared with known general lower bounds, this result indicates that the information on the sum of tasks substantially improves the performance ratio of on-line algorithms.     

Competitive Deadline Scheduling via Additional or Faster Processors

This paper studies on-line scheduling in a single-processor system that allows preemption. The aim is to maximize the total value of jobs completed by their deadlines. It is known that if the on-line scheduler is given a processor faster (say, two times faster) than the off-line scheduler, then there exists an on-line algorithm called that can achieve an O(1) competitive ratio. In this paper, we show that using additional unit-speed processors instead of a faster processor is a possible but not cost effective way to achieve an O(1) competitive ratio. Specifically, we find that-(logk) unit-speed processors are required, where k is the importance ratio. Another contribution of this paper is an improved analysis of the competitiveness of ; this new analysis enables us to show that , when extended to multi-processor systems, can still guarantee an O(1) competitive ratio.     

Barely Random Algorithms for Multiprocessor Scheduling

We consider randomized algorithms for on-line scheduling on identical machines. For two machines, a randomized algorithm achieving a competitive ratio of was found by Bartal et al. (1995). Seiden has presented a randomized algorithm which achieves competitive ratios of 1.55665, 1.65888, 1.73376, 1.78295, and 1.81681, for m=3,4,5,6,7, respectively (Seiden, 2000). A barely random algorithm is one which is a distribution over a constant number of deterministic strategies. The algorithms of Bartal et al. and Seiden are not barely random–in fact, these algorithms potentially make a random choice for each job scheduled. We present the first barely random on-line scheduling algorithms. In addition, our algorithms use less space and time than the previous algorithms, asymptotically.     

Competitive On-Line Scheduling with Level of Service

Motivated by an application in thinwire visualization, we study an abstract on-line scheduling problem where the size of each requested service can be scaled down by the scheduler. Thus, our problem embodies a notion of Level of Service that is increasingly important in multimedia applications. We give two schedulers and based on two simple heuristics, and generalize them into a class of greedy schedulers. We show that both and are 2-competitive, and any greedy scheduler is 3-competitive. These bounds are shown to be tight.     

Solving A\underline x =\underline b Using a Modified Conjugate Gradient Method Based on Roots of A

We consider the modified conjugate gradient procedure for solving A = in which the approximation space is based upon the Krylov space associated with A ^1/p and , for any integer p. For the square-root MCG (p=2) we establish a sharpened bound for the error at each iteration via Chebyshev polynomials in . We discuss the implications of the quickly accumulating effect of an error in in the initial stage, and find an error bound even in the presence of such accumulating errors. Although this accumulation of errors may limit the usefulness of this method when is unknown, it may still be successfully applied to a variety of small, almost-SPD problems, and can be used to jump-start the conjugate gradient method. Finally, we verify these theoretical results with numerical tests.     

Estimating the Optimal Margins of Embeddings in Euclidean Half Spaces

Concept classes can canonically be represented by matrices with entries 1 and –1. We use the singular value decomposition of this matrix to determine the optimal margins of embeddings of the concept classes of singletons and of half intervals in homogeneous Euclidean half spaces. For these concept classes the singular value decomposition can be used to construct optimal embeddings and also to prove the corresponding best possible upper bounds on the margin. We show that the optimal margin for embedding n singletons is and that the optimal margin for half intervals over {1,...,n} is . For the upper bounds on the margins we generalize a bound by Forster (2001). We also determine the optimal margin of some concept classes defined by circulant matrices up to a small constant factor, and we discuss the concept classes of monomials to point out limitations of our approach.     

Combining the Perceptron Algorithm with Logarithmic Simulated Annealing

We present results of computational experiments with an extension of the Perceptron algorithm by a special type of simulated annealing. The simulated annealing procedure employs a logarithmic cooling schedule , where is a parameter that depends on the underlying configuration space. For sample sets S of n-dimensional vectors generated by randomly chosen polynomials , we try to approximate the positive and negative examples by linear threshold functions. The approximations are computed by both the classical Perceptron algorithm and our extension with logarithmic cooling schedules. For and , the extension outperforms the classical Perceptron algorithm by about 15% when the sample size is sufficiently large. The parameter was chosen according to estimations of the maximum escape depth from local minima of the associated energy landscape.      

Biologically Inspired Autonomous Rover Control

Robotic missions beyond 2013 will likely be precursors to a manned habitat deployment on Mars. Such missions require robust control systems for long duration activities. Current single rover missions will evolve into deployment of multiple, heterogeneous cooperating robotic colonies. This paper describes the map-making memory and action selection mechanism of BISMARC ( iologically nspired ystem for ap-based utonomous over ontrol) that is currently under development at the Jet Propulsion Laboratory in Pasadena, CA (Huntsberger and Rose, Neutral Networks, 11(7/8):1497–1510). BISMARC is an integrated control system for long duration missions involving robots performing cooperative tasks.     

An Algebraic Approach to Propositional Fuzzy Logic

We investigate the variety corresponding to a logic (introduced in Esteva and Godo, 1998, and called there), which is the combination of ukasiewicz Logic and Product Logic, and in which Gödel Logic is interpretable. We present an alternative (and slightly simpler) axiomatization of such variety. We also investigate the variety, called the variety of algebras, corresponding to the logic obtained from by the adding of a constant and of a defining axiom for one half. We also connect algebras with structures, called f-semifields, arising from the theory of lattice-ordered rings, and prove that every algebra can be regarded as a structure whose domain is the interval [0, 1] of an f-semifield , and whose operations are the truncations of the operations of to [0, 1]. We prove that such a structure is uniquely determined by up to isomorphism, and we establish an equivalence between the category of algebras and that of f-semifields.     

Adaptive Anomaly Detection in Transaction-Oriented Networks

Adaptive algorithms for real-time and proactive detection of network/service anomalies, i.e., soft performance degradations, in transaction-oriented wide area networks (WANs) have been developed. These algorithms (i) adaptively sample and aggregate raw transaction records to compute service-class based traffic intensities, in which potential network anomalies are highlighted; (ii) construct dynamic and service-class based performance thresholds for detecting network and service anomalies; and (iii) perform service-class based and real-time network anomaly detection. These anomaly detection algorithms are implemented as a real-time software system called TRISTAN ( ansaction n antaneous nomaly otification), which is deployed in the AT&T Transaction Access Services (TAS) network. The TAS network is a commercially important, high volume (millions of transactions per day), multiple service classes (tens), hybrid telecom and data WAN that services transaction traffic such as credit card transactions in the US and neighboring countries. TRISTAN is demonstrated to be capable of automatically and adaptively detecting network/service anomalies and correctly identifying the corresponding "guilty" service classes in TAS. TRISTAN can detect network/service faults that elude detection by the traditional alarm-based network monitoring systems.     

Conditions for Instability of One Class of Nonlinear Nonautomomous Dynamic Systems

Consideration was given to the conditions for instability of the equilibrium states of a nonlinear nonautonomous dynamic systems obeying an ordinary vector differential equation of arbitrary order whose right-hand side satisfies the following conditions: (i) for any t 0, div 0$$ " align="middle" border="0"> almost everywhere on the set H that is a neighborhood of the equilibrium point of the system and (ii) at any point . The equilibrium states of such systems can be both stable and unstable. For one class of these systems, sufficient instability conditions were given, which enables one to carry out studies using only the information about the right-hand side of the system.     

Stability of Linear Difference and Differential Inclusions

Any given n×n matrix A is shown to be a restriction, to the A-invariant subspace, of a nonnegative N×N matrix B of spectral radius (B) arbitrarily close to (A). A difference inclusion , where is a compact set of matrices, is asymptotically stable if and only if can be extended to a set of nonnegative matrices B with or . Similar results are derived for differential inclusions.     

The Complexity of Learning According to Two Models of a Drifting Environment

We show that a bound on the rate of drift of the distribution generating the examples is sufficient for agnostic learning to relative accuracy , where c > 0 is a constant; this matches a known necessary condition to within a constant factor. We establish a sufficient condition for the realizable case, also matching a known necessary condition to within a constant factor. We provide a relatively simple proof of a bound of + on the sample complexity of agnostic learning in a fixed environment.     

Tracking the Best Disjunction

Littlestone developed a simple deterministic on-line learning algorithm for learning k-literal disjunctions. This algorithm (called ) keeps one weight for each of then variables and does multiplicative updates to its weights. We develop a randomized version of and prove bounds for an adaptation of the algorithm for the case when the disjunction may change over time. In this case a possible target disjunction schedule is a sequence of disjunctions (one per trial) and the shift size is the total number of literals that are added/removed from the disjunctions as one progresses through the sequence.We develop an algorithm that predicts nearly as well as the best disjunction schedule for an arbitrary sequence of examples. This algorithm that allows us to track the predictions of the best disjunction is hardly more complex than the original version. However, the amortized analysis needed for obtaining worst-case mistake bounds requires new techniques. In some cases our lower bounds show that the upper bounds of our algorithm have the right constant in front of the leading term in the mistake bound and almost the right constant in front of the second leading term. Computer experiments support our theoretical findings.     

Stability of the Logistic Population Model with Delayed Environmental Response

The population dynamics model , was considered. For this model with uniform distribution of delays and a _n = 0, nonnegativeness and convexity of the sequence a _k (0 k n) was shown to be the sufficient stability condition. Therefore, there is no need to constrain the reproduction rate and the mean delay .     

Two-Parameter Discrete Systems over a Residue Ring and Their Properties

A class of two-parameter discrete systems defined on the ring of class of residues of integers modulo m is studied. All solutions are shown to be periodic, stability conditions (equality of solutions to zero, beginning from a certain instant) and a controllability condition are formulated. Controllability is shown to guarantee stabilizability.     

Formal Solutions of Linear Ordinary Differential Equations Containing m-Hypergeometric Series

Let a linear homogeneous ordinary differential equation with polynomial coefficients over a field be given. For a singular point of the equation, the fundamental system of formal solutions that contain a finite number of power series with coefficients belonging to the algebraic extension of can be constructed by known algorithms. In this paper, an algorithm is suggested for construction of a space of formal solutions such that all series containing in these solutions have m-hypergeometric coefficients. The implementation of the algorithm in the computer algebra system Maple is discussed.     

Concurrent Sample Path Analysis of Discrete Event Systems

The sample path constructability problem for Discrete Event Systems (DES) involves the observation of a sample path under a particular parameter value of the system with the requirement to concurrently construct multiple sample paths of the DES under different values using only information available along the given sample path. This allows the on-line estimation of performance measures , not available in closed form, over a range of values of . We present a sample path coupling approach that solves the problem without imposing any restrictions on the event processes in the system. A specific time warping algorithm is described and its performance is analyzed in terms of computational cost. Our approach is illustrated through a number of simulation results.     

Algorithms and optimality of scheduling soft aperiodic requests in fixed-priority preemptive systems

In this paper, we investigate the problem of scheduling soft aperiodic requests in systems where periodic tasks are scheduled on a fixed-priority, preemptive basis. First, we show that given any queueing discipline for the aperiodic requests, no scheduling algorithm can minimize the response time of every aperiodic request and guarantee that the deadlines of the periodic tasks are met when the periodic tasks are scheduled on a fixed-priority, preemptive basis. We then develop two algorithms: Algorithm is locally optimal in that it minimizes the response time of the aperiodic request at the head of the aperiodic service queue. Algorithm is globally optimal in that it completes the current backlog of work in the aperiodic service queue as early as possible.