Optimal partitioning of random programs across two processors

The optimal partitioning of random distributed programs is discussed. It is concluded that the optimal partitioning of a homogeneous random program over a homogeneous distributed system either assigns all modules to a single processor, or distributes the modules as evenly as possible among all processors. The analysis rests heavily on the approximation which equates the expected maximum of a set of independent random variables with the set's maximum expectation. The results are strengthened by providing an approximation-free proof of this result for two processors under general conditions on the module execution time distribution. It is also shown that use of this approximation causes two of the previous central results to be false

Expected performance of m-solution backtracking

This paper derives upper bounds on the expected number of search tree nodes visited during an m-solution backtracking search, a search which terminates after some preselected number m problem solutions are found. The search behavior is assumed to have a general probabilistic structure. The results are stated in terms of node expansion and contraction. A visited search tree node is said to be expanding if the mean number of its children visited by the search exceeds 1 and is contracting otherwise. It is shown that if every node expands, or if every node contracts, then the number of search tree nodes visited by a search has an upper bound which is linear in the depth of the tree, in the mean number of children a node has, and in the number of solutions sought. Also derived are bounds linear in the depth of the tree in some situations where an upper portion of the tree contracts (expands), while the lower portion expands (contracts). While previous analyses of 1-solution backtracking have concluded that the expected performance is always linear in the tree depth, the model allows superlinear expected performance

"Bad business": capitalism and criminality in Agatha Christie's novels

To the casual reader, Agatha Christie’s fiction seems to be saturated by a deeply conservative culture and supportive of the capitalist status quo. There is indeed some evidence in Christie’s prose that she identified with conservativism. Yet despite her leanings she adopted a critical stance on the world of business. She repeatedly depicted financiers as criminals, even murderers, during the inter-war years and later, in the post-war period, blurred the line between businesses and criminal conspiracies. Christie also used the crookedness of business to provide capitalism’s victims with a motive for murder. The article explains the gap between Christie’s political views and her portrayal of business by arguing that Christie’s fundamental task was to fashion dystopias. In so doing she regarded it as more important to capture the spirit of the times than to propagandise in ways which matched her allegiances. Thus Christie’s engagement with private enterprise provides a valuable snapshot of a society more critical of capitalism and, particularly between the wars, more ready to consider alternatives to it, than is the case in contemporary society

"Doctor Who, Family and National Identity"

National identity is often intimately bound to connectedness to, independence from, and constructions of, family. Furthermore family remains integral to neoliberal capitalism such that efforts to develop national identity along capitalist lines are likely to involve engagement with it. Legal changes in Britain over the last forty years reflect these constructions. Doctor Who is a science-fiction programme in which an alien (the Doctor) has adventures with mainly human companions, travelling in time and space in a ship called the TARDIS. As the BBC’s longest-running television drama series, and one with a long-term focus on projecting Britishness, Doctor Who valuably charts how national identity has evolved. In the context of the Doctor’s companions in particular, Doctor Who’s treatment of family has altered starkly over time. This article identifies an orphan companions era in the programme’s early years in which characters’ families were either startlingly unmentioned or dead, leaving the TARDIS ‘family’ unchallenged. After a transitional phase in the 1980s in which each companion’s family assumes only fleeting significance, the programme’s post-2005 reboot ushered in an era of deep engagement with family in which families assume seminal importance. By putting family centre-stage Doctor Who captures the spirit of the age, marking a refashioning of British national identity in which family looms large. This reflects Britain’s transition from social democracy to neoliberalism. Distancing itself from conservatism, however, Doctor Who’s promotion of family goes hand in hand with the programme developing its own more progressive take on what constitutes the ‘good family’

Dynamic remapping of parallel computations with varying resource demands

A large class of computational problems is characterized by frequent synchronization, and computational requirements which change as a function of time. When such a problem must be solved on a message passing multiprocessor machine, the combination of these characteristics lead to system performance which decreases in time. Performance can be improved with periodic redistribution of computational load; however, redistribution can exact a sometimes large delay cost. We study the issue of deciding when to invoke a global load remapping mechanism. Such a decision policy must effectively weigh the costs of remapping against the performance benefits. We treat this problem by constructing two analytic models which exhibit stochastically decreasing performance. One model is quite tractable; we are able to describe the optimal remapping algorithm, and the optimal decision policy governing when to invoke that algorithm. However, computational complexity prohibits the use of the optimal remapping decision policy. We then study the performance of a general remapping policy on both analytic models. This policy attempts to minimize a statistic W(n) which measures the system degradation (including the cost of remapping) per computation step over a period of n steps. We show that as a function of time, the expected value of W(n) has at most one minimum, and that when this minimum exists it defines the optimal fixed-interval remapping policy. Our decision policy appeals to this result by remapping when it estimates that W(n) is minimized. Our performance data suggests that this policy effectively finds the natural frequency of remapping. We also use the analytic models to express the relationship between performance and remapping cost, number of processors, and the computation's stochastic activity

Statistical methodologies for the control of dynamic remapping

Following an initial mapping of a problem onto a multiprocessor machine or computer network, system performance often deteriorates with time. In order to maintain high performance, it may be necessary to remap the problem. The decision to remap must take into account measurements of performance deterioration, the cost of remapping, and the estimated benefits achieved by remapping. We examine the tradeoff between the costs and the benefits of remapping two qualitatively different kinds of problems. One problem assumes that performance deteriorates gradually, the other assumes that performance deteriorates suddenly. We consider a variety of policies for governing when to remap. In order to evaluate these policies, statistical models of problem behaviors are developed. Simulation results are presented which compare simple policies with computationally expensive optimal decision policies; these results demonstrate that for each problem type, the proposed simple policies are effective and robust