Scheduling MapReduce Jobs under Multi-Round Precedences

We consider non-preemptive scheduling of MapReduce jobs with multiple tasks in the practical scenario where each job requires several map-reduce rounds. We seek to minimize the average weighted completion time and consider scheduling on identical and unrelated parallel processors. For identical processors, we present LP-based O(1)-approximation algorithms. For unrelated processors, the approximation ratio naturally depends on the maximum number of rounds of any job. Since the number of rounds per job in typical MapReduce algorithms is a small constant, our scheduling algorithms achieve a small approximation ratio in practice. For the single-round case, we substantially improve on previously best known approximation guarantees for both identical and unrelated processors. Moreover, we conduct an experimental analysis and compare the performance of our algorithms against a fast heuristic and a lower bound on the optimal solution, thus demonstrating their promising practical performance

New Dependencies of Hierarchies in Polynomial Optimization

We compare four key hierarchies for solving Constrained Polynomial Optimization Problems (CPOP): Sum of Squares (SOS), Sum of Diagonally Dominant Polynomials (SDSOS), Sum of Nonnegative Circuits (SONC), and the Sherali Adams (SA) hierarchies. We prove a collection of dependencies among these hierarchies both for general CPOPs and for optimization problems on the Boolean hypercube. Key results include for the general case that the SONC and SOS hierarchy are polynomially incomparable, while SDSOS is contained in SONC. A direct consequence is the non-existence of a Putinar-like Positivstellensatz for SDSOS. On the Boolean hypercube, we show as a main result that Schm\"udgen-like versions of the hierarchies SDSOS*, SONC*, and SA* are polynomially equivalent. Moreover, we show that SA* is contained in any Schm\"udgen-like hierarchy that provides a O(n) degree bound.Comment: 26 pages, 4 figure

An Unusual Cause of Dementia: Essential Diagnostic Elements of Corticobasal Degeneration—A Case Report and Review of the Literature

Corticobasal degeneration (CBD) is an uncommon, sporadic, neurodegenerative disorder of mid- to late-adult life. We describe a further example of the pathologic heterogeneity of this condition. A 71-year-old woman initially presented dysarthria, clumsiness, progressive asymmetric bradykinesia, and rigidity in left arm. Rigidity gradually involved ipsilateral leg; postural instability with falls, blepharospasm, and dysphagia subsequently developed. She has been previously diagnosed as unresponsive Parkinson's Disease. At our clinical examination, she presented left upper-arm-fixed-dystonia, spasticity in left lower limb and pyramidal signs (Babinski and Hoffmann). Brain MRI showed asymmetric cortical atrophy in the right frontotemporal cortex. Neuropsychological examination showed an impairment in visuospatial functioning, frontal-executive dysfunction, and hemineglect. This case demonstrates that association of asymmetrical focal cortical and subcortical features remains the clinical hallmark of this condition. There are no absolute markers for the clinical diagnosis that is complicated by the variability of presentation involving also cognitive symptoms that are reviewed in the paper. Despite the difficulty of diagnosing CBD, somatosensory evoked potentials, motor evoked potentials, long latency reflexes, and correlations between results on electroencephalography (EEG) and electromyography (EMG) provide further support for a CBD diagnosis. These techniques are also used to identify neurophysiological correlates of the neurological signs of the disease

Universal Sequencing on an Unreliable Machine

We consider scheduling on an unreliable machine that may experience unexpected changes in processing speed or even full breakdowns. Our objective is to minimize ∑ wjf(Cj) for any nondecreasing, nonnegative, differentiable cost function f(Cj). We aim for a universal solution that performs well without adaptation for all cost functions for any possible machine behavior. We design a deterministic algorithm that finds a universal scheduling sequence with a solution value within 4 times the value of an optimal clairvoyant algorithm that knows the machine behavior in advance. A randomized version of this algorithm attains in expectation a ratio of e. We also show that both performance guarantees are best possible for any unbounded cost function. Our algorithms can be adapted to run in polynomial time with slightly increased cost. When jobs have individual release dates, the situation changes drastically. Even if all weights are equal, there are instances for which any universal solution is a factor of Ω(log n / log log n) worse than an optimal sequence for any unbounded cost function. Motivated by this hardness, we study the special case when the processing time of each job is proportional to its weight. We present a nontrivial algorithm with a small constant performance guarantee

An elitist quantum-inspired evolutionary algorithm for the flexible job-shop scheduling problem

The flexible job shop scheduling problem (FJSP) is vital to manufacturers especially in today’s constantly changing environment. It is a strongly NP-hard problem and therefore metaheuristics or heuristics are usually pursued to solve it. Most of the existing metaheuristics and heuristics, however, have low efficiency in convergence speed. To overcome this drawback, this paper develops an elitist quantum-inspired evolutionary algorithm. The algorithm aims to minimise the maximum completion time (makespan). It performs a global search with the quantum-inspired evolutionary algorithm and a local search with a method that is inspired by the motion mechanism of the electrons around an atomic nucleus. Three novel algorithms are proposed and their effect on the whole search is discussed. The elitist strategy is adopted to prevent the optimal solution from being destroyed during the evolutionary process. The results show that the proposed algorithm outperforms the best-known algorithms for FJSPs on most of the FJSP benchmarks

Universal Sequencing on a Single Machine

We consider scheduling on an unreliable machine that may experience unexpected changes in processing speed or even full breakdowns. We aim for a universal solution that performs well without adaptation for any possible machine behavior. For the objective of minimizing the total weighted completion time, we design a polynomial time deterministic algorithm that finds a universal scheduling sequence with a solution value within 4 times the value of an optimal clairvoyant algorithm that knows the disruptions in advance. A randomized version of this algorithm attains in expectation a ratio of e. We also show that both results are best possible among all universal solutions. As a direct consequence of our results, we answer affirmatively the question of whether a constant approximation algorithm exists for the offline version of the problem when machine unavailability periods are known in advance. When jobs have individual release dates, the situation changes drastically. Even if all weights are equal, there are instances for which any universal solution is a factor of Ω(log n/ log log n) worse than an optimal sequence. Motivated by this hardness, we study the special case when the processing time of each job is proportional to its weight. We present a non-trivial algorithm with a small constant performance guarantee. © 2010 Springer-Verlag

La chirurgia laparoscopica nel trattamento del prolasso del retto completo.

Sourcerecord Id Scopus 2048

Local excission of rectal tumours with transanal endoscopic microsurgery (TEM)

Sourcerecord Id Scopus 2172