Parallel Out-of-Core Sorting: The Third Way

Sorting very large datasets is a key subroutine in almost any application that is built on top of a large database. Two ways to sort out-of-core data dominate the literature: merging-based algorithms and partitioning-based algorithms. Within these two paradigms, all the programs that sort out-of-core data on a cluster rely on assumptions about the input distribution. We propose a third way of out-of-core sorting: oblivious algorithms. In all, we have developed six programs that sort out-of-core data on a cluster. The first three programs, based completely on Leighton\u27s columnsort algorithm, have a restriction on the maximum problem size that they can sort. The other three programs relax this restriction; two are based on our original algorithmic extensions to columnsort. We present experimental results to show that our algorithms perform well. To the best of our knowledge, the programs presented in this thesis are the first to sort out-of-core data on a cluster without making any simplifying assumptions about the distribution of the data to be sorted

Stupid columnsort tricks

Leighton’s columnsort algorithm sorts on an r × s mesh, subject to the restrictions that s is a divisor of r and that r ≥ 2s 2 (so that the mesh is tall and thin). We show how to mitigate both of these restrictions. One result is that the requirement that s is a divisor of r is unnecessary; columnsort sorts correctly whether or not s divides r. We present two algorithms that, as long as s is a perfect square, relax the restriction that r ≥ 2s 2; both reduce the exponent of s to 3/2. One algorithm requires r ≥ 4s 3/2 if s divides r and r ≥ 6s 3/2 if s does not divide r. The other algorithm requires r ≥ 4 3/2, and it requires s to be a divisor of r. Both algorithms have applications in increasing the maximum problem size in out-of-core sorting programs. The columnsort algorithm presented by Leighton in 1985 [Lei85] sorts N values on an r × s mesh, where rs = N, subject to three restrictions: 1. r must be even, 2. s must be a divisor of r (the divisibility restriction), an

Oblivious vs. distribution-based sorting: An experimental evaluation

We compare two algorithms for sorting out-of-core data on a distributed-memory cluster. One algorithm, Csort, is a 3-pass oblivious algorithm. The other, Dsort, makes three passes over the data and is based on the paradigm of distribution-based algorithms. In the context of out-of-core sorting, this study is the first comparison between the paradigms of distribution-based and oblivious algorithms. Dsort avoids two of the four steps of a typical distribution-based algorithm by making simplifying assumptions about the distribution of the input keys. Csort makes no assumptions about the keys. Despite the simplifying assumptions, the I/O and communication patterns of Dsort depend heavily on the exact sequence of input keys. Csort, on the other hand, takes advantage of predetermined I/O and communication patterns, governed entirely by the input size in order to overlap computation, communication, and I/O. Experimental evidence shows that, even on inputs that followed Dsort’s simplifying assumptions, Csort fared well. The running time of Dsort showed great variation across five input cases, whereas Csort sorted all of them in approximately the same amount of time. In fact, Dsort ran significantly faster than Csort in just one out of the five input cases: the one that was the most unrealistically skewed in favor of Dsort. A more robust implementation of Dsort—one without the simplifying assumptions—would run even slower.

Slabpose columnsort: A new oblivious algorithm for out-of-core sorting on distributed-memory clusters

Our goal is to develop a robust out-of-core sorting program for a distributed-memory cluster. The literature contains two dominant paradigms for out-of-core sorting algorithms: merging-based and partitioning-based. We explore a third paradigm, that of oblivious algorithms. Unlike the two dominant paradigms, oblivious algorithms do not depend on the input keys and therefore lead to predetermined I/O and communication patterns in an out-of-core setting. We have developed several outof-core sorting programs using this paradigm. Our baseline implementation, 3-pass columnsort, was based on Leighton’s columnsort algorithm. Though efficient in terms of I/O and communication, 3-pass columnsort has a restriction on the maximum problem size. As our first effort toward relaxing this restriction, we developed two implementations: subblock columnsort and M-columnsort. Both of these implementations incur substantial performance costs: subblock columnsort performs additional disk I/O, and M-columnsort needs substantial amounts of extra communication and computation. In this paper, we present slabpose columnsort, a new oblivious algorithm that we have designed explicitly for the out-of-core setting. Slabpose columnsort relaxes the problem-size restriction at no extra I/O or communication cost. Experimental evidence on a Beowulf cluster shows that unlike subblock columnsort and M-columnsort, slabpose columnsort runs almost as fast as 3-pass columnsort. To the best of our knowledge, our implementations are the first out-of-core multiprocessor sorting algorithms that make no assumptions about the keys and produce output that is perfectly load balanced and in the striped order assumed by the Parallel Disk Model

Epilepsy and religion

This study has focused on the interplay between epilepsy and religion. A total of 100 patients in the age range of 15-84 years were included in the study. The duration of epilepsy in these patients ranged from 1-35 years. The majority (66%) had generalized seizures and good to complete seizure control (77%). Regarding social/religious beliefs, 6% of the patients attributed their epilepsy to the curse of God and 14% saw their affliction as a form of punishment for bad deeds committed in the current or past life. Epilepsy was regarded as contagious by 13%. After the onset of epilepsy, 7% of the subjects became skeptics and less religious, while 29% became more religious. Only 2% reported mystic experiences. There was, however, no significant impact of the duration of epilepsy or seizure type on the pattern of religiosity. In 44 cases with symptomatic epilepsy, no definite correlation was observed between the lesion site and laterality and the religious temperament. Delay in seeking treatment and poor compliance due to false religious beliefs, ignorance, and superstition was observed in 33%. However, all religious beliefs were not maladaptive and overall, 80% cases felt that religion had helped them in coping with epilepsy

Relaxing the problem-size bound for out-of-core columnsort

Previous implementations of out-of-core columnsort limit the problem size to N ≤ � (M/P) 3 /2, where N is the number of records to sort, P is the number of processors, and M is the total number of records that the entire system can hold in its memory (so that M/P is the number of records that a single processor can hold in its memory). We implemented two variations to out-of-core columnsort that relax this restriction. Subblock columnsort is based on an algorithmic modification of the underlying columnsort algorithm, and it improves the problem-size bound to N ≤ (M/P) 5/3 /4 2/3 but at the cost of additional disk I/O. M-columnsort changes the notion of the column size in columnsort, improving the maximum problem size to N ≤ � M 3 /2 but at the cost of additional computation and communication. Experimental results on a Beowulf cluster show that both subblock columnsort and M-columnsort run well but that M-columnsort is faster. A further advantage of M-columnsort is that it handles a wider range of problem sizes than subblock columnsort. This research was supported in part by NSF Grant EIA-98-02068.

Columnsort Lives! An Efficient Out-of-Core Sorting Program

We present the design and implementation of a parallel out-of-core sorting algorithm, which is based on Leighton's columnsort algorithm. We show how to relax some of the steps of the original columnsort algorithm to permit a faster out-of-core implementation. Our algorithm requires only 4 passes over the data, and a 3-pass implementation is possible. Although there is a limit on the number of records that can be sorted---as a function of the memory used per processor---this upper limit need not be a severe restriction, and it increases superlinearly with the per-processor memory. To the best of our knowledge, our implementation is the first out-of-core multiprocessor sorting algorithm whose output is in the order assumed by the Parallel Disk Model. We define several measures of sorting efficiency and demonstrate that our implementation's sorting efficiency is competitive with that of NOW-Sort, a sorting algorithm developed to sort large amounts of data quickly on a cluster of workstations

Complexes of Triphenylphosphine Sulphide with Some Lewis Acids

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Association of dengue with longitudinally extensive transverse myelitis and subarachnoid hemorrhage: An unusual presentation

Association of dengue fever with transverse myelitis is a rare phenomenon; involvement of a long segment is even rarer. We describe a middle-aged female who presented with weakness of bilateral lower limbs and urinary retention 4 days after recovery from dengue fever. She, in addition, had a sensory level up to the level of nipples. Magnetic resonance imaging confirmed the diagnosis of longitudinally extensive transverse myelitis. Besides, the patient had spontaneous subarachnoid hemorrhage (SAH) in the absence of dengue hemorrhagic fever. The patient was started on steroids along with rehabilitation. Our case highlights the extensive involvement of spinal cord in the postinfectious phase of dengue and inclusion of this arboviral disease in the differential diagnoses of myelitis as well as an etiology of SAH

Speech Induced Primary Focal Lingual Dystonia

Isolated lingual dystonia is a rare form of focal dystonia. Speech-induced primary lingual dystonia is rarer still, with only eight cases reported worldwide till date. It is a challenge to differentiate it from psychogenic dystonia. This has therapeutic implications as directed speech therapy is an important modality of treatment in speech-induced primary lingual dystonia. We report one such case from our clinical practice