An Enhanced Multiway Sorting Network Based on n-Sorters

Merging-based sorting networks are an important family of sorting networks. Most merge sorting networks are based on 2-way or multi-way merging algorithms using 2-sorters as basic building blocks. An alternative is to use n-sorters, instead of 2-sorters, as the basic building blocks so as to greatly reduce the number of sorters as well as the latency. Based on a modified Leighton's columnsort algorithm, an n-way merging algorithm, referred to as SS-Mk, that uses n-sorters as basic building blocks was proposed. In this work, we first propose a new multiway merging algorithm with n-sorters as basic building blocks that merges n sorted lists of m values each in 1 + ceil(m/2) stages (n <= m). Based on our merging algorithm, we also propose a sorting algorithm, which requires O(N log2 N) basic sorters to sort N inputs. While the asymptotic complexity (in terms of the required number of sorters) of our sorting algorithm is the same as the SS-Mk, for wide ranges of N, our algorithm requires fewer sorters than the SS-Mk. Finally, we consider a binary sorting network, where the basic sorter is implemented in threshold logic and scales linearly with the number of inputs, and compare the complexity in terms of the required number of gates. For wide ranges of N, our algorithm requires fewer gates than the SS-Mk.Comment: 13 pages, 14 figure

A correctness proof of sorting by means of formal procedures

We consider a recursive sorting algorithm in which, in each invocation, a new variable and a new procedure (using the variable globally) are defined and the procedure is passed to recursive calls. This algorithm is proved correct with Hoare-style pre- and postassertions. We also discuss the same algorithm expressed as a functional program

Efficient spike-sorting of multi-state neurons using inter-spike intervals information

We demonstrate the efficacy of a new spike-sorting method based on a Markov Chain Monte Carlo (MCMC) algorithm by applying it to real data recorded from Purkinje cells (PCs) in young rat cerebellar slices. This algorithm is unique in its capability to estimate and make use of the firing statistics as well as the spike amplitude dynamics of the recorded neurons. PCs exhibit multiple discharge states, giving rise to multimodal interspike interval (ISI) histograms and to correlations between successive ISIs. The amplitude of the spikes generated by a PC in an "active" state decreases, a feature typical of many neurons from both vertebrates and invertebrates. These two features constitute a major and recurrent problem for all the presently available spike-sorting methods. We first show that a Hidden Markov Model with 3 log-Normal states provides a flexible and satisfying description of the complex firing of single PCs. We then incorporate this model into our previous MCMC based spike-sorting algorithm (Pouzat et al, 2004, J. Neurophys. 91, 2910-2928) and test this new algorithm on multi-unit recordings of bursting PCs. We show that our method successfully classifies the bursty spike trains fired by PCs by using an independent single unit recording from a patch-clamp pipette.Comment: 25 pages, to be published in Journal of Neurocience Method

An Optimized Input Sorting Algorithm

One of the fundamental issues in compute science is ordering a list of items. Although there is a huge number of sorting algorithms, sorting problem has attracted a great deal of research, because efficient sorting is important to optimize the use of other algorithms. Sorting involves rearranging information into either ascending or descending order. This paper presents a new sorting algorithm called Input Sort. This new algorithm is analyzed, implemented, tested and compared and results were promising