A simple optimal randomized algorithm for sorting on the PDM

The Parallel Disks Model (PDM) has been proposed to alleviate the I/O bottleneck that arises in the processing of massive data sets. Sorting has been extensively studied on the PDM model due to the fundamental nature of the problem. Several randomized algorithms are known for sorting. Most of the prior algorithms suffer from undue complications in memory layouts, implementation, or lack of tight analysis. In this paper we present a simple randomized algorithm that sorts in optimal time with high probablity and has all the desirable features for practical implementation

An Elegant Algorithm for the Construction of Suffix Arrays

The suffix array is a data structure that finds numerous applications in string processing problems for both linguistic texts and biological data. It has been introduced as a memory efficient alternative for suffix trees. The suffix array consists of the sorted suffixes of a string. There are several linear time suffix array construction algorithms (SACAs) known in the literature. However, one of the fastest algorithms in practice has a worst case run time of $O(n^2)$. The problem of designing practically and theoretically efficient techniques remains open. In this paper we present an elegant algorithm for suffix array construction which takes linear time with high probability; the probability is on the space of all possible inputs. Our algorithm is one of the simplest of the known SACAs and it opens up a new dimension of suffix array construction that has not been explored until now. Our algorithm is easily parallelizable. We offer parallel implementations on various parallel models of computing. We prove a lemma on the $\ell$-mers of a random string which might find independent applications. We also present another algorithm that utilizes the above algorithm. This algorithm is called RadixSA and has a worst case run time of $O(n\log{n})$. RadixSA introduces an idea that may find independent applications as a speedup technique for other SACAs. An empirical comparison of RadixSA with other algorithms on various datasets reveals that our algorithm is one of the fastest algorithms to date. The C++ source code is freely available at http://www.engr.uconn.edu/~man09004/radixSA.zi

Algorithmic ramifications of prefetching in memory hierarchy

External Memory models, most notable being the I-O Model [3], capture the effects of memory hierarchy and aid in algorithm design. More than a decade of architectural advancements have led to new features not captured in the I-O model - most notably the prefetching capability. We propose a relatively simple Prefetch model that incorporates data prefetching in the traditional I-O models and show how to design algorithms that can attain close to peak memory bandwidth. Unlike (the inverse of) memory latency, the memory bandwidth is much closer to the processing speed, thereby, intelligent use of prefetching can considerably mitigate the I-O bottleneck. For some fundamental problems, our algorithms attain running times approaching that of the idealized Random Access Machines under reasonable assumptions. Our work also explains the significantly superior performance of the I-O efficient algorithms in systems that support prefetching compared to ones that do not

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

Spin-the-bottle Sort and Annealing Sort: Oblivious Sorting via Round-robin Random Comparisons

We study sorting algorithms based on randomized round-robin comparisons. Specifically, we study Spin-the-bottle sort, where comparisons are unrestricted, and Annealing sort, where comparisons are restricted to a distance bounded by a \emph{temperature} parameter. Both algorithms are simple, randomized, data-oblivious sorting algorithms, which are useful in privacy-preserving computations, but, as we show, Annealing sort is much more efficient. We show that there is an input permutation that causes Spin-the-bottle sort to require $\Omega(n^2\log n)$ expected time in order to succeed, and that in $O(n^2\log n)$ time this algorithm succeeds with high probability for any input. We also show there is an implementation of Annealing sort that runs in $O(n\log n)$ time and succeeds with very high probability.Comment: Full version of a paper appearing in ANALCO 2011, in conjunction with SODA 201

Reduced Complexity Optimal Hard Decision Fusion under Neyman-Pearson Criterion

Distributed detection is an important part of many of the applications like wireless sensor networks, cooperative spectrum sensing in the cognitive radio network. Traditionally optimal non-randomized hard decision fusion rule under Neyman Pearson(NP) criterion is exponential in complexity. But recently [4] this was solved using dynamic programming. As mentioned in [4] that decision fusion problem exhibits semi-monotonic property in a special case. We use this property in our simulations and eventually apply dynamic programming to solve the problem with further reduced complexity. Further, we study the e�ect of using multiple antennas at FC with reduced complexity rule

Evaluating holistic aggregators efficiently for very large datasets

In data warehousing applications, numerous OLAP queries involve the processing of holistic aggregators such as computing the “top n,” median, quantiles, etc. In this paper, we present a novel approach called dynamic bucketing to efficiently evaluate these aggregators. We partition data into equiwidth buckets and further partition dense buckets into sub-buckets as needed by allocating and reclaiming memory space. The bucketing process dynamically adapts to the input order and distribution of input datasets. The histograms of the buckets and subbuckets are stored in our new data structure called structure trees. A recent selection algorithm based on regular sampling is generalized and its analysis extended. We have also compared our new algorithms with this generalized algorithm and several other recent algorithms. Experimental results show that our new algorithms significantly outperform prior ones not only in the runtime but also in accuracy

Global parameter identification of stochastic reaction networks from single trajectories

We consider the problem of inferring the unknown parameters of a stochastic biochemical network model from a single measured time-course of the concentration of some of the involved species. Such measurements are available, e.g., from live-cell fluorescence microscopy in image-based systems biology. In addition, fluctuation time-courses from, e.g., fluorescence correlation spectroscopy provide additional information about the system dynamics that can be used to more robustly infer parameters than when considering only mean concentrations. Estimating model parameters from a single experimental trajectory enables single-cell measurements and quantification of cell--cell variability. We propose a novel combination of an adaptive Monte Carlo sampler, called Gaussian Adaptation, and efficient exact stochastic simulation algorithms that allows parameter identification from single stochastic trajectories. We benchmark the proposed method on a linear and a non-linear reaction network at steady state and during transient phases. In addition, we demonstrate that the present method also provides an ellipsoidal volume estimate of the viable part of parameter space and is able to estimate the physical volume of the compartment in which the observed reactions take place.Comment: Article in print as a book chapter in Springer's "Advances in Systems Biology