Efficient Parallel Algorithms Research Articles

The complexity of the comparator circuit value problem

In 1990, Subramanian [1990] defined the complexity class CC as the set of problems log-space reducible to the comparator circuit value problem (CCV). He and Mayr showed that NL ⊆ CC ⊆ P, and proved that in addition to CCV several other problems are complete for CC, including the stable marriage problem, and finding the lexicographically first maximal matching in a bipartite graph. Although the class has not received much attention since then, we are interested in CC because we conjecture that it is incomparable with the parallel class NC which also satisfies NL ⊆ NC ⊆ P, and note that this conjecture implies that none of the CC-complete problems has an efficient polylog time parallel algorithm. We provide evidence for our conjecture by giving oracle settings in which relativized CC and relativized NC are incomparable. We give several alternative definitions of CC, including (among others) the class of problems computed by uniform polynomial-size families of comparator circuits supplied with copies of the input and its negation, the class of problems AC0-reducible to Ccv, and the class of problems computed by uniform AC0 circuits with AXccv gates. We also give a machine model for CC, which corresponds to its characterization as log-space uniform polynomial-size families of comparator circuits. These various characterizations show that CC is a robust class. Our techniques also show that the corresponding function class FCC is closed under composition. The main technical tool we employ is universal comparator circuits. Other results include a simpler proof of NL ⊆ CC, a more careful analysis showing the lexicographically first maximal matching problem and its variants are CC-complete under AC0 many-one reductions, and an explanation of the relation between the Gale--Shapley algorithm and Subramanian’s algorithm for stable marriage. This article continues the previous work of Cook et al. [2011], which focused on Cook-Nguyen style uniform proof complexity, answering several open questions raised in that article.

PARALLEL MINING OF LARGE MAXIMAL BICLIQUES USING ORDER PRESERVING GENERATORS

In this paper, we propose a parallel algorithm for mining large maximal bicliques from graph datasets. We propose POP-MBC (Parallel Order Preserving Maximal BiClique mining algorithm), a fast and memory efficient parallel algorithm, which enumerates all the maximal bicliques independently and concurrently across several processors without any synchronization between the processors. The POP-MBC algorithm is highly memory efficient since it does not store the previously computed patterns in the main memory and requires only the dataset to be stored in the memory. To enhance the load sharing among different nodes, POP-MBC uses a round robin strategy which enables to achieve load balancing as high as 90%. We have also incorporated bit-vectors and numerous optimization techniques exploiting the symmetric property of the graph dataset to reduce the memory consumption and overall running time of the algorithm. Our comp rehensive experimental analyses involving publicly available datasets show that our algorithm distributes the load among the different processors equally and takes less memory, less running time than other maximal biclique mining algorithms.

Parallel spectral-element direction splitting method for incompressible Navier–Stokes equations

An efficient parallel algorithm for the time dependent incompressible Navier–Stokes equations is developed in this paper. The time discretization is based on a direction splitting method which only requires solving a sequence of one-dimensional Poisson type equations at each time step. Then, a spectral-element method is used to approximate these one-dimensional problems. A Schur-complement approach is used to decouple the computation of interface nodes from that of interior nodes, allowing an efficient parallel implementation. The unconditional stability of the full discretized scheme is rigorously proved for the two-dimensional case. Numerical results are presented to show that this algorithm retains the same order of accuracy as a usual spectral-element projection type schemes but it is much more efficient, particularly on massively parallel computers.

An efficient parallel algorithm for accelerating computational protein design.

Motivation: Structure-based computational protein design (SCPR) is an important topic in protein engineering. Under the assumption of a rigid backbone and a finite set of discrete conformations of side-chains, various methods have been proposed to address this problem. A popular method is to combine the dead-end elimination (DEE) and A* tree search algorithms, which provably finds the global minimum energy conformation (GMEC) solution.Results: In this article, we improve the efficiency of computing A* heuristic functions for protein design and propose a variant of A* algorithm in which the search process can be performed on a single GPU in a massively parallel fashion. In addition, we make some efforts to address the memory exceeding problem in A* search. As a result, our enhancements can achieve a significant speedup of the A*-based protein design algorithm by four orders of magnitude on large-scale test data through pre-computation and parallelization, while still maintaining an acceptable memory overhead. We also show that our parallel A* search algorithm could be successfully combined with iMinDEE, a state-of-the-art DEE criterion, for rotamer pruning to further improve SCPR with the consideration of continuous side-chain flexibility.Availability: Our software is available and distributed open-source under the GNU Lesser General License Version 2.1 (GNU, February 1999). The source code can be downloaded from http://www.cs.duke.edu/donaldlab/osprey.php or http://iiis.tsinghua.edu.cn/∼compbio/software.html.Contact: zengjy321@tsinghua.edu.cnSupplementary information: Supplementary data are available at Bioinformatics online.

Coarse grain load balance algorithm for detecting similar regions in DNA and proteins sequences

The tremendous quantity and quality of data obtained by conformations of DNA and protein sequences makes their analysis very time consuming, complex, expensive and impractical. Therefore, the feasible way to identify new sequences is to compare them with well-known sequences available in established genetic databank. Comparing sequences may reveal functional, structural, and evolutionary analogies between sequences. Needleman and Wunsch (NW), and Smith and Waterman (SW) algorithms are pioneers in dynamic programming matrix for comparing two sequences with gap penalty function. However, for long sequences both methods contribute toward time and space complexity. FASTA and BLAST are heuristic method based on hitting techniques for fast detection of similar region; unfortunately they produced results with no sensitivity. There remains a need for an efficient method(s) that can detect similar regions in two sequences with accurate results and reasonable time. In this paper, we extend an existing approach to develop an efficient parallel algorithm for pairwise local sequence alignment. Our method is based on load-balancing algorithm with the CPU scheduling technique in order to accelerate the calculation of data-dependency problem in sequences alignment. Using X86-based PC with eight logical processors we able to apply 4 MBP on the proposed algorithm with a speedup of 33% increase compared to the original SW algorithm.

Coarse Grain Load Balance Algorithm for Detecting Similar Regions in DNA and Proteins Sequences

The tremendous quantity and quality of data obtained by conformations of DNA and protein sequences makes their analysis very time consuming, complex, expensive and impractical. Therefore, the feasible way to identify new sequences is to compare them with well-known sequences available in established genetic databank. Comparing sequences may reveal functional, structural, and evolutionary analogies between sequences. Needleman and Wunsch (NW), and Smith and Waterman (SW) algorithms are pioneers in dynamic programming matrix for comparing two sequences with gap penalty function. However, for long sequences both methods contribute toward time and space complexity. FASTA and BLAST are heuristic method based on hitting techniques for fast detection of similar region; unfortunately they produced results with no sensitivity. There remains a need for an efficient method(s) that can detect similar regions in two sequences with accurate results and reasonable time. In this paper, we extend an existing approach to develop an efficient parallel algorithm for pairwise local sequence alignment. Our method is based on load-balancing algorithm with the CPU scheduling technique in order to accelerate the calculation of data-dependency problem in sequences alignment. Using X86-based PC with eight logical processors we able to apply 4 MBP on the proposed algorithm with a speedup of 33% increase compared to the original SW algorithm.

Parallel iterative solution of the Hermite Collocation equations on GPUs II

Hermite Collocation is a high order finite element method for Boundary Value Problems modelling applications in several fields of science and engineering. Application of this integration free numerical solver for the solution of linear BVPs results in a large and sparse general system of algebraic equations, suggesting the usage of an efficient iterative solver especially for realistic simulations. In part I of this work an efficient parallel algorithm of the Schur complement method coupled with Bi-Conjugate Gradient Stabilized (BiCGSTAB) iterative solver has been designed for multicore computing architectures with a Graphics Processing Unit (GPU). In the present work the proposed algorithm has been extended for high performance computing environments consisting of multiprocessor machines with multiple GPUs. Since this is a distributed GPU and shared CPU memory parallel architecture, a hybrid memory treatment is needed for the development of the parallel algorithm. The realization of the algorithm took place on a multiprocessor machine HP SL390 with Tesla M2070 GPUs using the OpenMP and OpenACC standards. Execution time measurements reveal the efficiency of the parallel implementation.

Efficient sequential and parallel algorithms for record linkage

Background and objectiveIntegrating data from multiple sources is a crucial and challenging problem. Even though there exist numerous algorithms for record linkage or deduplication, they suffer from either large time needs or restrictions on the number of datasets that they can integrate. In this paper we report efficient sequential and parallel algorithms for record linkage which handle any number of datasets and outperform previous algorithms.MethodsOur algorithms employ hierarchical clustering algorithms as the basis. A key idea that we use is radix sorting on certain attributes to eliminate identical records before any further processing. Another novel idea is to form a graph that links similar records and find the connected components.ResultsOur sequential and parallel algorithms have been tested on a real dataset of 1 083 878 records and synthetic datasets ranging in size from 50 000 to 9 000 000 records. Our sequential algorithm runs at least two times faster, for any dataset, than the previous best-known algorithm, the two-phase algorithm using faster computation of the edit distance (TPA (FCED)). The speedups obtained by our parallel algorithm are almost linear. For example, we get a speedup of 7.5 with 8 cores (residing in a single node), 14.1 with 16 cores (residing in two nodes), and 26.4 with 32 cores (residing in four nodes).ConclusionsWe have compared the performance of our sequential algorithm with TPA (FCED) and found that our algorithm outperforms the previous one. The accuracy is the same as that of this previous best-known algorithm.

Special issue on soft computing techniques in cluster and grid computing systems

The resolution of complex problems requires the use of advanced approximate algorithms and huge computational resources to find accurate solutions in reasonable time. Computing clusters, as well as GPGPUs, grids, and cloud computing infrastructures arise as appropriate innovative computing platforms to implement and execute such algorithms and find accurate solutions to complex problems arising in many application areas. This special issue contains extended versions of the best papers presented in HPCLATAM-2012 and SCCG-2012 conferences, as well as other novel contributions. In total, 27 papers were submitted to the special issue, from which only 10 were finally accepted for publication. These are outstanding contributions proposing novel designs of highly efficient parallel algorithms to solve complex problems, or dealing with salient problems in the fields of grid and cloud computing. In the first paper of this compilation, “Approximating Static List Schedules in Dynamic Multithreaded Applications”, Camargo et al. propose in their contribution the use of list algorithms to optimally schedule algorithms in a multi-thread environment. The difficulty of the approach deals with the fact that a dynamic environment is considered, and no assumptions are assumed to be known about the programs. A novel algorithm is presented to build a directed cyclic graph representing a multithread program from a data flow description, in form of a directed acyclic graph. Several

Parallelizing dynamic programming through rank convergence

This paper proposes an efficient parallel algorithm for an important class of dynamic programming problems that includes Viterbi, Needleman-Wunsch, Smith-Waterman, and Longest Common Subsequence. In dynamic programming, the subproblems that do not depend on each other, and thus can be computed in parallel, form stages or wavefronts. The algorithm presented in this paper provides additional parallelism allowing multiple stages to be computed in parallel despite dependences among them. The correctness and the performance of the algorithm relies on rank convergence properties of matrix multiplication in the tropical semiring, formed with plus as the multiplicative operation and max as the additive operation. This paper demonstrates the efficiency of the parallel algorithm by showing significant speed ups on a variety of important dynamic programming problems. In particular, the parallel Viterbi decoder is up-to 24x faster (with 64 processors) than a highly optimized commercial baseline.

A Survey on Parallel Computing and its Applications in Data-Parallel Problems Using GPU Architectures

AbstractParallel computing has become an important subject in the field of computer science and has proven to be critical when researching high performance solutions. The evolution of computer architectures (multi-coreandmany-core) towards a higher number of cores can only confirm that parallelism is the method of choice for speeding up an algorithm. In the last decade, the graphics processing unit, or GPU, has gained an important place in the field of high performance computing (HPC) because of its low cost and massive parallel processing power. Super-computing has become, for the first time, available to anyone at the price of a desktop computer. In this paper, we survey the concept of parallel computing and especially GPU computing. Achieving efficient parallel algorithms for the GPU is not a trivial task, there are several technical restrictions that must be satisfied in order to achieve the expected performance. Some of these limitations are consequences of the underlying architecture of the GPU and the theoretical models behind it. Our goal is to present a set of theoretical and technical concepts that are often required to understand the GPU and itsmassive parallelismmodel. In particular, we show how this new technology can help the field ofcomputational physics,especially when the problem isdata-parallel.We present four examples of computational physics problems;n-body, collision detection, Potts modelandcellular automatasimulations. These examples well represent the kind of problems that are suitable for GPU computing. By understanding the GPU architecture and its massive parallelism programming model, one can overcome many of the technical limitations found along the way, design better GPU-based algorithms for computational physics problems and achieve speedups that can reach up to two orders of magnitude when compared to sequential implementations.

Efficient sequential and parallel algorithms for planted motif search.

BackgroundMotif searching is an important step in the detection of rare events occurring in a set of DNA or protein sequences. One formulation of the problem is known as (l,d)-motif search or Planted Motif Search (PMS). In PMS we are given two integers l and d and n biological sequences. We want to find all sequences of length l that appear in each of the input sequences with at most d mismatches. The PMS problem is NP-complete. PMS algorithms are typically evaluated on certain instances considered challenging. Despite ample research in the area, a considerable performance gap exists because many state of the art algorithms have large runtimes even for moderately challenging instances.ResultsThis paper presents a fast exact parallel PMS algorithm called PMS8. PMS8 is the first algorithm to solve the challenging (l,d) instances (25,10) and (26,11). PMS8 is also efficient on instances with larger l and d such as (50,21). We include a comparison of PMS8 with several state of the art algorithms on multiple problem instances. This paper also presents necessary and sufficient conditions for 3 l-mers to have a common d-neighbor. The program is freely available at http://engr.uconn.edu/~man09004/PMS8/.ConclusionsWe present PMS8, an efficient exact algorithm for Planted Motif Search. PMS8 introduces novel ideas for generating common neighborhoods. We have also implemented a parallel version for this algorithm. PMS8 can solve instances not solved by any previous algorithms.

Parallel dynamic programming for solving the optimal search binary tree problem on CGM

This paper presents an efficient coarse grain multicomputer CGM parallel algorithm for the cost of the optimal binary search tree problem OBST problem. In the previous best CGM algorithm for this problem, the size of the local memory of each processor is not bounded. And even, in the worst case, its running time reduces to the one of Knuth's sequential algorithm for the same problem, bringing no gain by parallelising OBST. Our CGM algorithm uses Knuth's sequential algorithm for local computations to perform in time as well as the best previous CGM algorithm. Moreover, each processor can process at most two blocks and thus avoid the severe drawback raised above of the previous work.

Learning Continuous Time Bayesian Network Classifiers Using MapReduce

Parameter and structural learning on continuous time Bayesian network classifiers are challenging tasks when you are dealing with big data. This paper describes an efficient scalable parallel algorithm for parameter and structural learning in the case of complete data using the MapReduce framework. Two popular instances of classifiers are analyzed, namely the continuous time naive Bayes and the continuous time tree augmented naive Bayes. Details of the proposed algorithm are presented using Hadoop, an open-source implementation of a distributed file system and the MapReduce framework for distributed data processing. Performance evaluation of the designed algorithm shows a robust parallel scaling.

Efficient parallel algorithm for multiple sequence alignments with regular expression constraints on graphics processing units

Multiple sequence alignments with constraints has become an important problem in computational biology. The concept of constrained sequence alignment is proposed to incorporate the biologist's domain knowledge into sequence alignments such that the user-specified residues/segments are aligned together in the alignment results. Over the past decade, a series of constrained multiple sequence alignment tools were proposed in the literature. RE-MuSiC is the newest tool with the regular expression constraints and useful for a wide range of biological applications. However, the computation time of REMuSiC is large for a large amount of sequences or long sequences and this problem limits the application usage. Therefore, in this paper, a tool, GPU-REMuSiC v1.0, is proposed to reduce the computation time of RE-MuSiC by using the graphics processing units with CUDA. GPU-REMuSiC v1.0 can achieve 29× speedups for overall computation time by the experimental results.

An efficient reconciliation algorithm for social networks

People today typically use multiple online social networks (Facebook, Twitter, Google+, LinkedIn, etc.). Each online network represents a subset of their "real" ego-networks. An interesting and challenging problem is to reconcile these online networks, that is, to identify all the accounts belonging to the same individual. Besides providing a richer understanding of social dynamics, the problem has a number of practical applications. At first sight, this problem appears algorithmically challenging. Fortunately, a small fraction of individuals explicitly link their accounts across multiple networks; our work leverages these connections to identify a very large fraction of the network. Our main contributions are to mathematically formalize the problem for the first time, and to design a simple, local, and efficient parallel algorithm to solve it. We are able to prove strong theoretical guarantees on the algorithm's performance on well-established network models (Random Graphs, Preferential Attachment). We also experimentally confirm the effectiveness of the algorithm on synthetic and real social network data sets.

An Efficient Parallel Algorithm for Large Scale Hydrothermal System Operation Planning

This paper presents an efficient parallel algorithm applied to the problem of large scale hydrothermal system operation planning. This problem is solved by stochastic dual dynamic programming. A plan of operation is determined for each stage of the planning period with the objective of minimizing the expected cost of operation over the planning horizon. For each state, the hydrothermal operation problem is modeled as a linear programming problem and the dual variables associated with the solution are used to construct the Benders cuts. The plan of operation is represented by the future cost function, which is approximated by a piecewise linear function, constructed iteratively by the Benders cuts. An optimized parallelization strategy is applied to both the forward and backward cycles of the dynamic programming convergence process with very high parallel efficiency. For a planning horizon of 5 years and 200 inflow scenarios for each reservoir, the sequential solution for the Brazilian system requires almost 15 hours of processing time. The parallel algorithm obtains exactly the same solution in less than 23 min on 64 cores and in less than 17 min on 128 cores.

Accelerating Pattern Matching Using a Novel Parallel Algorithm on GPUs

Graphics processing units (GPUs) have attracted a lot of attention due to their cost-effective and enormous power for massive data parallel computing. In this paper, we propose a novel parallel algorithm for exact pattern matching on GPUs. A traditional exact pattern matching algorithm matches multiple patterns simultaneously by traversing a special state machine called an Aho-Corasick machine. Considering the particular parallel architecture of GPUs, in this paper, we first propose an efficient state machine on which we perform very efficient parallel algorithms. Also, several techniques are introduced to do optimization on GPUs, including reducing global memory transactions of input buffer, reducing latency of transition table lookup, eliminating output table accesses, avoiding bank-conflict of shared memory, coalescing writes to global memory, and enhancing data transmission via peripheral component interconnect express. We evaluate the performance of the proposed algorithm using attack patterns from Snort V2.8 and input streams from DEFCON. The experimental results show that the proposed algorithm performed on NVIDIA GPUs achieves up to 143.16-Gbps throughput, 14.74 times faster than the Aho-Corasick algorithm implemented on a 3.06-GHz quad-core CPU with the OpenMP. The library of the proposed algorithm is publically accessible through Google Code.

Parallel computation of skyline and reverse skyline queries using mapreduce

The skyline operator and its variants such as dynamic skyline and reverse skyline operators have attracted considerable attention recently due to their broad applications. However, computations of such operators are challenging today since there is an increasing trend of applications to deal with big data. For such data-intensive applications, the MapReduce framework has been widely used recently.In this paper, we propose efficient parallel algorithms for processing the skyline and its variants using MapReduce. We first build histograms to effectively prune out nonskyline (non-reverse skyline) points in advance. We next partition data based on the regions divided by the histograms and compute candidate (reverse) skyline points for each region independently using MapReduce. Finally, we check whether each candidate point is actually a (reverse) skyline point in every region independently. Our performance study confirms the effectiveness and scalability of the proposed algorithms.

High performance computing for drug development on K computer

Massively parallel computations (MP-CAFEE) ware developed to calculate absolute binding free energies of small molecules bound to a protein by all-atom molecular dynamics. It uses the nonequilibrium work measurement and Bennett acceptance ratio methods to calculate the free energy difference between the bound and unbound states. The FUJI force field was developed in order to assign force field parameters to arbitrary organic molecules in a unified manner including proteins and nucleic acids. Its dihedral parameters agree with the torsion energy profiles calculated by high-level ab initio molecular orbital theory for the model systems of protein backbone. Comparing with various force fields it agrees well with recent observations by vibrational spectroscopy on Ramachandran angle's population of alanine dipeptide in water. MP-CAFEE with FUJI force field has an efficient parallel algorithm and enough accuracy for computer aided drug design.