Practical Runtime Research Articles

Practical and efficient algorithms for the geometric hitting set problem

The geometric hitting set problem is one of the basic geometric combinatorial optimization problems: given a set P of points and a set D of geometric objects in the plane, the goal is to compute a small-sized subset of P that hits all objects in D. Recently Agarwal and Pan (2014) presented a near-linear time algorithm for the case where D consists of disks in the plane. The algorithm uses sophisticated geometric tools and data structures with large resulting constants. In this paper, we design a hitting-set algorithm for this case without the use of these data-structures, and present experimental evidence that our new algorithm has near-linear running time in practice, and computes hitting sets within 1.3-factor of the optimal hitting set. We further present dnet, a public source-code module that incorporates this improvement, enabling fast and efficient computation of small-sized hitting sets in practice.

Parallel Data Partitioning Algorithms for Optimization of Data-Parallel Applications on Modern Extreme-Scale Multicore Platforms for Performance and Energy

Data partitioning algorithms aiming to minimize the execution time and the energy of computations in self-adaptable data-parallel applications on modern extreme-scale multicore platforms must address two critical challenges. First, they must take into account the new complexities inherent in these platforms such as severe resource contention and non-uniform memory access. Second, they must have low practical runtime and memory costs. The sequential data partitioning algorithms addressing the first challenge have a theoretical time complexity of O( $m * m * p * p$ ) where $m$ is the number of points in the discrete speed/energy function and $p$ is the number of available processors. They, however, exhibit high practical runtime cost and excessive memory footprint, therefore, rendering them impracticable for employment in self-adaptable applications executing on extreme-scale multicore platforms. We present, in this paper, the parallel data partitioning algorithms that address both the challenges. They take as input the functional models of performance and energy consumption against problem size and output workload distributions, which are globally optimal solutions. They have a low time complexity of O( $m * m * p$ ) thereby providing a linear speedup of O( $p$ ) and low memory complexity of O( $n$ ) where $n$ is the workload size expressed as a multiple of granularity. They employ dynamic programming approach, which also facilitates the easier integration of performance and energy models of communications. We experimentally study the practical cost of application of our algorithms in two data-parallel applications, matrix multiplication and fast Fourier transform, on a cluster in Grid’5000 platform. We demonstrate that their practical runtime and memory costs are low making them ideal for employment in self-adaptable applications. We also show that the parallel algorithms exhibit tremendous speedups over the sequential algorithms. Finally, using theoretical analysis for a forecast exascale platform, we demonstrate that the parallel algorithms have negligible execution times compared to the matrix multiplication application executing on the platform.

Improved quick hypervolume algorithm

In this paper, we present a significant improvement of the Quick Hypervolume algorithm, one of the state-of-the-art algorithms for calculating the exact hypervolume of the space dominated by a set of d-dimensional points. This value is often used as the quality indicator in the multiobjective evolutionary algorithms and other multiobjective metaheuristics and the efficiency of calculating this indicator is of crucial importance especially in the case of large sets or many dimensional objective spaces. We use a similar divide and conquer scheme as in the original Quick Hypervolume algorithm, but in our algorithm we split the problem into smaller sub-problems in a different way. Through both theoretical analysis and a computational study we show that our approach improves the computational complexity of the algorithm and practical running times.

A fast algorithm for the all-pairs suffix–prefix problem

The all-pairs suffix–prefix problem occurs as a subproblem of DNA sequence assembly where it is the most time-consuming part of the whole assembly. Although there are algorithms for the all-pairs suffix–prefix problem which are optimal in the asymptotic time complexity, they are slower than SOF and Readjoiner which are state-of-the-art algorithms used in practice. In this paper we present an algorithm for the all-pairs suffix–prefix problem that uses a simple data structure for storing input strings and advanced algorithmic techniques for matching, which together lead to fast running time in practice. Our algorithm is 14 times faster than SOF and 18 times faster than Readjoiner on average in real datasets and random datasets.

Distributed Computing Architecture for Optimal Control of Distribution Feeders With Smart Loads

This paper presents a distributed computing architecture for solving a distribution optimal power flow (DOPF) model based on a smart grid communication middleware (SGCM) system. The system is modeled as an unbalanced three-phase distribution system, which includes different kind of loads and various components of distribution systems. In this paper, fixed loads are modeled as constant impedance, current and power loads, and neural network models of controllable smart loads are integrated into the DOPF model. A genetic algorithm is used to determine the optimal solutions for controllable devices, in particular load tap changers, switched capacitors, and smart loads in the context of an energy management system for practical feeders, accounting for the fact that smart loads consumption should not be significantly affected by network constraints. Since the number of control variables in a realistic distribution power system is large, solving the DOPF for real-time applications is computationally expensive. Hence, to reduce computational times, a decentralized system with parallel computing nodes based on an SGCM system is proposed. Using a “MapReduce” model, the SGCM system runs the DOPF model, communicates between master and worker computing nodes, and sends/receives data among different parts of parallel computing system. Compared to a centralized approach, the proposed architecture is shown to yield better optimal solutions in terms of reducing energy losses and/or energy drawn from the substation within adequate practical run-times for a realistic test feeder.

A New Efficient Algorithm for the Frequent Gene Team Problem.

The focus of this paper is the frequent gene team problem. Given a quorum parameter μ and a set of m genomes, the problem is to find gene teams that occur in at least μ of the given genomes. In this paper, a new algorithm is presented. Previous solutions are efficient only when μ is small. Unlike previous solutions, the presented algorithm does not rely on examining every combination of μ genomes. Its time complexity is independent of μ. Under some realistic assumptions, the practical running time is estimated to be , where n is the maximum length of the input genomes. Experiments showed that the presented algorithm is extremely efficient. For any μ, it takes less than 1 second to process 100 bacterial genomes and takes only 10 minutes to process 2,000 genomes. The presented algorithm can be used as an effective tool for large scale genome analyses.

Large-scale three-dimensional phase-field simulations for phase coarsening at ultrahigh volume fraction on high-performance architectures

A parallel algorithm for large-scale three-dimensional phase-field simulations of phase coarsening is developed and implemented on high-performance architectures. From the large-scale simulations, a new kinetics in phase coarsening in the region of ultrahigh volume fraction is found. The parallel implementation is capable of harnessing the greater computer power available from high-performance architectures. The parallelized code enables increase in three-dimensional simulation system size up to a 5123 grid cube. Through the parallelized code, practical runtime can be achieved for three-dimensional large-scale simulations, and the statistical significance of the results from these high resolution parallel simulations are greatly improved over those obtainable from serial simulations. A detailed performance analysis on speed-up and scalability is presented, showing good scalability which improves with increasing problem size. In addition, a model for prediction of runtime is developed, which shows a good agreement with actual run time from numerical tests.

An improved algorithm for the all-pairs suffix–prefix problem

Finding all longest suffix–prefix matches for a collection of strings is known as the all pairs suffix–prefix match problem and its main application is de novo genome assembly. This problem is well studied in stringology and has been solved optimally in 1992 by Gusfield et al. [8] using suffix trees. In 2010, Ohlebusch and Gog [13] proposed an alternative solution based on enhanced suffix arrays which has also optimal time complexity but is faster in practice. In this article, we present another optimal algorithm based on enhanced suffix arrays which further improves the practical running time. Our new solution solves the problem locally for each string, scanning the enhanced suffix array backwards to avoid the processing of suffixes that are no suffix–prefix matching candidates. In an empirical evaluation we observed that the new algorithm is over two times faster and more space-efficient than the method proposed by Ohlebusch and Gog. When compared to Readjoiner [5], a good practical solution, our algorithm is faster for small overlap lengths, in pace with theoretical optimality.

Efficiency of lambda-encodings in total type theory

AbstractThis paper proposes a new typed lambda-encoding for inductive types which, for Peano numerals, has the expected time complexities for basic operations like addition and multiplication, has a constant-time predecessor function, and requires only quadratic space to encode a numeral. This improves on the exponential space required by the Parigot encoding. Like the Parigot encoding, the new encoding is typable in System F-omega plus positive-recursive type definitions, a total type theory. The new encoding is compared with previous ones through a significant case study: mergesort using Braun trees. The practical runtime efficiency of the new encoding, and the Church and Parigot encodings, are compared by two translations, one to Racket and one to Haskell, on a small suite of benchmarks.

Algorithmic Differentiation of Numerical Methods

We discuss software tool support for the algorithmic differentiation (AD), also known as automatic differentiation, of numerical simulation programs that contain calls to solvers for parameterized systems of n nonlinear equations. The local computational overhead and the additional memory requirement for the computation of directional derivatives or adjoints of the solution of the nonlinear system with respect to the parameters can quickly become prohibitive for large values of n . Both are reduced drastically by analytical (and symbolic) approaches to differentiation of the underlying numerical methods. Following the discussion of the proposed terminology, we develop the algorithmic formalism building on prior work by other colleagues and present an implementation based on the AD software dco/c++. A representative case study supports the theoretically obtained computational complexity results with practical runtime measurements.

A metaheuristic approach for efficient and effective sketch-to-metric map alignment

ABSTRACTSketching as a natural mode for human communication and creative processes presents opportunities for improving human–computer interaction in geospatial information systems. However, to use a sketch map as user input, it must be localized within the underlying spatial data set of the information system, the base metric map. This can be achieved by a matching process called qualitative map alignment in which qualitative spatial representations of the two input maps are used to establish correspondences between each sketched object and one or more objects in the metric map. The challenge is that, to the best of our knowledge, no method for matching qualitative spatial representations suggested so far is applicable in realistic scenarios due to excessively long runtimes, incorrect algorithm design or the inability to use more than one spatial aspect at a time. We address these challenges with a metaheuristic algorithm which uses novel data structures to match qualitative spatial representations of a pair of maps. We present the design, data structures and performance evaluation of the algorithm using real-world sketch and metric maps as well as on synthetic data. Our algorithm is novel in two main aspects. Firstly, it employs a novel system of matrices known as local compatibility matrices, which facilitate the computation of estimates for the future size of a partial alignment and allow several types of constraints to be used at the same time. Secondly, the heuristic it computes has a higher accuracy than the state-of-the-art heuristic for this task, yet requires less computation. Our algorithm is also a general method for matching labelled graphs, a special case of which is the one involving complete graphs whose edges are labelled with spatial relations. The results of our evaluation demonstrate practical runtime performance and high solution quality.

Computing all hybridization networks for multiple binary phylogenetic input trees.

BackgroundThe computation of phylogenetic trees on the same set of species that are based on different orthologous genes can lead to incongruent trees. One possible explanation for this behavior are interspecific hybridization events recombining genes of different species. An important approach to analyze such events is the computation of hybridization networks.ResultsThis work presents the first algorithm computing the hybridization number as well as a set of representative hybridization networks for multiple binary phylogenetic input trees on the same set of taxa. To improve its practical runtime, we show how this algorithm can be parallelized. Moreover, we demonstrate the efficiency of the software Hybroscale, containing an implementation of our algorithm, by comparing it to PIRNv2.0, which is so far the best available software computing the exact hybridization number for multiple binary phylogenetic trees on the same set of taxa. The algorithm is part of the software Hybroscale, which was developed specifically for the investigation of hybridization networks including their computation and visualization. Hybroscale is freely available1 and runs on all three major operating systems.ConclusionOur simulation study indicates that our approach is on average 100 times faster than PIRNv2.0. Moreover, we show how Hybroscale improves the interpretation of the reported hybridization networks by adding certain features to its graphical representation.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-015-0660-7) contains supplementary material, which is available to authorized users.

Sampling based scene-space video processing

Many compelling video processing effects can be achieved if per-pixel depth information and 3D camera calibrations are known. However, the success of such methods is highly dependent on the accuracy of this "scene-space" information. We present a novel, sampling-based framework for processing video that enables high-quality scene-space video effects in the presence of inevitable errors in depth and camera pose estimation. Instead of trying to improve the explicit 3D scene representation, the key idea of our method is to exploit the high redundancy of approximate scene information that arises due to most scene points being visible multiple times across many frames of video. Based on this observation, we propose a novel pixel gathering and filtering approach. The gathering step is general and collects pixel samples in scene-space, while the filtering step is application-specific and computes a desired output video from the gathered sample sets. Our approach is easily parallelizable and has been implemented on GPU, allowing us to take full advantage of large volumes of video data and facilitating practical runtimes on HD video using a standard desktop computer. Our generic scene-space formulation is able to comprehensively describe a multitude of video processing applications such as denoising, deblurring, super resolution, object removal, computational shutter functions, and other scene-space camera effects. We present results for various casually captured, hand-held, moving, compressed, monocular videos depicting challenging scenes recorded in uncontrolled environments.

A flood risk analysis model with topographical inundation and life-loss

Quantified models of flood risk that incorporate an explicit representation of the performance of flood defence infrastructure are becoming an increasingly important component of efforts to manage flood risk. The models have been applied to support a wide range of decisions, including long-term strategic planning, assessment of investment needs and shorter-term asset management. The model currently applied in practice by the Environment Agency in England and Wales makes a number of simplifying assumptions to achieve computationally practical run-times. One of these simplifications relates to the volume-based flood-spreading algorithm that is applied. This paper describes the implementation of a new time-based inundation model within the existing risk analysis modelling approach. The new inundation model offers a significant increase in the representation of the physical processes within the flood simulation component of the risk analysis model. It also offers new outputs in terms of estimates of maximum depths and flood velocities. Velocities are known to be an important factor in flood-related fatalities. A simplified method to estimate life-loss has been combined with new output from the improved inundation model to illustrate how estimates of risk to life could be provided.

Bootstrap-based differential gene expression analysis for RNA-Seq data with and without replicates.

A major application of RNA-Seq is to perform differential gene expression analysis. Many tools exist to analyze differentially expressed genes in the presence of biological replicates. Frequently, however, RNA-Seq experiments have no or very few biological replicates and development of methods for detecting differentially expressed genes in these scenarios is still an active research area.In this paper we introduce a novel method, called IsoDE, for differential gene expression analysis based on bootstrapping. We compared IsoDE against four existing methods (Fisher's exact test, GFOLD, edgeR and Cuffdiff) on RNA-Seq datasets generated using three different sequencing technologies, both with and without replicates. Experiments on MAQC RNA-Seq datasets without replicates show that IsoDE has consistently high accuracy as defined by the qPCR ground truth, frequently higher than that of the compared methods, particularly for low coverage data and at lower fold change thresholds. In experiments on RNA-Seq datasets with up to 7 replicates, IsoDE has also achieved high accuracy. Furthermore, unlike GFOLD and edgeR, IsoDE accuracy varies smoothly with the number of replicates, and is relatively uniform across the entire range of gene expression levels.The proposed non-parametric method based on bootstrapping has practical running time, and achieves robust performance over a broad range of technologies, number of replicates, sequencing depths, and minimum fold change thresholds.

The generic model query language GMQL – Conceptual specification, implementation, and runtime evaluation

The generic model query language GMQL is designed to query collections of conceptual models created in arbitrary graph-based modelling languages. Querying conceptual models means searching for particular model subgraphs that comply with a predefined pattern query. Such a query specifies the structural and semantic properties of the model fragment to be returned. In this paper, we derive requirements for a generic model query language from the literature and formally specify the language’s syntax and semantics. We conduct an analysis of GMQL׳s theoretical and practical runtime performance concluding that it returns query results within satisfactory time. Given its generic nature, GMQL contributes to a broad range of different model analysis scenarios ranging from business process compliance management to model translation and business process weakness detection. As GMQL returns results with acceptable runtime performance, it can be used to query large collections of hundreds or thousands of conceptual models containing not only process models, but also data models or organizational charts. In this paper, we furthermore evaluate GMQL against the backdrop of existing query approaches thereby carving out its advantages and limitations as well as pointing toward future research.

Efficient algorithms for cluster editing

The cluster editing problem consists of transforming an input graph $$G$$G into a cluster graph (a disjoint union of complete graphs) by performing a minimum number of edge editing operations. Each edge editing operation consists of either adding a new edge or removing an existing edge. In this paper we propose new theoretical results on data reduction and instance generation for the cluster editing problem, as well as two algorithms based on coupling an exact method to, respectively, a GRASP or ILS heuristic. Experimental results show that the proposed algorithms are able to find high-quality solutions in practical runtime.

Practical SAHN Clustering for Very Large Data Sets and Expensive Distance Metrics

Sequential agglomerative hierarchical non-overlapping (SAHN) clustering techniques belong to the classical clustering methods applied heavily in many application domains, e.g., in cheminformatics. Asymptotically optimal SAHN clustering algorithms are known for arbitrary dissimilarity measures, but their quadratic time and space complexity even in the best case still limits the applicability to small data sets. We present a new pivot based heuristic SAHN clustering algorithm exploiting the properties of metric distance measures in order to obtain a best-case runtime of O(nlogn) for the input size n. Our approach requires only linear space and supports median and centroid linkage. It is especially suitable for expensive distance measures, as it needs only a linear number of exact distance computations. This aspect is demonstrated in our extensive experimental evaluation, where we apply our algorithm to large graph databases in combination with computationally demanding graph distance metrics. We compare our approach to exact state-of-the-art SAHN algorithms in terms of quality and runtime on real-world and synthetic instances including vector and graph data. The evaluations show a subquadratic runtime in practice and a very low memory footprint. Our approach yields high-quality clusterings and is able to rediscover planted cluster structures in synthetic data sets.

A Highly Practical Approach toward Achieving Minimum Data Sets Storage Cost in the Cloud

Massive computation power and storage capacity of cloud computing systems allow scientists to deploy computation and data intensive applications without infrastructure investment, where large application data sets can be stored in the cloud. Based on the pay-as-you-go model, storage strategies and benchmarking approaches have been developed for cost-effectively storing large volume of generated application data sets in the cloud. However, they are either insufficiently cost-effective for the storage or impractical to be used at runtime. In this paper, toward achieving the minimum cost benchmark, we propose a novel highly cost-effective and practical storage strategy that can automatically decide whether a generated data set should be stored or not at runtime in the cloud. The main focus of this strategy is the local-optimization for the tradeoff between computation and storage, while secondarily also taking users' (optional) preferences on storage into consideration. Both theoretical analysis and simulations conducted on general (random) data sets as well as specific real world applications with Amazon's cost model show that the cost-effectiveness of our strategy is close to or even the same as the minimum cost benchmark, and the efficiency is very high for practical runtime utilization in the cloud.

GPU‐based relative fuzzy connectedness image segmentation

Recently, clinical radiological research and practice are becoming increasingly quantitative. Further, images continue to increase in size and volume. For quantitative radiology to become practical, it is crucial that image segmentation algorithms and their implementations are rapid and yield practical run time on very large data sets. The purpose of this paper is to present a parallel version of an algorithm that belongs to the family of fuzzy connectedness (FC) algorithms, to achieve an interactive speed for segmenting large medical image data sets. The most common FC segmentations, optimizing an [script-l](∞)-based energy, are known as relative fuzzy connectedness (RFC) and iterative relative fuzzy connectedness (IRFC). Both RFC and IRFC objects (of which IRFC contains RFC) can be found via linear time algorithms, linear with respect to the image size. The new algorithm, P-ORFC (for parallel optimal RFC), which is implemented by using NVIDIA's Compute Unified Device Architecture (CUDA) platform, considerably improves the computational speed of the above mentioned CPU based IRFC algorithm. Experiments based on four data sets of small, medium, large, and super data size, achieved speedup factors of 32.8×, 22.9×, 20.9×, and 17.5×, correspondingly, on the NVIDIA Tesla C1060 platform. Although the output of P-ORFC need not precisely match that of IRFC output, it is very close to it and, as the authors prove, always lies between the RFC and IRFC objects. A parallel version of a top-of-the-line algorithm in the family of FC has been developed on the NVIDIA GPUs. An interactive speed of segmentation has been achieved, even for the largest medical image data set. Such GPU implementations may play a crucial role in automatic anatomy recognition in clinical radiology.