Design and analysis of sequential and parallel single-source shortest-paths algorithms

We study the performance of algorithms for the Single-Source Shortest-Paths (SSSP) problem on graphs with n nodes and m edges with nonnegative random weights. All previously known SSSP algorithms for directed graphs required superlinear time. Wie give the first SSSP algorithms that provably achieve linear O(n-m)average-case execution time on arbitrary directed graphs with random edge weights. For independent edge weights, the linear-time bound holds with high probability, too. Additionally, our result implies improved average-case bounds for the All-Pairs Shortest-Paths (APSP) problem on sparse graphs, and it yields the first theoretical average-case analysis for the "Approximate Bucket Implementation" of Dijkstra\u27s SSSP algorithm (ABI-Dijkstra). Futhermore, we give constructive proofs for the existence of graph classes with random edge weights on which ABI-Dijkstra and several other well-known SSSP algorithms require superlinear average-case time. Besides the classical sequential (single processor) model of computation we also consider parallel computing: we give the currently fastest average-case linear-work parallel SSSP algorithms for large graph classes with random edge weights, e.g., sparse rondom graphs and graphs modeling the WWW, telephone calls or social networks.In dieser Arbeit untersuchen wir die Laufzeiten von Algorithmen für das Kürzeste-Wege Problem (Single-Source Shortest-Paths, SSSP) auf Graphen mit n Knoten, M Kanten und nichtnegativen zufälligen Kantengewichten. Alle bisherigen SSSP Algorithmen benötigen auf gerichteten Graphen superlineare Zeit. Wir stellen den ersten SSSP Algorithmus vor, der auf beliebigen gerichteten Graphen mit zufälligen Kantengewichten eine beweisbar lineare average-case-Komplexität O(n+m)aufweist. Sind die Kantengewichte unabhängig, so wird die lineare Zeitschranke auch mit hoher Wahrscheinlichkeit eingehalten. Außerdem impliziert unser Ergebnis verbesserte average-case-Schranken für das All-Pairs Shortest-Paths (APSP) Problem auf dünnen Graphen und liefert die erste theoretische average-case-Analyse für die "Approximate Bucket Implementierung" von Dijkstras SSSP Algorithmus (ABI-Dijkstra). Weiterhin führen wir konstruktive Existenzbeweise für Graphklassen mit zufälligen Kantengewichten, auf denen ABI-Dijkstra und mehrere andere bekannte SSSP Algorithmen durchschnittlich superlineare Zeit benötigen. Neben dem klassischen seriellen (Ein-Prozessor) Berechnungsmodell betrachten wir auch Parallelverarbeitung; für umfangreiche Graphklassen mit zufälligen Kantengewichten wie z.B. dünne Zufallsgraphen oder Modelle für das WWW, Telefonanrufe oder soziale Netzwerke stellen wir die derzeit schnellsten parallelen SSSP Algorithmen mit durchschnittlich linearer Arbeit vor

Multilevel Weighted Support Vector Machine for Classification on Healthcare Data with Missing Values

This work is motivated by the needs of predictive analytics on healthcare data as represented by Electronic Medical Records. Such data is invariably problematic: noisy, with missing entries, with imbalance in classes of interests, leading to serious bias in predictive modeling. Since standard data mining methods often produce poor performance measures, we argue for development of specialized techniques of data-preprocessing and classification. In this paper, we propose a new method to simultaneously classify large datasets and reduce the effects of missing values. It is based on a multilevel framework of the cost-sensitive SVM and the expected maximization imputation method for missing values, which relies on iterated regression analyses. We compare classification results of multilevel SVM-based algorithms on public benchmark datasets with imbalanced classes and missing values as well as real data in health applications, and show that our multilevel SVM-based method produces fast, and more accurate and robust classification results.Comment: arXiv admin note: substantial text overlap with arXiv:1503.0625

Data distribution and performance optimization models for parallel data mining

Ankara : The Department of Computer Engineering and the Graduate School of Engineering and Science of Bilkent University, 2013.Thesis (Ph. D.) -- Bilkent University, 2013.Includes bibliographical references leaves 117-128.We have embarked upon a multitude of approaches to improve the efficiency of selected fundamental tasks in data mining. The present thesis is concerned with improving the efficiency of parallel processing methods for large amounts of data. We have devised new parallel frequent itemset mining algorithms that work on both sparse and dense datasets, and 1-D and 2-D parallel algorithms for the all-pairs similarity problem. Two new parallel frequent itemset mining (FIM) algorithms named NoClique and NoClique2 parallelize our sequential vertical frequent itemset mining algorithm named bitdrill, and uses a method based on graph partitioning by vertex separator (GPVS) to distribute and selectively replicate items. The method operates on a graph where vertices correspond to frequent items and edges correspond to frequent itemsets of size two. We show that partitioning this graph by a vertex separator is sufficient to decide a distribution of the items such that the sub-databases determined by the item distribution can be mined independently. This distribution entails an amount of data replication, which may be reduced by setting appropriate weights to vertices. The data distribution scheme is used in the design of two new parallel frequent itemset mining algorithms. Both algorithms replicate the items that correspond to the separator. NoClique replicates the work induced by the separator and NoClique2 computes the same work collectively. Computational load balancing and minimization of redundant or collective work may be achieved by assigning appropriate load estimates to vertices. The performance is compared to another parallelization that replicates all items, and ParDCI algorithm. We introduce another parallel FIM method using a variation of item distribution with selective item replication. We extend the GPVS model for parallel FIM we have proposed earlier, by relaxing the condition of independent mining. Instead of finding independently mined item sets, we may minimize the amount of communication and partition the candidates in a fine-grained manner. We introduce a hypergraph partitioning model of the parallel computation where vertices correspond to candidates and hyperedges correspond to items. A load estimate is assigned to each candidate with vertex weights, and item frequencies are given as hyperedge weights. The model is shown to minimize data replication and balance load accurately. We also introduce a re-partitioning model since we can generate only so many levels of candidates at once, using fixed vertices to model previous item distribution/replication. Experiments show that we improve over the higher load imbalance of NoClique2 algorithm for the same problem instances at the cost of additional parallel overhead. For the all-pairs similarity problem, we extend recent efficient sequential algorithms to a parallel setting, and obtain document-wise and term-wise parallelizations of a fast sequential algorithm, as well as an elegant combination of two algorithms that yield a 2-D distribution of the data. Two effective algorithmic optimizations for the term-wise case are reported that make the term-wise parallelization feasible. These optimizations exploit local pruning and block processing of a number of vectors, in order to decrease communication costs, the number of candidates, and communication/computation imbalance. The correctness of local pruning is proven. Also, a recursive term-wise parallelization is introduced. The performance of the algorithms are shown to be favorable in extensive experiments, as well as the utility of two major optimizations.Özkural, ErayPh.D

On parallel Branch and Bound frameworks for Global Optimization

Branch and Bound (B&B) algorithms are known to exhibit an irregularity of the search tree. Therefore, developing a parallel approach for this kind of algorithms is a challenge. The efficiency of a B&B algorithm depends on the chosen Branching, Bounding, Selection, Rejection, and Termination rules. The question we investigate is how the chosen platform consisting of programming language, used libraries, or skeletons influences programming effort and algorithm performance. Selection rule and data management structures are usually hidden to programmers for frameworks with a high level of abstraction, as well as the load balancing strategy, when the algorithm is run in parallel. We investigate the question by implementing a multidimensional Global Optimization B&B algorithm with the help of three frameworks with a different level of abstraction (from more to less): Bobpp, Threading Building Blocks (TBB), and a customized Pthread implementation. The following has been found. The Bobpp implementation is easy to code, but exhibits the poorest scalability. On the contrast, the TBB and Pthread implementations scale almost linearly on the used platform. The TBB approach shows a slightly better productivity

Generic parallel implementations for Tabu Search

Tabu Search (TS) is a meta-heuristic for solving combinatorial optimization problems. A review of existing implementations for TS reveals that, on the one hand, these implementations are ad hoc and, on the other hand, most of them run in a sequential setting. Indeed, the reported parallel implementations are few as compared to the sequential implementations. Due to increase in computing resources, especially in LAN environments, it is quite desirable to obtain parallel implementations of TS for solving problems arising in fields others than computer science, such as biology, control theory, etc., in which researchers and practitioners are less familiar with parallel programming. In this work we present a generic implementation of TS able to be run in sequential and parallel settings. The key point in our approach is the design and implementation in C++ of an algorithmic skeleton for TS embedding its main flow as well as several parallel implementations for the method. This is achieved through a separation of concerns: elements related to TS are provided by the skeleton, whereas the problem-dependent elements are expected to be provided by the user according to a fixed interface using purely sequential constructs. Thus, the skeleton has a unique interface but is expected to have many instantiations for concrete problems, all of them being able to run in a straightforward way using different parallel implementations. In order to assess the effectiveness of our approach, we have applied it to several NP-hard combinatorial optimization problems. We have considered developing time, flexibility and easiness of use, quality of solutions and computation efficiency. We have observed that our approach allows fast developing of problem instantiations. Moreover, the skeleton allows the user to configure and implement in different ways internal methods related to TS. Furthermore, the results obtained by our generic parallel implementations are efficient and report good quality results compared to the ones reported by ad hoc implementations. We exemplify our approach through the application to the 0-1 Multidimensional Knapsack problem. The experimental results obtained for standard benchmarks of this problem show that, in spite of the genericity and flexibility of our implementation, the resulting program provides high quality solutions very close to the optimal ones.Postprint (published version