Solution of graph problems by means of the STAR-machine being implemented on GPUS

Для решения многих задач на графах построены эффективные алгоритмы на ассоциативных параллельных процессорах. Но на данный момент нет широко используемых ассоциативных архитектур. Однако с развитием графических ускорителей появилась возможность реализовывать ассоциативные параллельные модели без существенной потери эффективности вычислений, что позволяет применять ассоциативные алгоритмы на практике. Представляется реализация абстрактной модели ассоциативной параллельной обработки данных (STAR-маши-на) на графических ускорителях с помощью технологии CUDA. Измеряется производительность реализации и показывается её эффективность для решения задач на графах на примере алгоритма Уоршалла нахождения транзитивного замыкания ориентированного графа. На графе с 5000 вершин последовательный алгоритм Уоршалла выполнялся за 884,622 с, ассоциативная параллельная версия — за 64,454с (ускорение в 13 раз), а ассоциативная параллельная версия, адаптированная под GPU, — за 0,372с (ускорение в 2 378 раз)

Efficient Algorithms and Data Structures for Massive Data Sets

For many algorithmic problems, traditional algorithms that optimise on the number of instructions executed prove expensive on I/Os. Novel and very different design techniques, when applied to these problems, can produce algorithms that are I/O efficient. This thesis adds to the growing chorus of such results. The computational models we use are the external memory model and the W-Stream model. On the external memory model, we obtain the following results. (1) An I/O efficient algorithm for computing minimum spanning trees of graphs that improves on the performance of the best known algorithm. (2) The first external memory version of soft heap, an approximate meldable priority queue. (3) Hard heap, the first meldable external memory priority queue that matches the amortised I/O performance of the known external memory priority queues, while allowing a meld operation at the same amortised cost. (4) I/O efficient exact, approximate and randomised algorithms for the minimum cut problem, which has not been explored before on the external memory model. (5) Some lower and upper bounds on I/Os for interval graphs. On the W-Stream model, we obtain the following results. (1) Algorithms for various tree problems and list ranking that match the performance of the best known algorithms and are easier to implement than them. (2) Pass efficient algorithms for sorting, and the maximal independent set problems, that improve on the best known algorithms. (3) Pass efficient algorithms for the graphs problems of finding vertex-colouring, approximate single source shortest paths, maximal matching, and approximate weighted vertex cover. (4) Lower bounds on passes for list ranking and maximal matching. We propose two variants of the W-Stream model, and design algorithms for the maximal independent set, vertex-colouring, and planar graph single source shortest paths problems on those models.Comment: PhD Thesis (144 pages

Analysis and Approximation of Optimal Co-Scheduling on CMP

In recent years, the increasing design complexity and the problems of power and heat dissipation have caused a shift in processor technology to favor Chip Multiprocessors. In Chip Multiprocessors (CMP) architecture, it is common that multiple cores share some on-chip cache. The sharing may cause cache thrashing and contention among co-running jobs. Job co-scheduling is an approach to tackling the problem by assigning jobs to cores appropriately so that the contention and consequent performance degradations are minimized. This dissertation aims to tackle two of the most prominent challenges in job co-scheduling.;The first challenge is in the computational complexity for determining optimal job co-schedules. This dissertation presents one of the first systematic analyses on the complexity of job co-scheduling. Besides proving the NP completeness of job co-scheduling, it introduces a set of algorithms, based on graph theory and Integer/Linear Programming, for computing optimal co-schedules or their lower bounds in scenarios with or without job migrations. For complex cases, it empirically demonstrates the feasibility for approximating the optimal schedules effectively by proposing several heuristics-based algorithms. These discoveries facilitate the assessment of job co-schedulers by providing necessary baselines, and shed insights to the development of practical co-scheduling systems.;The second challenge resides in the prediction of the performance of processes co-running on a shared cache. This dissertation explores the influence on co-run performance prediction imposed by co-runners, program inputs, and cache configurations. Through a sequence of formal analysis, we derive an analytical co-run locality model, uncovering the inherent statistical connections between the data references of programs single-runs and their co-run locality. The model offers theoretical insights on co-run locality analysis and leads to a lightweight approach for fast prediction of shared cache performance. We demonstrate the effectiveness of the model in enabling proactive job co-scheduling.;Together, the two-dimensional findings open up many new opportunities for cache management on modern CMP by laying the foundation for job co-scheduling, and enhancing the understanding to data locality and cache sharing significantly

Algorithms incorporating concurrency and caching

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. 189-203).This thesis describes provably good algorithms for modern large-scale computer systems, including today's multicores. Designing efficient algorithms for these systems involves overcoming many challenges, including concurrency (dealing with parallel accesses to the same data) and caching (achieving good memory performance.) This thesis includes two parallel algorithms that focus on testing for atomicity violations in a parallel fork-join program. These algorithms augment a parallel program with a data structure that answers queries about the program's structure, on the fly. Specifically, one data structure, called SP-ordered-bags, maintains the series-parallel relationships among threads, which is vital for uncovering race conditions (bugs) in the program. Another data structure, called XConflict, aids in detecting conflicts in a transactional-memory system with nested parallel transactions. For a program with work T and span To, maintaining either data structure adds an overhead of PT, to the running time of the parallel program when executed on P processors using an efficient scheduler, yielding a total runtime of O(T1/P + PTo). For each of these data structures, queries can be answered in 0(1) time. This thesis also introduces the compressed sparse rows (CSB) storage format for sparse matrices, which allows both Ax and ATx to be computed efficiently in parallel, where A is an n x n sparse matrix with nnz > n nonzeros and x is a dense n-vector. The parallel multiplication algorithm uses e(nnz) work and ... span, yielding a parallelism of ... , which is amply high for virtually any large matrix.(cont.) Also addressing concurrency, this thesis considers two scheduling problems. The first scheduling problem, motivated by transactional memory, considers randomized backoff when jobs have different lengths. I give an analysis showing that binary exponential backoff achieves makespan V2e(6v 1- i ) with high probability, where V is the total length of all n contending jobs. This bound is significantly larger than when jobs are all the same size. A variant of exponential backoff, however, achieves makespan of ... with high probability. I also present the size-hashed backoff protocol, specifically designed for jobs having different lengths, that achieves makespan ... with high probability. The second scheduling problem considers scheduling n unit-length jobs on m unrelated machines, where each job may fail probabilistically. Specifically, an input consists of a set of n jobs, a directed acyclic graph G describing the precedence constraints among jobs, and a failure probability qij for each job j and machine i. The goal is to find a schedule that minimizes the expected makespan. I give an O(log log(min {m, n}))-approximation for the case of independent jobs (when there are no precedence constraints) and an O(log(n + m) log log(min {m, n}))-approximation algorithm when precedence constraints form disjoint chains. This chain algorithm can be extended into one that supports precedence constraints that are trees, which worsens the approximation by another log(n) factor. To address caching, this thesis includes several new variants of cache-oblivious dynamic dictionaries.(cont.) A cache-oblivious dictionary fills the same niche as a classic B-tree, but it does so without tuning for particular memory parameters. Thus, cache-oblivious dictionaries optimize for all levels of a multilevel hierarchy and are more portable than traditional B-trees. I describe how to add concurrency to several previously existing cache-oblivious dictionaries. I also describe two new data structures that achieve significantly cheaper insertions with a small overhead on searches. The cache-oblivious lookahead array (COLA) supports insertions/deletions and searches in O((1/B) log N) and O(log N) memory transfers, respectively, where B is the block size, M is the memory size, and N is the number of elements in the data structure. The xDict supports these operations in O((1/1B E1-) logB(N/M)) and O((1/)0logB(N/M)) memory transfers, respectively, where 0 < E < 1 is a tunable parameter. Also on caching, this thesis answers the question: what is the worst possible page-replacement strategy? The goal of this whimsical chapter is to devise an online strategy that achieves the highest possible fraction of page faults / cache misses as compared to the worst offline strategy. I show that there is no deterministic strategy that is competitive with the worst offline. I also give a randomized strategy based on the most recently used heuristic and show that it is the worst possible pagereplacement policy. On a more serious note, I also show that direct mapping is, in some sense, a worst possible page-replacement policy. Finally, this thesis includes a new algorithm, following a new approach, for the problem of maintaining a topological ordering of a dag as edges are dynamically inserted.(cont.) The main result included here is an O(n2 log n) algorithm for maintaining a topological ordering in the presence of up to m < n(n - 1)/2 edge insertions. In contrast, the previously best algorithm has a total running time of O(min { m3/ 2, n5/2 }). Although these algorithms are not parallel and do not exhibit particularly good locality, some of the data structural techniques employed in my solution are similar to others in this thesis.by Jeremy T. Fineman.Ph.D

Data Structures for Efficient String Algorithms

This thesis deals with data structures that are mostly useful in the area of string matching and string mining. Our main result is an O(n)-time preprocessing scheme for an array of n numbers such that subsequent queries asking for the position of a minimum element in a specified interval can be answered in constant time (so-called RMQs for Range Minimum Queries). The space for this data structure is 2n+o(n) bits, which is shown to be asymptotically optimal in a general setting. This improves all previous results on this problem. The main techniques for deriving this result rely on combinatorial properties of arrays and so-called Cartesian Trees. For compressible input arrays we show that further space can be saved, while not affecting the time bounds. For the two-dimensional variant of the RMQ-problem we give a preprocessing scheme with quasi-optimal time bounds, but with an asymptotic increase in space consumption of a factor of log(n). It is well known that algorithms for answering RMQs in constant time are useful for many different algorithmic tasks (e.g., the computation of lowest common ancestors in trees); in the second part of this thesis we give several new applications of the RMQ-problem. We show that our preprocessing scheme for RMQ (and a variant thereof) leads to improvements in the space- and time-consumption of the Enhanced Suffix Array, a collection of arrays that can be used for many tasks in pattern matching. In particular, we will see that in conjunction with the suffix- and LCP-array 2n+o(n) bits of additional space (coming from our RMQ-scheme) are sufficient to find all occ occurrences of a (usually short) pattern of length m in a (usually long) text of length n in O(m*s+occ) time, where s denotes the size of the alphabet. This is certainly optimal if the size of the alphabet is constant; for non-constant alphabets we can improve this to O(m*log(s)+occ) locating time, replacing our original scheme with a data structure of size approximately 2.54n bits. Again by using RMQs, we then show how to solve frequency-related string mining tasks in optimal time. In a final chapter we propose a space- and time-optimal algorithm for computing suffix arrays on texts that are logically divided into words, if one is just interested in finding all word-aligned occurrences of a pattern. Apart from the theoretical improvements made in this thesis, most of our algorithms are also of practical value; we underline this fact by empirical tests and comparisons on real-word problem instances. In most cases our algorithms outperform previous approaches by all means

Algorithm Engineering for fundamental Sorting and Graph Problems

Fundamental Algorithms build a basis knowledge for every computer science undergraduate or a professional programmer. It is a set of basic techniques one can find in any (good) coursebook on algorithms and data structures. In this thesis we try to close the gap between theoretically worst-case optimal classical algorithms and the real-world circumstances one face under the assumptions imposed by the data size, limited main memory or available parallelism

Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization

International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM