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

Tolérance aux pannes dans des environnements de calcul parallèle et distribué (optimisation des stratégies de sauvegarde/reprise et ordonnancement)

Le passage de l'échelle des nouvelles plates-formes de calcul parallèle et distribué soulève de nombreux défis scientifiques. À terme, il est envisageable de voir apparaître des applications composées d'un milliard de processus exécutés sur des systèmes à un million de coeurs. Cette augmentation fulgurante du nombre de processeurs pose un défi de résilience incontournable, puisque ces applications devraient faire face à plusieurs pannes par jours. Pour assurer une bonne exécution dans ce contexte hautement perturbé par des interruptions, de nombreuses techniques de tolérance aux pannes telle que l'approche de sauvegarde et reprise (checkpoint) ont été imaginées et étudiées. Cependant, l'intégration de ces approches de tolérance aux pannes dans le couple formé par l'application et la plate-forme d'exécution soulève des problématiques d'optimisation pour déterminer le compromis entre le surcoût induit par le mécanisme de tolérance aux pannes d'un coté et l'impact des pannes sur l'exécution d'un autre coté. Dans la première partie de cette thèse nous concevons deux modèles de performance stochastique (minimisation de l'impact des pannes et du surcoût des points de sauvegarde sur l'espérance du temps de complétion de l'exécution en fonction de la distribution d'inter-arrivées des pannes). Dans la première variante l'objectif est la minimisation de l'espérance du temps de complétion en considérant que l'application est de nature préemptive. Nous exhibons dans ce cas de figure tout d'abord une expression analytique de la période de sauvegarde optimale quand le taux de panne et le surcoût des points de sauvegarde sont constants. Par contre dans le cas où le taux de panne ou les surcoûts des points de sauvegarde sont arbitraires nous présentons une approche numérique pour calculer l'ordonnancement optimal des points de sauvegarde. Dans la deuxième variante, l'objectif est la minimisation de l'espérance de la quantité totale de temps perdu avant la première panne en considérant les applications de nature non-préemptive. Dans ce cas de figure, nous démontrons tout d'abord que si les surcoûts des points sauvegarde sont arbitraires alors le problème du meilleur ordonnancement des points de sauvegarde est NP-complet. Ensuite, nous exhibons un schéma de programmation dynamique pour calculer un ordonnancement optimal. Dans la deuxième partie de cette thèse nous nous focalisons sur la conception des stratégies d'ordonnancement tolérant aux pannes qui optimisent à la fois le temps de complétion de la dernière tâche et la probabilité de succès de l'application. Nous mettons en évidence dans ce cas de figure qu'en fonction de la nature de la distribution de pannes, les deux objectifs à optimiser sont tantôt antagonistes, tantôt congruents. Ensuite en fonction de la nature de distribution de pannes nous donnons des approches d'ordonnancement avec des ratios de performance garantis par rapport aux deux objectifs.The parallel computing platforms available today are increasingly larger. Typically the emerging parallel platforms will be composed of several millions of CPU cores running up to a billion of threads. This intensive growth of the number of parallel threads will make the application subject to more and more failures. Consequently it is necessary to develop efficient strategies providing safe and reliable completion for HPC parallel applications. Checkpointing is one of the most popular and efficient technique for developing fault-tolerant applications on such a context. However, checkpoint operations are costly in terms of time, computation and network communications. This will certainly affect the global performance of the application. In the first part of this thesis, we propose a performance model that expresses formally the checkpoint scheduling problem. Two variants of the problem have been considered. In the first variant, the objective is the minimization of the expected completion time. Under this model we prove that when the failure rate and the checkpoint cost are constant the optimal checkpoint strategy is necessarily periodic. For the general problem when the failure rate and the checkpoint cost are arbitrary we provide a numerical solution for the problem. In the second variant if the problem, we exhibit the tradeoff between the impact of the checkpoints operations and the lost computation due to failures. In particular, we prove that the checkpoint scheduling problem is NP-hard even in the simple case of uniform failure distribution. We also present a dynamic programming scheme for determining the optimal checkpointing times in all the variants of the problem. In the second part of this thesis, we design several fault tolerant scheduling algorithms that minimize the application makespan and in the same time maximize the application reliability. Mainly, in this part we point out that the growth rate of the failure distribution determines the relationship between both objectives. More precisely we show that when the failure rate is decreasing the two objectives are antagonist. In the second hand when the failure rate is increasing both objective are congruent. Finally, we provide approximation algorithms for both failure rate cases.SAVOIE-SCD - Bib.électronique (730659901) / SudocGRENOBLE1/INP-Bib.électronique (384210012) / SudocGRENOBLE2/3-Bib.électronique (384219901) / SudocSudocFranceF