Aspects of practical implementations of PRAM algorithms

The PRAM is a shared memory model of parallel computation which abstracts away from inessential engineering details. It provides a very simple architecture independent model and provides a good programming environment. Theoreticians of the computer science community have proved that it is possible to emulate the theoretical PRAM model using current technology. Solutions have been found for effectively interconnecting processing elements, for routing data on these networks and for distributing the data among memory modules without hotspots. This thesis reviews this emulation and the possibilities it provides for large scale general purpose parallel computation. The emulation employs a bridging model which acts as an interface between the actual hardware and the PRAM model. We review the evidence that such a scheme can achieve scalable parallel performance and portable parallel software and that PRAM algorithms can be optimally implemented on such practical models. In the course of this review we presented the following new results: 1. Concerning parallel approximation algorithms, we describe an NC algorithm for findings an approximation to a minimum weight perfect matching in a complete weighted graph. The algorithm is conceptually very simple and it is also the first NC-approximation algorithm for the task with a sub-linear performance ratio. 2. Concerning graph embedding, we describe dense edge-disjoint embeddings of the complete binary tree with n leaves in the following n-node communication networks: the hypercube, the dc Bruijn and shuffle-exchange networks and the 2-dimcnsional mesh. In the embeddings the maximum distance from a leaf to the root of the tree is asymptotically optimally short. The embeddings facilitate efficient implementation of many PRAM algorithms on networks employing these graphs as interconnection networks. 3. Concerning bulk synchronous algorithmic, we describe scalable transportable algorithms for the following three commonly required types of computation; balanced tree computations. Fast Fourier Transforms and matrix multiplications

Parallel Batch-Dynamic Graph Connectivity

In this paper, we study batch parallel algorithms for the dynamic connectivity problem, a fundamental problem that has received considerable attention in the sequential setting. The most well known sequential algorithm for dynamic connectivity is the elegant level-set algorithm of Holm, de Lichtenberg and Thorup (HDT), which achieves $O(\log^2 n)$ amortized time per edge insertion or deletion, and $O(\log n / \log\log n)$ time per query. We design a parallel batch-dynamic connectivity algorithm that is work-efficient with respect to the HDT algorithm for small batch sizes, and is asymptotically faster when the average batch size is sufficiently large. Given a sequence of batched updates, where $\Delta$ is the average batch size of all deletions, our algorithm achieves $O(\log n \log(1 + n / \Delta))$ expected amortized work per edge insertion and deletion and $O(\log^3 n)$ depth w.h.p. Our algorithm answers a batch of $k$ connectivity queries in $O(k \log(1 + n/k))$ expected work and $O(\log n)$ depth w.h.p. To the best of our knowledge, our algorithm is the first parallel batch-dynamic algorithm for connectivity.Comment: This is the full version of the paper appearing in the ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), 201

Fast Distributed Algorithms for LP-Type Problems of Bounded Dimension

In this paper we present various distributed algorithms for LP-type problems in the well-known gossip model. LP-type problems include many important classes of problems such as (integer) linear programming, geometric problems like smallest enclosing ball and polytope distance, and set problems like hitting set and set cover. In the gossip model, a node can only push information to or pull information from nodes chosen uniformly at random. Protocols for the gossip model are usually very practical due to their fast convergence, their simplicity, and their stability under stress and disruptions. Our algorithms are very efficient (logarithmic rounds or better with just polylogarithmic communication work per node per round) whenever the combinatorial dimension of the given LP-type problem is constant, even if the size of the given LP-type problem is polynomially large in the number of nodes

Causal Consistency: Beyond Memory

In distributed systems where strong consistency is costly when not impossible, causal consistency provides a valuable abstraction to represent program executions as partial orders. In addition to the sequential program order of each computing entity, causal order also contains the semantic links between the events that affect the shared objects -- messages emission and reception in a communication channel , reads and writes on a shared register. Usual approaches based on semantic links are very difficult to adapt to other data types such as queues or counters because they require a specific analysis of causal dependencies for each data type. This paper presents a new approach to define causal consistency for any abstract data type based on sequential specifications. It explores, formalizes and studies the differences between three variations of causal consistency and highlights them in the light of PRAM, eventual consistency and sequential consistency: weak causal consistency, that captures the notion of causality preservation when focusing on convergence ; causal convergence that mixes weak causal consistency and convergence; and causal consistency, that coincides with causal memory when applied to shared memory.Comment: 21st ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, Mar 2016, Barcelone, Spai

Implementing the conjugate gradient algorithm on multi-core systems

In linear solvers, like the conjugate gradient algorithm, sparse-matrix vector multiplication is an important kernel. Due to the sparseness of the matrices, the solver runs relatively slow. For digital optical tomography (DOT), a large set of linear equations have to be solved which currently takes in the order of hours on desktop computers. Our goal was to speed up the conjugate gradient solver. In this paper we present the results of applying multiple optimization techniques and exploiting multi-core solutions offered by two recently introduced architectures: Intel’s Woodcrest\ud general purpose processor and NVIDIA’s G80 graphical processing unit. Using these techniques for these architectures, a speedup of a factor three\ud has been achieved