Architecture independent parallel selection with applications to parallel priority queues

AbstractWe present a randomized selection algorithm whose performance is analyzed in an architecture independent way on the bulk-synchronous parallel (BSP) model of computation along with an application of this algorithm to dynamic data structures, namely parallel priority queues. We show that our algorithms improve previous results upon both the communication requirements and the amount of parallel slack required to achieve optimal performance. We also establish that optimality to within small multiplicative constant factors can be achieved for a wide range of parallel machines. While these algorithms are fairly simple themselves, descriptions of their performance in terms of the BSP parameters is somewhat involved; the main reward of quantifying these complications is that it allows transportable software to be written for parallel machines that fit the model

Option Price Valuations

We introduce an architecture independent approach in describing how computations such as those involved in American or European-style option valuations can be performed in parallel in the binomial-tree model. In particular we present an algorithm for the multiplicative binomial tree option-pricing model that can also be directly generalized to the general additive binomial tree model. The algorithm is described and analyzed in an architecture independent setting and running time and performance characteristics are expressed in terms of problem size n, which is the time horizon, and the parameters p, L and g of the bulk-synchronous parallel model of computation. In particular, our algorithm achieves optimal theoretical speedup O(p) and is thus within a 1 + o(1) multiplicative factor of the corresponding sequential method

Trinomial-Tree Based Parallel Option Price Valuations

We examine how trinomial-tree based computations such as those involved in American or European-style option price valuations can be performed in parallel. Towards this we introduce a parallel algorithm for performing such computations on trinomial trees. The algorithm is described and analyzed in an architecture independent setting and achieves optimal theoretical speedup O(p) and is thus within a 1+o(1) multiplicative factor of the corresponding sequential method. We verify the practicality and plausibility of the designed algorithm by carrying out an experimental study of an implementation of the algorithm on a high-latency parallel system, a cluster of PC workstations. The algorithmic and programming methodology used to design and analyze the algorithm allows its implementation to work with only recompilation of the source code under two parallel programming libraries: MPI (LAM-MPI) and BSPlib thus making the implementation not only architecture but also communication-library independent

Parallel option price . . . the Explicit Finite Difference Method

We show how computations such as those involved in American or European-style option price valuations with the explicit finite difference method can be performed in parallel. Towards this we introduce a latency tolerant parallel algorithm for performing such computations efficiently that achieves optimal theoretical speedup p, where p is the number of processor of the parallel system. An implementation of the parallel algorithm and evaluation of its performance is carried out by performing an experimental study on a high-latency parallel system consisting of a cluster of 16 PC workstations. Our implementation of the parallel algorithm is not only architecture but also communication library independent: the same code works under LAM-MPI and BSPlib, two libraries that facilitate parallel programming

PARALLEL OPTION PRICE VALUATIONS WITH THE EXPLICIT FINITE DIFFERENCE METHOD ∗

Abstract. We show how computations such as those involvedin American or European-style option price valuations with the explicit finite difference method can be performed in parallel. Towards this we introduce a latency tolerant parallel algorithm for performing such computations efficiently that achieves optimal theoretical speedup p, wherep is the number of processor of the parallel system. An implementation of the parallel algorithm has been undertaken, and an evaluation of its performance is carriedout by performing an experimental study on a high-latency PC cluster, andat a smaller scale, on a multi-core processor using in addition the SWARM parallel computing framework for multi-core processors. Our implementation of the parallel algorithm is not only architecture but also communication library independent: the same code works under LAM-MPI and Open MPI and also BSPlib, two sets of library frameworks that facilitate parallel programming. The suitability of our approach to multi-core processors is also established

An Architecture Independent Study of Parallel Segment Trees

In this work we study the computation, communication and synchronization requirements related to the construction and search of parallel segment trees in an architecture independent way. Our proposed algorithms are optimal in space and time compared to the sequential algorithms utilized to solve the corresponding problems and are described in the context of the Bulk-Synchronous Parallel (BSP) model of computation. Our methods are more scalable (i.e. work for larger values of p relative to n, the problem size) than other segment tree related algorithms that have been described on other realistic distributed-memory parallel models and provide a natural way to approach searching problems on the BSP model that maintain a balanced query load among the processors