Randomized selection in n+C+o(n) comparisons

In this paper we present a randomized selection algorithm that with high probability 1−1/n^ρ, for any constant ρ>1 requires n+C+o(n) comparisons to determine the Cth order statistic of n keys thus matching a corresponding lower bound on the average number of comparisons required. Low order terms in the number of comparisons performed can also be reduced by extending the algorithm of Floyd and Rivest and analyzing its resulting performance more carefully.     

Probabilistic integer sorting

We introduce a probabilistic sequential algorithm for stable sorting n uniformly distributed keys in an arbitrary range. The algorithm runs in linear time and sorts all but a very small fraction of the input sequences; the best previously known bound was . An EREW PRAM extension of this sequential algorithm sorts in O((n/p+lgp)lgn/lg(n/p+lgn)) time using p?n processors under the same probabilistic conditions. For a CRCW PRAM we improve upon the probabilistic bound of obtained by Rajasekaran and Sen to derive a bound. Additionally, we present experimental results for the sequential algorithm that establish the practicality of our method.     

Parallel Option Price Valuations with 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 has been undertaken, and an evaluation of its performance is carried out by performing an experimental study on a high-latency PC cluster, and at 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.