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Future architectures designed to deliver exascale performance motivate the need for novel algorithmic changes in order to fully exploit their capabilities. In this paper, the performance of several numerical algorithms, characterised by varying degrees of memory and computational intensity, are evaluated in the context of finite difference methods for fluid dynamics problems. It is shown that, by storing some of the evaluated derivatives as single thread- or process-local variables in memory, or recomputing the derivatives on-the-fly, a speed-up of ~2 can be obtained compared to traditional algorithms that store all derivatives in global arrays.
We introduce a new model of computation: the online LOCAL model (OLOCAL). In this model, the adversary reveals the nodes of the input graph one by one, in the same way as in classical online algorithms, but for each new node the algorithm can also in
In the unit-cost comparison model, a black box takes an input two items and outputs the result of the comparison. Problems like sorting and searching have been studied in this model, and it has been generalized to include the concept of priced inform
The spatial join is a popular operation in spatial database systems and its evaluation is a well-studied problem. As main memories become bigger and faster and commodity hardware supports parallel processing, there is a need to revamp classic join al
Simulations of physical phenomena are essential to the expedient design of precision components in aerospace and other high-tech industries. These phenomena are often described by mathematical models involving partial differential equations (PDEs) wi
Suppose we sequentially put $n$ balls into $n$ bins. If we put each ball into a random bin then the heaviest bin will contain ${sim}log n/loglog n$ balls with high probability. However, Azar, Broder, Karlin and Upfal [SIAM J. Comput. 29 (1999) 180--2