Variable elimination is a general technique for constraint processing. It is often discarded because of its high space complexity. However, it can be extremely useful when combined with other techniques. In this paper we study the applicability of variable elimination to the challenging problem of finding still-lifes. We illustrate several alternatives: variable elimination as a stand-alone algorithm, interleaved with search, and as a source of good quality lower bounds. We show that these techniques are the best known option both theoretically and empirically. In our experiments we have been able to solve the n = 20 instance, which is far beyond reach with alternative approaches.
Abstract-Partial Differential Equations (PDE) are the heart of most simulations in many scientific fields, from Fluid Mechanics to Astrophysics. One the most popular mathematical schemes to solve a PDE is Finite Difference (FD). In this work we map a PDE-FD algorithm called Reverse Time Migration to a GPU using CUDA. This seismic imaging (Geophysics) algorithm is widely used in the oil industry. GPUs are natural contenders in the aftermath of the clock race, in particular for High-performance Computing (HPC). Due to GPU characteristics, the parallelism paradigm shifts from the classical threads plus SIMD to Single Program Multiple Data (SPMD). The NVIDIA GTX 280 implementation outperforms homogeneous CPUs up to 9x (Intel Harpertown E5420) and up to 14x (IBM PPC 970). These preliminary results confirm that GPUs are a real option for HPC, from performance to programmability.
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