This article presents asymptotically optimal algorithms for rectangular matrix transpose, fast Fourier transform (FFT), and sorting on computers with multiple levels of caching. Unlike previous optimal algorithms, these algorithms are cache oblivious : no variables dependent on hardware parameters, such as cache size and cache-line length, need to be tuned to achieve optimality. Nevertheless, these algorithms use an optimal amount of work and move data optimally among multiple levels of cache. For a cache with size M and cache-line length B where M = Ω ( B 2 ), the number of cache misses for an m × n matrix transpose is Θ (1 + mn / B ). The number of cache misses for either an n -point FFT or the sorting of n numbers is Θ (1 + ( n / B )(1 + log M n )). We also give a Θ ( mnp )-work algorithm to multiply an m × n matrix by an n × p matrix that incurs Θ (1 + ( mn + np + mp )/ B + mnp / B √ M ) cache faults. We introduce an “ideal-cache” model to analyze our algorithms. We prove that an optimal cache-oblivious algorithm designed for two levels of memory is also optimal for multiple levels and that the assumption of optimal replacement in the ideal-cache model can be simulated efficiently by LRU replacement. We offer empirical evidence that cache-oblivious algorithms perform well in practice.

The Alu family of Short interspersed repeats (SINEs) account for a significant portion of the "junk DNA" within the mammalian genome. Thousands of copies of Alu subfamilies are scattered essentially randomly through the human genome. The relative abundance of these repeats provides a rich fossil record of primate and human history. Since Alus have no known functionality, a great deal of ambiguity surrounds their amplification and evolution. Herein, using parsimony approach, we investigate the popular belief that the vast majority of Alu amplification is derived from a small subset of Alu master genes. Our results indicate that the classification of Alu subfamilies reported in literature is incomplete. Furthermore, we summarize some of the factors relevant to the use of the Alu family of repeats in bioinformatic assays

This paper presents asymptotically optimal algorithms for rectangular matrix transpose, FFT, and sorting on computers with multiple levels of caching. Unlike previous optimal algorithms, these algorithms are cache oblivious: no variables dependent on hardware parameters, such as cache size and cache-line length, need to be tuned to achieve optimality. Nevertheless, these algorithms use an optimal amount of work and move data optimally among multiple levels of cache. For a cache with size Z and cache-line length L where Z=/spl Omega/(L/sup 2/) the number of cache misses for an m/spl times/n matrix transpose is /spl Theta/(1+mn/L). The number of cache misses for either an n-point FFT or the sorting of n numbers is /spl Theta/(1+(n/L)(1+log/sub Z/n)). We also give an /spl Theta/(mnp)-work algorithm to multiply an m/spl times/n matrix by an n/spl times/p matrix that incurs /spl Theta/(1+(mn+np+mp)/L+mnp/L/spl radic/Z) cache faults. We introduce an "ideal-cache" model to analyze our algorithms. We prove that an optimal cache-oblivious algorithm designed for two levels of memory is also optimal for multiple levels and that the assumption of optimal replacement in the ideal-cache model. Can be simulated efficiently by LRU replacement. We also provide preliminary empirical results on the effectiveness of cache-oblivious algorithms in practice.