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Full-Text Articles in Physical Sciences and Mathematics
A Novel Weighted-Graph-Based Grouping Algorithm For Metadata Prefetching, Peng Gu, Jun Wang, Yifeng Zhu, Hong Jiang, Pengju Shang
A Novel Weighted-Graph-Based Grouping Algorithm For Metadata Prefetching, Peng Gu, Jun Wang, Yifeng Zhu, Hong Jiang, Pengju Shang
Yifeng Zhu
Although data prefetching algorithms have been extensively studied for years, there is no counterpart research done for metadata access performance. Existing data prefetching algorithms, either lack of emphasis on group prefetching, or bearing a high level of computational complexity, do not work well with metadata prefetching cases. Therefore, an efficient, accurate, and distributed metadata-oriented prefetching scheme is critical to leverage the overall performance in large distributed storage systems. In this paper, we present a novel weighted-graph-based prefetching technique, built on both direct and indirect successor relationship, to reap performance benefit from prefetching specifically for clustered metadata servers, an arrangement envisioned …
Computing Prime Harmonic Sums, Eric Bach, Dominic Klyve, Jonathan P. Sorenson
Computing Prime Harmonic Sums, Eric Bach, Dominic Klyve, Jonathan P. Sorenson
Jonathan P. Sorenson
We discuss a method for computing Σ �≤� 1/�, using time about �2/3 and space about �1/3. It is based on the Meissel-Lehmer algorithm for computing the prime-counting function �(�), which was adapted and improved by Lagarias, Miller, and Odlyzko. We used this algorithm to determine the first point at which the prime harmonic sum first crosses.
Computing Prime Harmonic Sums, Eric Bach, Dominic Klyve, Jonathan P. Sorenson
Computing Prime Harmonic Sums, Eric Bach, Dominic Klyve, Jonathan P. Sorenson
Jonathan P. Sorenson
We discuss a method for computing Σ �≤� 1/�, using time about �2/3 and space about �1/3. It is based on the Meissel-Lehmer algorithm for computing the prime-counting function �(�), which was adapted and improved by Lagarias, Miller, and Odlyzko. We used this algorithm to determine the first point at which the prime harmonic sum first crosses.
Modular Exponentiation Via The Explicit Chinese Remainder Theorem, Daniel J. Bernstein, Jonathan P. Sorenson
Modular Exponentiation Via The Explicit Chinese Remainder Theorem, Daniel J. Bernstein, Jonathan P. Sorenson
Jonathan P. Sorenson
In this paper we consider the problem of computing xe mod m for large integers x, e, and m. This is the bottleneck in Rabin’s algorithm for testing primality, the Diffie-Hellman algorithm for exchanging cryptographic keys, and many other common algorithms.
Modular Exponentiation Via The Explicit Chinese Remainder Theorem, Daniel J. Bernstein, Jonathan P. Sorenson
Modular Exponentiation Via The Explicit Chinese Remainder Theorem, Daniel J. Bernstein, Jonathan P. Sorenson
Jonathan P. Sorenson
In this paper we consider the problem of computing xe mod m for large integers x, e, and m. This is the bottleneck in Rabin’s algorithm for testing primality, the Diffie-Hellman algorithm for exchanging cryptographic keys, and many other common algorithms.
The Pseudosquares Prime Sieve, Jonathan P. Sorenson
The Pseudosquares Prime Sieve, Jonathan P. Sorenson
Jonathan P. Sorenson
We present the pseudosquares prime sieve, which finds all primes up to n.
Fast Bounds On The Distribution Of Smooth Numbers, Scott T. Parsell, Jonathan P. Sorenson
Fast Bounds On The Distribution Of Smooth Numbers, Scott T. Parsell, Jonathan P. Sorenson
Jonathan P. Sorenson
In this paper we present improvements to Bernstein’s algorithm, which finds rigorous upper and lower bounds for (x, y).