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## Chapter 5

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**Chapter 5**The Sieve of Eratosthenes**Introduction**Sequential Algorithm**- Interleaved Data Decomposition 2, 2+p, 2+2p, … 3,**3+p, 3+2p, … ……… Data Decomposition Options**- Block Data Decomposition**(Grouped Scheme) The first element controlled by process i is r = n mod p The last element controlled by process i is The process controlling a particular array element j is**(Distributed Scheme)**The first element controlled by process i is The last element controlled by process i is The process controlling a particular array element j is**Benchmarking**The time needed to mark a particular cell as being the multiple of a prime is (The sequential algorithm has time complexity O(n ln ln n))**- Eliminate Broadcast**- Reorganize loops - exchange the inner and outer loops to improve cache hits