Models 3 Professor Ioana Banicescu CSE 8843 The

Models 3 Professor Ioana Banicescu CSE 8843

The work-time presentation framework of parallel algorithms: WT paradigm: provides a 2 level top-down description of parallel algorithm Upper-level: suppresses details of the algorithm Lower-level: follows general scheduling principle and results in a full PRAM description Upper-level WT: Goal: describe the algorithm in terms of sequence of time units, where each time unit may include any number of concurrent operation Work: Total number of operations used Eg: For l <= i <= u par do, the statements corresponding to all values of I between l and u are executed concurrently.

Lower Level: • Suppose that WT presentation of the algorithm results in a parallel algorithm that runs in T(n) time units while performing W(n) work. • Using WT scheduling principle, we can almost always adapt this algorithm to run on a p processor PRAM in: <= W(n)/p + T(n) parallel steps The WT scheduling principle: a) Let Wi(n) be the number of operations performed in time unit i, 1 <= i <= T(n) b) Simulate each set of Wi(n) operations in Wi(n)/p parallel steps by the p processors for each 1<=i<=T(n)

• During each time unit i, the Wi(n) operations are scheduled as evenly as possible among available p processors. • During time units 1 and 2, each PE is scheduled to execute the same number of operations. • During time unit 3, the p-th PE executes one less operation than are executed by remaining PEs. • During time unit 4, there are only k possible concurrent operations.