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By Alan Parker

The formulation of (1.3), (1.4), (1.5),(1.6) are all wrong!

Can't think it, 4 formulation in first web page are all have blunders. perhaps the writer fell so sleepy whilst he is penning this publication!

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11 Planar Graph where f returns a set of edges. html (2 of 6) [6/22/2003 10:12:27 PM] Algorithms and Data Structures in C++:Algorithms Thus in Eq. 45, . 12. 5 Parallel Algorithms This section presents some fundamental properties and definitions used in parallel processing. html (3 of 6) [6/22/2003 10:12:27 PM] Algorithms and Data Structures in C++:Algorithms This is known as Amdahl's Law. The ratio shows that even with an infinite amount of computing power an algorithm with a sequential component can only achieve the speedup in Eq.

For these functions the asymptotic behavior is exhibited when n ≥ 1050. Although f1 ∈ Θ (en) it has a value of 1 for n < 1050. In a pragmatic sense it would be desirable to have a problem with time complexity f1 rather than f2. Typically, however, this phenomenon will not appear and generally one might assume that it is better to have an algorithm which is Θ (1) rather than Θ (en). One should always remember that the constants of order can be significant in real problems. 2 Induction Simple induction is a two step process: • Establish the result for the case N = 1 • Show that if is true for the case N = n then it is true for the case N = n+1 This will establish the result for all n > 1.

Each stage is to be executed in the same amount of time. The flow is divided into k distinct stages. The output of the jth stage becomes the input to the (j + 1) th stage. 13. As seen in the figure the first output is ready after four time steps Each subsequent output is ready after one additional time step. Pipelining becomes efficient when more than one output is required. For many algorithms it may not be possible to subdivide the task into k equal stages to create the pipeline. 14. 14 Pipelining In the figure TSEQ is the time for the algorithm to execute sequentially.

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