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Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

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To evaluate the performance of the parallel heuristic search algorithms,<br />

Mahanti <strong>and</strong> Daniels defined two alternative formula for speed-up.<br />

Let S(P) be the speed-up due to P processors; let N(P) be the number of nodes<br />

generated on P processors. So, the average generation cycle time is N(P) / P.<br />

Thus for a uniprocesor, the generation time is N(1) /1. Consequently, the<br />

speed up S(P) is given by<br />

S(P) = [N(1) /1] / [N (P) / P]<br />

= P N(1) / N (P) = S1 ,say. (22.1)<br />

The above calculation presumes the full utilization of the processors. But<br />

during the load balancing phase, the processor will be idle. Thus the following<br />

correction can be made in the last formulation.<br />

Let CG (P) be the actual number of generation cycles, then<br />

S(P) = CG (1) / CG (P) = N(1) / CG (P) (22.2)<br />

Let tG be the time required in single node generation cycle <strong>and</strong> TL (P) be the<br />

averaged load balancing time. Then<br />

S (P) = [CG (1) tG] / [ CG (P) (tG + TL (P) / CG (P) ) (22.3)<br />

Mahanti <strong>and</strong> Daniels experimented with 4K, 8K <strong>and</strong> 16K number of<br />

parallel processors <strong>and</strong> found the speed-up by the second formula to lie in the<br />

range of ( 2/3 to 3 /4) for most cases. They also observed that the maximum<br />

experimental speed-up occurs when partial expansion <strong>and</strong> generous load<br />

balancing are employed.<br />

It may be noted that there exist a number of related works [9] on<br />

realization of intelligent search techniques on parallel architecture. This book,<br />

which is aimed at a wider audience, unfortunately does not have the scope to<br />

report them.

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