Using graph partitioning algorithms as an example, we demonstrate the often underestimated influence of these

random-number generators on the result of the heuristic algorithms.

Monte Carlo applications are widely perceived as embarrassingly parallel.(1) The truth of this notion depends, to a large extent, on the quality of the parallel random-number generators used.

We present the rationale for the design of SPRNG, outline the overall design methodology, which is based on full-period parameterized random-number generators, and then detail the suite of randomness tests that is included in SPRNG.

That's precisely what occurred in 1995, when Wagner, then a graduate student at Berkeley, and his fellow student Ian Goldberg cracked the random-number generator used by the Netscape web browser to secure online transactions.

Another early random-number generator extracted randomness from a very retro source: lava lamps, whose illuminated blobs move unpredictably.

For the underlying uniform random-number generator we have used the library prng-2.2 [Lendl 1997].

These tests have demonstrated that for small ratio ??, the quality of the normal generators is strongly correlated with the quality of the underlying uniform random-number generator. Especially, using randu results in a normal generator of bad quality.

This packet then serves as the seed value for a computer-based

random-number generator. Each such value starts a chain of mathematical operations that produces a different string of apparently random digits.

For every problem, 40 runs were performed reflecting eight iteration settings (16, 32, 64, 128, 256, 512, 1024, and 2048 iterations) and five

random-number generator seeds (1, 2, 3, 4, 5) for each iteration setting.

"As far as we could tell, we had exhausted every possibility -- except the

random-number generator," he remarks.

"What we want is enough experience so that we can provide guidelines about when not to use a particular

random-number generator."

However, the most widely used multiplicative, congruential

random-number generators with modulus [2.sup.31] - 1 have a cycle length of about 2.1 x [10.sup.9].