BOUNCE discussion@mcqmc.org: Admin request: /^subject:\s*help\b/i

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• Date: Tue, 31 Aug 1999 18:13:20 +0800 (HKT)
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From: "Simin He" <hsm@cti.com.cn>
To: <discussion@www.mcqmc.org>
Subject: Help: some questions 
Date: Tue, 31 Aug 1999 18:02:46 +0800
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Hi,

I have read a survey on derandomization in
computaional geometry. It seems that derandomiztion in geometry is more
different from than similar to quasi-monte carlo method. May I list some for
your confirmation:
(0) These two approaches are similar in that they both want to get rid of
the randomness inside the algorithm.
(1) Quasi Monte Carlo approach is to seek BETTER results than purely random
algorithm, but derandomization is to reach the SAME result of randomized
algorithm by a derterministic one.
(2) Quasi Monte Carlo approach can be understood directly or
intuitionistic, while derandomized algorithms can be hardly understood
without appealing to their underlying randomized counterpart, as you
mentioned in the paper.
(3) Quasi Monte Carlo approach are mainly based on number-theoretic
construction, while dedandomization is based on quite different yet more
approaches.

Are these assertions true? Please tell me if they are in fact irrelevant  to
each other?

I am more interested in QMC method at present, I have some further
questions:
(1) It seems that  discrepancy=sup|.| is popular. I know there are other
measures of uniformity of a point set, such as dispersion=max.min.d(.).
Which is the best from the viewpoint of theretic property, easiness to
construct, easiness to compute, symmetry? When possible, it seems that
points by orthogonal design is the best. How do you think of them?
(2) Besides numerical integration, any other applications? Optimization? Can
you mention a few concrete examples? How if the dimension is too large?
(3) It seems to me that discrepancy is not symmetric, and can not be
extended to discrete domain, e.g. to construct a uniform point set of K
points in a space of {0,1}^N. ?

Sorry to ask so many questions. I wish I did not bother you too much.

Yours,

Simin He





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