From: Peter R <peter_r@gmx.com>
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Message-Id: <32D6AD7B-5EA2-4FC3-AB5A-A43C7482F2F9@gmx.com>
Date: Sun, 30 Aug 2015 10:00:37 -0700
To: "bitcoin-dev@lists.linuxfoundation.org Dev"
	<bitcoin-dev@lists.linuxfoundation.org>
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Subject: [bitcoin-dev]  Unlimited Max Blocksize (reprise)
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Hello Tom, Daniele --

Thank you Tom for pointing out the knapsack problem to all of us.  I =
will include a note about it when I make the other corrections to the =
Fee Market paper.

I agree with what Daniele said previously.  The other "non-greedy" =
solutions to the knapsack problem are most relevant when one is choosing =
from a smaller number of items where certain items have a size similar =
to the size of the knapsack itself.  For example, these other solutions =
would be useful if transactions were often 50 kB, 100 kB, 400 kB in =
size, and we were trying to find the optimal TX set to fit into a 1 MB =
block. =20

However, since the average transaction size is ~500 bytes, even with a =
block size limit of 1 MB, we are looking at up to 2000 transactions.  =
The quantization effects become small.  Rather than 22 triangles as =
shown in Fig. 3 (http://imgur.com/rWxZddg), there are hundreds or a few =
thousands, and we can reasonably approximate the discrete set of points =
as a continuous curve.  Like Daniele pointed out, the greedy algorithm =
assumed in the paper is asymptotically optimal in such a case.

Best regards,
Peter=

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<html><head><meta http-equiv=3D"Content-Type" content=3D"text/html =
charset=3Dus-ascii"></head><body style=3D"word-wrap: break-word; =
-webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">Hello =
Tom, Daniele --<div><br></div><div>Thank you Tom for pointing out the =
knapsack problem to all of us. &nbsp;I will include a note about it when =
I make the other corrections to the Fee Market =
paper.</div><div><br></div><div>I agree with what Daniele said =
previously. &nbsp;The other "non-greedy" solutions to the knapsack =
problem are most relevant when one is choosing from a smaller number of =
items where certain items have a size similar to the size of the =
knapsack itself. &nbsp;For example, these other solutions would be =
useful if transactions were often 50 kB, 100 kB, 400 kB in size, and we =
were trying to find the optimal TX set to fit into a 1 MB block. =
&nbsp;<div><br></div><div>However, since the average transaction size is =
~500 bytes, even with a block size limit of 1 MB, we are looking at up =
to 2000 transactions. &nbsp;The quantization effects become small. =
&nbsp;Rather than 22 triangles as shown in Fig. 3 (<a =
href=3D"http://imgur.com/rWxZddg">http://imgur.com/rWxZddg</a>), there =
are hundreds or a few thousands, and we can reasonably approximate the =
discrete set of points as a continuous curve. &nbsp;Like Daniele pointed =
out, the greedy algorithm assumed in the paper is asymptotically optimal =
in such a case.</div><div><br></div><div>Best =
regards,</div><div>Peter</div></div></body></html>=

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