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Friday, June 1, 2001
An optimalisation problem
In my work, I encountered an
optimalisation problem, which can be described as follows:
Given a set E, a set V, and
a function T of E and V to a real number.
Find a mapping M of E to V such that the following
expression is minimal:
Sum { Max { T(e,v)
 e in E and M(e) = v
}
 v in { M(e)  e in E }
}
I thought some time about an algorithm that would
find a mapping meeting the requirement, or at least
one that would come very close. I had some kind of
feeling that this might be a
NPcomplete problem.
After some thinking, I though that I had found a good
algorithm. It looks like this:
 Start with a mapping M_{0} such that:
And { T(e,M_{0}(e)) <= Min { T(e,v)  v in V }
 e in E }
 Given a mapping M_{n} see if there is
a mapping M_{n+1}, that differs for one value of E,
and that is better. If such a mapping exists, repeat this
step.
I thought that this was quite a good algorithm that would
quickly find a (near) optimal solution. And I still think it
does for the problem domain from which it was derived from.
However, this morning, I discovered that it is indeed a
NPcomplete problem. One way of proving that a certain
problem is NPcomplete is by proving that it is a superset
of another NPcomplete problem. I realized that the
problem described here is a superset of the
Minimum Vertex Cover. To show this, I have to proof
that each Minimum Vertex Cover problem can be mapped onto
a problem like the one described here. Now, that is not
so difficult. The Minimum Vertex Cover for a graph G(E,V)
can be mapped on the problem described here, by defining
the function T such that T(e,v) equal to 1 if the vertex
v is on of the end points of the edge e, and otherwise
equal to infinitive. It is obvious that each mapping M
defines the vertex cover { M(e)  e in E }.
The value of the expression that needs to be minimized
equals to the number of elements in the vertex cover.
Finding a mapping for which the value of the expression
is minimal, is thus equivalent with finding the Minimum
Vertex Cover.
The algorithm which I proposed is thus rather useless
in some typical cases. For those typical cases, in both
steps there are just many mappings to choose from.
It might be the case that the algorithm does work good,
if always only one mapping can be chosen in each step.
During the algorithm one can tell something about how
well the algorithm performs based on all the values
for the expression that are found for all mappings that
are being searched.
Monday, June 4, 2001
Andy can bike
Yesterday evening, my mother went
walking with Andy on his treewheeler. She had to push him all the
time, as he refused to do anything himself. We have
been pushing him around for more than a year now.
My father had attached some
shoe holders onto the peddles, such that we could
strap his shoes to the peddles.
Tonight, Annabel came to call
me. LiXia had gone out
walking with Andy. There outside on the street
I saw how Andy could now bike by himself. I looked
as he finally understood what biking is all about.
He was biking around as fast as he could. Of course,
I immediately phoned my mother to tell her the good news.
Friday, June 15, 2001
Sending a video tape
Today, we sent a tape about Andy's
eating behaviour to the "Winckelsteegh"
with a short note. The tape also contained some recordings
made on the daycare center were Andy is going every day,
which really surprised us, because he was eating there
almost without any problems at all, and even cooperating
a little. This really astonished us.
(followup)
Sunday, June 17, 2001
Revival and prosecution
We had some one from Open Doors preaching today.
Open Doors is an organisation that works amongh
the prosecuted church. He reminded us that in
more than 60% of the world Christians are
prosecuted for their faith. That means that we
are living in the small part where we are still
free to practice our religion. This speaker told
how they some years ago told the Christians of
some countries that they should prepare for prosecution,
and that these Christians were simply saying that there
was not going to be any prosecution in their countries.
But the reality is now that they are being prosecuted
in their countries!
He furthermore stated, that also in our country
we could encounter prosecution. That it is a reality
that our government is no longer considering religion
an important issue. And indeed, we are living
in an
atheistic country.
But his most important statement was that church
history has told us that revival and prosecution often
go hand in hand. We should not think that because
every thing is so peacefull in our country, that
God will spare us the prosecution. But maybe He
will also give us a revival at the same time!
(followup)
Pulling out a tooth
Today, Annabel had bumped
against something with her loose tooth.
This evening, when standing in the bathroom, I saw
that the tooth was now indeed very loose, and I told
Annabel to pull it out. She pushed a little, and
indeed her tooth came out.
Wednesday, June 20, 2001
Ear tubes
This morning, I took Andy
to the hospital because he needed new tubes in his
ears. This will be his third set of ear tubes.
Last week his ENT had noticed that one ear did
not have a tube anymore. He did not bother to check
the other ear, because Andy was giving a lot of
trouble. Andy was the first one this morning. When
I brought him into the room, he started to cry,
but soon after the had put the cap over his mouth,
he fell asleep. When he woke up, he was quite
confused, and wanted me to scratch his neck and
back. He often wants us to scratch him there, so
it was nothing strange in itself. But he kept on
complaining. Only when the brought in the next
child, he suddenly watched her with interest, and
he became quiet. Not much later we went home.
I also got a box with the old ear tube that was still
present in the other ear.
This afternoon, I found a note with the first
hunderd digits of pi. I told my colleagues that
I had learned them by heart before,
and that it was not so difficult at all. I told them
I could learn them by heart again in ten minutes. I did
this while I walked to the restrooms. And indeed
I only made three mistakes when I wrote them down
ten minutes later.
Tuesday, June 26, 2001
Power failure
Around 11:34 in the morning, we had a very short power dip,
enough to make all computers and file servers to reboot.
Around a quarter past twelve, it was announced that it would
still take several ours before one of hour major file servers
will be available again.
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