
Graph of NP-Complete Problems - imgabe
http://page.mi.fu-berlin.de/aneumann/npc.html
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wozer
I was wondering what the arrows actually mean. Turns out A->B means that A can
be reduced to B (using a "polynomial-time many-one reduction"). So if we
assume that B is NP-complete, A is too.

So it all boils down to showing that Circuit Satisfiability is NP-complete. I
guess this graph shows the order in which the reductions were actually done
for the first time. When I was at college, we reduced everthing to 3-SAT and
directly proved that 3-SAT is NP-complete, I think.

~~~
mariorz
_> Turns out A->B means that A can be reduced to B (using a "polynomial-time
many-one reduction"). So if we assume that B is NP-complete, A is too._

It's the other way around. For a given problem to be NP-complete requires that
every problem in the NP superset be reducible to it in polynomial time. So in
the A->B case, if we know A to be NP-complete, we have just proved every
problem in NP is also reducible to B in polynomial time, by ways of any-NP-
problem->A->B, ergo B is NP-complete.

~~~
jacobscott
A well known quote (in the right circles):

"Real men reduce from 3SAT" -- Christos Papadimitriou
[<http://www.cs.berkeley.edu/~christos/>]

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andreyf
For those wondering:

 _dot - makes ``hierarchical'' or layered drawings of directed graphs. The
layout algorithm aims edges in the same direction (top to bottom, or left to
right) and then attempts to avoid edge crossings and reduce edge length._

 _neato and fdp - make ``spring model'' layouts. neato uses the Kamada-Kawai
algorithm, which is equivalent to statistical multi-dimensional scaling. fdp
implements the Fruchterman-Reingold heuristic including a multigrid solver
that handles larger graphs and clustered undirected graphs._

source: <http://www.graphviz.org/>

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randomwalker
I'm not entirely sure I see the value of this. Note that it doesn't tell us
much about the state of the world, but rather more about the historical order
in which these problems were inducted into the NP-completeness club. And by
the time enough data points have been added to the picture to cover a
meaningful fraction of the NP-complete problems that have been studied, will
it even be possible to make sense of the humongous graph?

There are meaningful distinctions within NP-complete problems, such as whether
they are easy to approximate. Perhaps if the graph incorporated that
information, I can see this going somewhere..

~~~
Shamiq
It is incredibly useful for us kids just now learning about algorithms and
trying to see if the problem described in the text book is reducible to a
known NPC problem.

