Re: [igraph] help with cohesion.blocks (again...)

[uxzmdlj02]

Hm, I always assumed that using combn and specifying FUN would be  
fastest, like using "apply" funcitons.

I took the graph.antichains algorithm from Kanevsky's article, with  
modification. The goal is to find all antichains in the graph g, where  
an antichain is defined as a set of vertices such that for each pair  
of vertices i and j in the set i is neither a predecessor nor a  
successor of j.
Kanevsky has two algorithms to find antichains, a recursive version (p. 
419) that I do not understand, and a "parallel" version (p.420) that I  
sort of understand. My function is a modified version of his parallel  
algorithm. The difference is that my version is redundant, and relies  
on R's unique() function. This is a problem, but I do not understand  
the enumeration he describes in steps 3 and 4. His algorithm is  
(quoted):
1. Form a transitive closure L^+ of an input network L.
2. Take every vertex as antichain
3. Repeat log(n) times: Find all antichains of the double size using  
antichains of the current size
4. Find all other antichains of all other sizes using at most log(n)  
independent sets of sizes of powers of 2.
5. Find all closed sets in the network using antichains.

Step 3 I'm ok with, but step 4 seems very vague. Instead of doing  
this, my function does not check if the output of step 3 has twice the  
size as the current size. In fact now that I'm looking at this again,  
I'm nervous that my version could miss some antichains if they not a  
subset of one that comes out in step 3.

I've been trying again for the past while to make sense of his  
recursive version to check the consistency, but it is still a mystery.

Do you have a copy of the article, Gabor? Citation is:
A. Kanevsky. On the number of minimum size separating vertex sets in a  
graph and how to find all of them. Proceedings of the 1st ACM-SIAM  
Symposium on Discrete Algorithms, 1:411–21, 1990.

Peter

On Jan 30, 2008, at 3:20 PM, Gabor Csardi csardi-at-rmki.kfki.hu | 
igraph-help| wrote:

> On Wed, Jan 30, 2008 at 03:05:57PM -0600, address@hidden  
> wrote:
> > Hi Simone,
> >
> > I checked out your network, and it is taking a very long time. The
> > hangup is in the graph.antichains() function, which is part of the
> > algorithm for finding all minimal-size cutsets of a graph. Things run
> > quickly with your network until you get to the 7th subgraph with
> > cohesion 14. I don't remember precisely, but the best known algorithm
> > for finding all minimal-size cutsets is around O(k^5) for a k- 
> > cohesive
> > graph. Your network is very dense and has a maximally-cohesive
> > subgraph of over 14.
> >
> > Basically, I don't think it's a bug, I just think that it's a tricky
> > network to run cohesive blocking on. I've run the code on some graphs
> > with aobut 170 nodes, but much less dense than yours, and it has  
> > taken
> > days to finish running parallel on two 2.2Ghz processors. Cohesive
> > blocking is an inherently slow process. (This is one of the reasons
> > that k-cores are more widely used in the network literature: they are
> > trivial to compute and often map very close to cohesive blocks on  
> > real
> > networks.) I've considered rewriting some of the trickier bits of  
> > code
> > in C instead of interpreted R, which would speed things up
> > considerably, but that's a ways down the road if ever.
> >
> > My suggestions for you now are:
> > 1)  try out using the parallel processing options if you have a  
> > multi-
> > core machine or access to an MPI network on multiple computers. Other
> > than that there is not much that can be done.
>
> I don't think that would help much with this graph, you need at  
> least 5Gb
> of memory, and that is a very optimistic guess. The main problem is
> not that graph.antichains() is slow, but that the memory requirements
> are very high. Btw. it can be speeded up easily by not using
> combn() for generating the combination, but something faster, i did
>
> tmp <- get.edgelist(graph.full(acount))+1
>
> which is kind of a hack, and that made it run into the memory limit.
> Peter, can you summarize in five lines what graph.antichains() is
> supposed to do? Just to see if it is worth thinking on a less
> demanding implementation.
>
> Thanks,
> G.
>
>
> > 2) try running the function with verbose output
> > ("cohesive.blocks(mynet,verbose=T)") and see if it's getting hung up
> > on one subgraph for more than a couple of hours or if it's progresing
> > slowly.
> >
> > Sorry I can't be of more help.
> > Peter
> >
> > On Jan 30, 2008, at 5:10 AM, Simone Gabbriellini simone.gabbriellini-
> > at-......... |igraph-help| wrote:
> >
> > > Hello list,
> > >
> > > I am experiencing a problem with cohesion.blocks().. I have 25
> > > multiplex networks, and everything runs ok for almost all of them,  
> > > but
> > > with 6 of them there is a problem: the computation starts but never
> > > ends... I leave the computer calculating the blocks even for 30
> > > minutes, but no result appear..
> > > I have no clue what's happening, I receive no error message from R
> > >
> > > thanks for your help,
> > > simone
> > >
> > > this is one of the "incriminated" network (.net format):
> > >
> > > *Vertices 41
> > > 1 "Aiken"
> > > 2 "Ainon"
> > > 3 "Aniat"
> > > 4 "azor"
> > > 5 "Brenn Tantor"
> > > 6 "Bube"
> > > 7 "Fds"
> > > 8 "Flazzer"
> > > 9 "Frederick Brae"
> > > 10 "Gae"
> > > 11 "ginkobiloba"
> > > 12 "Hunter999"
> > > 13 "Iced"
> > > 14 "ilBestio"
> > > 15 "Klingo"
> > > 16 "Kveldersen"
> > > 17 "Lej"
> > > 18 "Lukenet"
> > > 19 "Madix"
> > > 20 "Manand"
> > > 21 "Marco_Rsr"
> > > 22 "milordz"
> > > 23 "Mondovich"
> > > 24 "Nemi"
> > > 25 "Nimion"
> > > 26 "OrkoPazZo"
> > > 27 "Ouba"
> > > 28 "Pendragon"
> > > 29 "Quill"
> > > 30 "reasae"
> > > 31 "rukwa"
> > > 32 "Sephi"
> > > 33 "Shariz"
> > > 34 "Shin Xaqer"
> > > 35 "Shiny"
> > > 36 "Simus"
> > > 37 "skyline"
> > > 38 "Stryker"
> > > 39 "Sualtan"
> > > 40 "Tremors"
> > > 41 "Yusaku"
> > > *Arcs
> > > 9    10    1    c blue
> > > 9    27    1    c blue
> > > 9    24    1    c blue
> > > 9    5    1    c blue
> > > 9    37    1    c blue
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> > > 27    5    1    c red
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> > > 27    33    1    c red
> > > 27    32    1    c red
> > > 27    10    1    c red
> > > 29    39    1    c red
> > > 29    26    1    c red
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> > > 40    15    1    c red
> > > 40    37    1    c red
> > >
> > >
> > > _______________________________________________
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> >
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> >
> > _______________________________________________
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> Csardi Gabor <address@hidden>    UNIL DGM
>
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