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Re: [igraph] help with cohesion.blocks (again...)
|
From: |
uxzmdlj02 |
|
Subject: |
Re: [igraph] help with cohesion.blocks (again...) |
|
Date: |
Fri, 1 Feb 2008 12:30:53 -0600 |
Hi,
I did some research into alternate cutset-finding algorithms and found
this one from 1995:
C. Patvardhan, V. C. Prasad, and V. P. Pyara. Vertex cutsets of
undirected graphs. Reliability, IEEE
Transactions on, 44(2):347–353, June 1995.
The article presents an algorithm for finding all minimal vertex
cutsets, not minimum-size cutsets, so it will return cutsets of size 3
for a two-cohesive graph as long as no subset of that cutset is also a
cutset. I went ahead and implemented it, simply ignoring any cutsets
larger than the size we're looking for. I shoehorned it in to
Kanevsky's algorithm very inefficiently (lots of redundant searching),
but it looks like it goes much much faster, at least on Simone's
dataset (about 3 seconds for full cohesive blocks!). I'll include the
code here so others can use it, and I'll try to get rid of the
redundancy and it use it in the official function itself. I'll do some
testing, but I suspect that it will be much faster on smaller graphs
with high edge density but might be slower on larger, sparser
networks. We'll see.
In any case here's the code. The funciton kCutsets2() is a replacement
for kCutsets, and sets up and calls the two other functions (one
wrapper, one recursive).
kCutsets2 <- function(g, k=NULL, cl=NULL,
verbose=igraph.par("verbose")){
if(!is.igraph(g)){
stop("g must be an igraph object")
}
if(is.directed(g)) g <- as.undirected(g)
res <- list()
if(is.null(k)){
if(!is.connected(g)){
k <- 0
}else if(min(degree(g))<=1){
k <- 1
} else {
k <- vertex.connectivity(g)
}
}
## quick and simple cases
if(k==0 || vcount(g) <=2) return(list(numeric()))
if(k==1){ # for 1-connected graphs
return(articulation.points(g))
}
## begin algorithm
v <- as.numeric(V(g))
K <- v[order(degree(g), decreasing=TRUE)][1:k] #2a
if(is.cutset(K, g)) res <- c(res, list(K))
for(i in K){
for(j in setdiff(v,K)){
if(!(j %in% unlist(neighborhood(g,1,i))) &&
vertex.connectivity(g,i,j)==k){
if(verbose) cat(i,j,";")
minCutSets <- findAllMinimalCutsetsST(g,i,j)
res <- c(res,minCutSets[lapply(minCutSets,length)==k])
}
}
}
if(verbose) cat("\n")
return(unique(lapply(res,sort)))
}
findAllMinimalCutsetsST <- function(g,s,t){
findAllMinimalCutsetsST.recurse(g,s,t,t,list())
}
findAllMinimalCutsetsST.recurse <- function(g,Vs,T,t,res){
## Direct implementation of Algorithm from Patvardhan et al (1995)
#1. Vx set of all vertices adjacent to S but not in S
Vx <- setdiff(unique(unlist(neighborhood(g,1,Vs))),Vs)
#2. If t is in Vx, stop
if(t %in% Vx) return(res)
#3. get component of G-Vx containing T
Vt <- unlist(neighborhood(delete.edges(g,E(g)
[from(Vx)]),vcount(g),t))
#4. Create Z subset of Vx not adjacent to Vt
Z <- setdiff(Vx,unlist(neighborhood(g,1,Vt)))
#5. If Z intersects T then stop
if(any(T %in% Z)) return(res)
#6. Grow Vs
Vs <- union(Vs,Z)
#7. Create Vc
Vc <- setdiff(Vx,Z)
#8. Output Vc
res <- c(res,list(Vc))
#9. Create Tprime
Tprime <- numeric()
#10. Begin loop
while(length(setdiff(Vc,Tprime))>0){
#11. Remove some v in Vc but not in Tprime
v <- setdiff(Vc,Tprime)[1]
#12. Recurse
res <-
findAllMinimalCutsetsST.recurse(g,c(Vs,v),c(T,Tprime),t,res)
#13. Grow Tprime
Tprime <- c(Tprime,v)
}
res
}
On Jan 30, 2008, at 4:39 PM, uxzmdlj02-at-sneakemail.com |igraph-help|
wrote:
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
9 11 1 c blue
9 14 1 c blue
37 10 1 c blue
37 27 1 c blue
37 24 1 c blue
37 5 1 c blue
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27 5 1 c red
27 26 1 c red
27 37 1 c red
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
29 15 1 c red
29 10 1 c red
29 33 1 c red
29 27 1 c red
32 26 1 c red
32 15 1 c red
32 39 1 c red
32 27 1 c red
32 14 1 c red
32 10 1 c red
33 27 1 c red
33 29 1 c red
33 26 1 c red
37 5 1 c red
37 27 1 c red
37 26 1 c red
37 40 1 c red
39 32 1 c red
39 16 1 c red
39 29 1 c red
39 14 1 c red
39 15 1 c red
39 26 1 c red
39 27 1 c red
39 10 1 c red
40 5 1 c red
40 27 1 c red
40 26 1 c red
40 15 1 c red
40 37 1 c red
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Csardi Gabor <address@hidden> UNIL DGM
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- Re: [igraph] help with cohesion.blocks (again...),
uxzmdlj02 <=
- Re: [igraph] help with cohesion.blocks (again...), Gabor Csardi, 2008/02/02
- Re: [igraph] help with cohesion.blocks (again...), Gabor Csardi, 2008/02/02
- Re: [igraph] help with cohesion.blocks (again...), uxzmdlj02, 2008/02/02
- Re: [igraph] help with cohesion.blocks (again...), Simone Gabbriellini, 2008/02/04
- Re: [igraph] help with cohesion.blocks (again...), Gabor Csardi, 2008/02/04
- Re: [igraph] help with cohesion.blocks (again...), Gabor Csardi, 2008/02/05
- Re: [igraph] help with cohesion.blocks (again...), Simone Gabbriellini, 2008/02/05