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#
# Reference:
# A hypergraph model for the yeast protein complex network
# By E. Ramadan, A. Tarafdar, A. Pothen
# Procs. Workshop High Performance Computational Biology, IEEE/ACM 2004
#
# algorithm for computing the k-core of a hypergraph:
# ===================================================
#
# while there are vertices with degree < k do
# {
# for each such vertex v do
# {
# for each hyperedge f associated with v do
# {
# delet v from adj(f)
# decrement d(f) by 1
# if f is non-maximal then
# {
# for each vertex w associated with f do
# {
# delete f from adj(w)
# decrement d(w) by 1
# if ( d(w) < k then
# {
# include w in list of vertices with degree < k
# }
# }
# }
# }
# }
# }
#
kCoresHypergraph <- function(hg)
{
nv <- numNodes(hg)
core <- array(0, nv, dimnames = list(nodes(hg)))
im <- inciMat(hg)
ne <- ncol(im)
v_deg <- sort(rowSums(im))
k_num <- 0
for ( i in 1:nv )
{
v <- names(v_deg)[i]
k_num <- max(v_deg[v], k_num)
core[v] <- k_num
# v's hyperedges
he_set <- which(im[v,] == 1)
im[v, he_set] <- 0
# remove non-maximal hyperedges
# (1) selective approach
for ( f in names(he_set) )
{
# hyperedges adjacent to f
r_chosen <- which(im[, f] == 1)
c_chosen <- which(im[r_chosen, ] > 0)
im_sub <- matrix(im[r_chosen, c_chosen], nrow=length(r_chosen), ncol=length(c_chosen))
rownames(im_sub) <- names(r_chosen)
colnames(im_sub) <- names(c_chosen)
for ( g in names(c_chosen) )
if ( f != g && im_sub[, f] == im_sub[, g] )
{
im[, f] <- 0
}
}
v_deg <- sort(rowSums(im))
## # (2) brute-force approach
## for ( f in he_set )
## {
## for ( g in 1:ne )
## if ( f != g && sum(im[, f] & im[, g]) == sum(im[, f]) )
## {
## im[, f] <- 0
## }
## }
## v_deg <- sort(rowSums(im))
}
core
}
#
# greedy algorithm for computing an approximate minimum weight vertex
# cover of a hypergraph
# ===================================================================
#
# F[i] is the set of hy[eredges not yet covered by a partial vertex cover
# at the begining of the i-th iteration
#
# cost function alpha(v) = w(v) / | adj(v) intersect F[i] |
# which distributes the weight of the vertex equally among the hyperedges
# it belongs to that are currently uncovered.
#
# at each step, it chooses a vertex with minimum cost alpha(v) to include
# in the partial cover, deletes all hyperedges it covers
#
# initialize:
# i = 1; // iteration number
# C = 0; // cover
# F[1] = F;
# // hyperedges yet to be covered
# while F[i] != 0 do
# {
# for ( v in V - C ) do
# {
# choose a vectex v[i] with min cost alpha(v);
# add v[i] to the cover C;
# F[i+1] = F[i] - adj(v[i]);
# i = i+1;
# }
# }
#
vCoverHypergraph <- function(hg, vW=rep(1, numNodes(hg)))
{
V <- nodes(hg)
im <- inciMat(hg)
names(vW) <- V
deg <- rowSums(im)
C <- names(which(deg == 0))
F <- setdiff(V, C)
while ( length(F) > 1 )
{
# choose a vectex v[i] with min cost alpha(v)
deg <- rowSums(im)
vW_cur <- vW / deg
v <- names(which.min(vW_cur))
C <- c(C, v)
adj_he <- names(which(im[v,] == 1))
im[v, ] <- 0
im[, adj_he] <- 0
r_chosen <- names(which(rowSums(im) > 0))
c_chosen <- names(which(colSums(im) > 0))
im <- im[r_chosen, c_chosen, drop = FALSE]
vW <- vW[r_chosen]
F <- r_chosen
}
C
}
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