[igraph] Longest path in weighted DAG

[Ananya Muddukrishna]

Hi,

I have implemented longest path calculation of a weighted DAG using R 
igraph.

My implementation shown below is slow for large graphs.

I would greatly appreciate any hints to speed it up. Any thoughts on how 
far my implementation is from the best known/typical algorithm is also 
welcome.

Thanks!

# g is the igraph DAG
# g <- graph.tree(10000, 2, mode="out")
# E(g)$weight <- round(runif(length(E(g))),2) * 50
# Topological sort
tsg <- topological.sort(g)
# Set root path attributes
# Root distance
V(g)[tsg[1]]$rdist <- 0
# Path to root
V(g)[tsg[1]]$rpath <- tsg[1]
# Get longest path from root to every node
for(node in tsg[-1])
{
  # Get distance from node's predecessors
  w <- E(g)[to(node)]$weight
  # Get distance from root to node's predecessors
  d <- V(g)[nei(node,mode="in")]$rdist
  # Add distances (assuming one-one corr.)
  wd <- w+d
  # Set node's distance from root to max of added distances
  mwd <- max(wd)
  V(g)[node]$rdist <- mwd
  # Set node's path from root to path of max of added distances
  mwdn <- as.vector(V(g)[nei(node,mode="in")])[match(mwd,wd)]
  V(g)[node]$rpath <- list(c(unlist(V(g)[mwdn]$rpath), node))
}
# Longest path length is the largest distance from root
lpl <- max(V(g)$rdist)
# Enumerate longest path
lpm <- unlist(V(g)[match(lpl,V(g)$rdist)]$rpath)
V(g)$critical <- 0
g <- set.vertex.attribute(g, name="critical", index=lpm, value=1)

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Best regards,
Ananya

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Ananya Muddukrishna
Ph.D. student
KTH Royal Institute of Technology
http://www.kth.se/profile/ananya/