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Network flow balancing constraint in R


Network flow balancing constraint in R

By : user2175488
Date : October 15 2020, 08:10 AM
should help you out Here's an example of minimum cost flow using igraph and Rsymphony with sparse matrix (slam package) :
Given this input :
code :
library(igraph)
nodes <- data.frame(name=paste0("N",1:8),
                    supply=c(10,20,0,-5,0,0,-15,-10))

edges <- data.frame(nodefrom = paste0("N",c( 1, 2, 2, 2, 3, 3, 4, 5, 5, 6, 7)),
                    nodeto   = paste0("N",c( 4, 1, 3, 6, 4, 5, 7, 6, 7, 8, 8)),
                    cost     = c( 2, 1, 0, 6, 1, 4, 5, 2, 7, 8, 9),
                    capacity = c(15,10,10,10, 5,10,10,20,15,10,15),
                    name     = paste0("E",1:11))
G <- graph.data.frame(edges)
V(G)$supply <- nodes$supply[match(V(G)$name,nodes$name)]
# plot the graph
set.seed(3)
par(mar=c(0,0,0,0))
plot(G, vertex.size=30,
     vertex.label=paste0(V(G)$name,' (',V(G)$supply,')'),
     vertex.color='lightblue', edge.arrow.size=0.5,
     edge.label=paste0(E(G)$name,' (',E(G)$cost,',',E(G)$capacity,')')
     )
library(Rsymphony)
library(slam)

nVars <- ecount(G)
obj <- E(G)$cost
bounds <- list(upper=list(1:nVars,E(G)$capacity),lower=list(1:nVars,rep(0,nVars)))
types <- rep('C',ecount(G))

mat <- simple_triplet_zero_matrix(nrow=nrow(nodes),ncol=nrow(edges))
colnames(mat) <- E(G)$name
rownames(mat) <- V(G)$name
rhs <- -V(G)$supply
dir <- rep('==',vcount(G))
for(v in V(G)){
  outEdges <- E(G)[from(v)]$name
  inEdges <- E(G)[to(v)]$name
  mat[v,match(inEdges,colnames(mat))] <- 1
  mat[v,match(outEdges,colnames(mat))] <- -1
}

output <- Rsymphony_solve_LP(obj=obj,
                   mat=mat,
                   dir=dir,
                   rhs=rhs,
                   bounds=bounds,
                   types=types,
                   max=FALSE,
                   write_lp = TRUE)

# plot the solution
set.seed(3)
par(mar=c(0,0,0,0))
plot(G, vertex.size=30,
     vertex.label=paste0(V(G)$name,' (',V(G)$supply,')'),
     vertex.color='lightblue', edge.arrow.size=0.5,
     edge.label=paste0(E(G)$name,' flow = ',output$solution))


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How do I stop network flooding using Windows 2003 Network Load balancing?

How do I stop network flooding using Windows 2003 Network Load balancing?


By : thomas
Date : March 29 2020, 07:55 AM
Any of those help If you can find an old "dumb" hub, you can run the node NIC's through it, or if your switch is managable you can set the ports up so that they do not remember the MAC address to IP address mappings.
I will say that I have had horrible experience with WLBS (the 2003+ version of NLB) in regards to port flooding. We have an existing load balanced system where we have the load balanced NIC's going into a VLAN to keep the traffic separate and we've turned off the MAC address to IP mapping in order to reduce the problem. We are migrating the load balancing off of WLBS; however, due to the reliability of this configuration.
SSIS Control Flow - set a precedent constraint on entire group of Data Flow tasks

SSIS Control Flow - set a precedent constraint on entire group of Data Flow tasks


By : user2606988
Date : March 29 2020, 07:55 AM
To fix the issue you can do You can take advantage of a Sequence Container. Add a Sequence container to your task flow. Then move (drag and drop will do it) all of your data flow tasks into the container. Now you can create a single precedence constraint from your Execute SQL Task to the Sequence container. Everything in the Sequence Container will not execute until the rules of the Precedence Constraint are met.
How To Convert A Pre-Flow Push Network With Excess Flow To A Flow Network

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By : duwolfde
Date : March 29 2020, 07:55 AM
may help you . If you really need the max flow (it's possible to derive a min cut directly from the preflow and use it to verify the preflow), then I know of two approaches.
The first approach is covered in the original Goldberg--Tarjan paper on the push relabel algorithm. In essence, the second phase is implemented almost exactly as the first. The only difference is that the source is held at distance n (instead of the sink, at distance 0). This has the effect of routing the excesses back to the source.
How to apply Ford-Fulkerson algorithm to a graph to find maximum flow in a flow network?

How to apply Ford-Fulkerson algorithm to a graph to find maximum flow in a flow network?


By : João Costa
Date : March 29 2020, 07:55 AM
To fix this issue Best I know ( link ), wikipedia ( link ) and first alternative Google hit ( Link ).
Ford-Fulkerson Labeling Algorithm (Initialization) Let x be an initial feasible flow (e.g. x(e) = 0 for all e in E). (Flow augmentation) If there are no augmenting path from s to t on the residual network, then stop. The present x is a max flow. If there is a flow augmenting path p, replace the flow x as 2. x(e)=x(e)+delta if e is a forward arc on p. x(e)=x(e)-delta if e is a backward arc on p. where delta is a minimum value of residual capacity on p. Repeat this step.
Flow network with source S and sink T, How to find maximal flow between any 2 vertex?

Flow network with source S and sink T, How to find maximal flow between any 2 vertex?


By : Tarovk
Date : March 29 2020, 07:55 AM
To fix the issue you can do The problem you are facing is called maximal flow algorithm and it has multiple solutions, and all of them are polynomial.
You could use Ford–Fulkerson algorithm,because it is easy to understand and as you can see wiki page have all the things you want about this algorithm.
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