memes

Think of the election as a Bus route from source, S, to Target, T. a directed graph G=(V,E), where V is the set of vertices (nodes) and E is the set of edges. Each edge (i,j)∈E has an associated non-negative cost (or length) c~ij~

Let x~ij~​ be a binary variable that equals 1 if edge (i,j) is included in the shortest path, and 0 otherwise.

Minimize ∑​_(i,j)∈E [c~ij~​x~ij~​]

Subject to:

∑_j:(s,j)∈E[x~sj~]−∑_i:(i,s)∈E [x~is~]=1

∑_i:(i,t)∈E [x~it~]−∑_j:(t,j)∈E [x~tj]~=−1

∑_i:(i,k)∈E [x~ik~]−∑_j:(k,j)∈E [x~kj~]=0∀k∈V∖{s,t}

x~ij~∈{0,1}∀(i,j)∈E