Information-theoretic Compression of Weighted Graphs

Set Partitioning Problem (SPP): I given a ground set Ω = {x1, . . . , xn}, I a collection of admissible subsets P = {X1, . . . ,Xm} ⊆ 2, I a cost function c : P → R, I find a partition X of Ω using subsets in P and minimising the sum of the costs minX ∑ X∈X c(X ). Complete SPP (CSPP): I All subsets are admissible: P = 2 Bidimensional Complete SPP (CSPP×CSPP): I The ground set is a Cartesian product: Ω = Ω1 × Ω2 I Admissible subsets are all Cartesian products: P = 21 × 22 I In our case: Ω1 = Ω2 = VG , X = E , and c(V1,V2) = comp(V1,V2) + β loss(V1,V2) (see on the right) Optimisation Algorithm: Dynamic programming algorithm (branching, recursion, memoization, non-redundancy) https://github.com/Lamarche-Perrin/optimal_partition