Figure 2

Solving the maximum likelihood ILP via graph decomposition. (a) Graph decomposition into 2-connected components: Red (1-cut) node splits the graph into two 2-connected components A and B. The ILP is solved for each component separately. If the direction of the cut node in the ILP solution for B is opposite to the one in the solution for A, then the solution of B is inverted. Then ILP solutions for A and B are collapsed into the parent solution. (b) Graph decomposition into two 3-connected components: Red and yellow (2-cut) nodes split the graph into two 3-connected components A and B. The ILP is solved for component A twice - for the same and the opposite directions assigned to two 2-cut nodes. Then these two solutions are used in the objective for the ILP of component B. Finally, ILP solutions for A and B are collapsed into the parent solution.