The successive shortest path algorithm selects in each iteration the cheapest path in the current network.

What does the cheapest path mean in the minimum cost flow problem? How do we select the paths in each iteration (what is the maths)?

Trace the execution of the first and second iterations of the successive shortest path algorithm on this instance of the minimum-cost flow problem. Assume that whenever there is a choice of nodes, the smallest node in the lexicographical order is selected. (For example, pl before p2.) Show the paths selected in the first and second iterations. Show also the flow on the edges of the network at the end of the second iteration. pl/m1 rl/m1 (80,5) pl (60, 50) (90, 0) r1 (90, 6) pl/m2 rl/m2 +70 (80,5) (70, 40) (70, 0) -100 (80, 6) (60, 5) p2/m1 r2/m1 p2 (80, 45) (70, 0) (60,5) r2 (50, 5) +120 (90, 40) -90 (40, 0) (80, 7) p2/m2 r2/m2 Trace the execution of the first and second iterations of the successive shortest path algorithm on this instance of the minimum-cost flow problem. Assume that whenever there is a choice of nodes, the smallest node in the lexicographical order is selected. (For example, pl before p2.) Show the paths selected in the first and second iterations. Show also the flow on the edges of the network at the end of the second iteration. pl/m1 rl/m1 (80,5) pl (60, 50) (90, 0) r1 (90, 6) pl/m2 rl/m2 +70 (80,5) (70, 40) (70, 0) -100 (80, 6) (60, 5) p2/m1 r2/m1 p2 (80, 45) (70, 0) (60,5) r2 (50, 5) +120 (90, 40) -90 (40, 0) (80, 7) p2/m2 r2/m2