1
15.082 and 6.855J
The Successive Shortest Path Algorithm
and the Capacity Scaling Algorithm
for the Minimum Cost Flow Problem

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2
Pseudo-Flows
A
pseudo-flow
is a "flow" vector x
such that
0
≤
x
≤
u.
Let e(i) denote the
excess
(deficit) at node i.
The
infeasiblity
of the pseudo-flow
is
∑
e(i)>0
e(i).

3
Supplies/Demands, Capacities, and Flows
1
2
3
5
4
10,
5
5
-2
20,
0
25,
13
20,
20
30,
3
23
What is e(i) for
each node i?
What is the
infeasibility of
the flow?
20,
0
25,
0
-7
-19