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cs-312:hw20.5 [2015/03/06 23:40] ringger [Question 2] |
cs-312:hw20.5 [2015/03/08 00:52] (current) ringger [Question 2] |
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=== Question 2 === | === Question 2 === | ||

Linear Programming and the Maximum Flow Problem: Consider the directed graph $G=(E,V)$. Without loss of generality, let $s$ be the source vertex and $t$ be the sink vertex in $V$. For each edge $(u,v)\in E$, let $c_{uv}$ denote the capacity of that edge. Now, formulate the '''general''' maximum flow problem (not a specific instance) as a linear programming problem as follows: | Linear Programming and the Maximum Flow Problem: Consider the directed graph $G=(E,V)$. Without loss of generality, let $s$ be the source vertex and $t$ be the sink vertex in $V$. For each edge $(u,v)\in E$, let $c_{uv}$ denote the capacity of that edge. Now, formulate the '''general''' maximum flow problem (not a specific instance) as a linear programming problem as follows: | ||

- | * (a) First, define the variables. | + | * (a) First, define the variables. (I recommend representing the flows through each edge as your variables.) |

* (b) Second, use those variables to formulate all of the necessary elements (i.e., objective function and constraints) of a linear program in algebraic terms. | * (b) Second, use those variables to formulate all of the necessary elements (i.e., objective function and constraints) of a linear program in algebraic terms. | ||