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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.
  
cs-312/hw20.5.txt ยท Last modified: 2015/03/08 00:52 by ringger
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