Min cost flow finds the minimum weight of the maximum flow in the network. Use {0,1} capacities to turn it to matching. It can be modified for maximum weight.
http://community.topcoder.com/tc?module=Static&d1=tutorials&d2=minimumCostFlow1
http://community.topcoder.com/tc?module=Static&d1=tutorials&d2=minimumCostFlow2
http://community.topcoder.com/tc?module=Static&d1=tutorials&d2=minimumCostFlow3
Bojan Serafimov
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