The Parsimonious Property of Cut Covering Problems And Its Applications

Cover The Parsimonious Property of Cut Covering Problems And Its Applications
The Parsimonious Property of Cut Covering Problems And Its Applications
Dimitris Bertsimas
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Proof : For the purpose of contradiction we assume the contrary. Therefore, there exists a coimter- example on the least number of nodes, with / proper and c integral. We may further assume that 5Ze€£;'^(^) 's minimal.
Suppose there is a u with f{v) = 0. Let /' denote the restriction of f on V \ {v} . It can easily be checked that /' is still proper. By the minimallity of the counter-example, Since the optimal solution in /P/'(0) is also feasible in /P/(0), /^/(0)

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