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Lecture25 - Today's topics CSE 421 Algorithms Richard...

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1 CSE 421 Algorithms Richard Anderson Lecture 25 Open Pit Mining Today’s topics Open Pit Mining Problem Task Selection Problem Reduction to Min Cut problem S, T is a cut if S, T is a partition of the vertices with s in S and t in T The capacity of an S, T cut is the sum of the capacities of all edges going from S to T Open Pit Mining Each unit of earth has a profit (possibly negative) Getting to the ore below the surface requires removing the dirt above Test drilling gives reasonable estimates of costs Plan an optimal mining operation Mine Graph -3 -10 -4 3 -2 -3 -1 8 -2 4 3 -1 -7 -10 -1 Determine an optimal mine -10 -10 -10 -10 -10 -5 -1 -10 -10 -10 -10 -3 -3 4 6 -10 -10 -4 -3 7 8 1 -10 -4 3 -2 6 4 -10 2 4 -10 -3 4 -10 -4 4 3 -10 -10 -10 3 -3 -10 -10 -10 -10 -1 -10 -10 -10 -10 -10 -7 Generalization Precedence graph G=(V,E) Each v in V has a profit p(v) A set F if feasible if when w in F, and (v,w) in E, then v in F. Find a feasible set to maximize the profit 5 -10 6 -1 -2 -3 4 -4
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2 Min cut algorithm for profit maximization
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