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Lecture24 - Today's topics Problem Reductions CSE 421...

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1 CSE 421 Algorithms Richard Anderson Lecture 24 Network Flow Applications Today’s topics Problem Reductions – Undirected Flow to Flow – Bipartite Matching – Disjoint Path Problem • Circulations Lowerbound constraints on flows Survey design Problem Reduction Reduce Problem A to Problem B – Convert an instance of Problem A to an instance Problem B – Use a solution of Problem B to get a solution to Problem A • Practical – Use a program for Problem B to solve Problem A • Theoretical – Show that Problem B is at least as hard as Problem A Problem Reduction Examples Reduce the problem of finding the Maximum of a set of integers to finding the Minimum of a set of integers Find the maximum of: 8, -3, 2, 12, 1, -6 Construct an equivalent minimization problem Undirected Network Flow Undirected graph with edge capacities Flow may go either direction along the edges (subject to the capacity constraints) u s t v 10 10 5 20 20 Construct an equivalent flow problem

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Lecture24 - Today's topics Problem Reductions CSE 421...

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