Sol3 - AMS/MBA 546(Fall 2010 Estie Arkin Network Flows Solution sketch to homework set 3 1 Recall the weighted max acyclic subgraph problem Given a

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Unformatted text preview: AMS/MBA 546 (Fall, 2010) Estie Arkin Network Flows: Solution sketch to homework set # 3 1). Recall the weighted max acyclic subgraph problem : Given a directed graph D = ( N,A ), with weights on the arcs w ij ≥ 0, find a subset of the arcs a ′ ⊂ A such that D ′ = ( N,A ′ ) is acyclic, and the weight of A ′ , w ( A ′ ), is as large as possible. Consider the following greedy algorithm: Sort the arcs by weight, from largest to smallest, consider the arcs in this order, and insert an arc into A ′ as long as it does not create a directed cycle with the arcs already in A ′ . (At the start A ′ is empty.) Clearly this algorithm yields a feasible solution, however, the weight of A ′ can be much less than opt , the weight of an optimal solution. Describe a family of directed graphs for which w ( A ′ ) /opt ≤ c/n , where c is some constant (that does not depend on n ) and n is the number of nodes in your graph....
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This note was uploaded on 01/31/2011 for the course AMS 546 taught by Professor Arkin,e during the Fall '08 term at SUNY Stony Brook.

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