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Hiren patel (hkp4027) Ujjval patel (ujp4126)

Network Flow. Hiren patel (hkp4027) Ujjval patel (ujp4126). Problem Defination:. Implement the Ford-Fulkerson algorithm for computing network flow in bipartite graphs. Ford Fulkerson Algorithm. Initialize flow f to 0 While there exists an augment path p

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Hiren patel (hkp4027) Ujjval patel (ujp4126)

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  1. Network Flow Hiren patel (hkp4027) Ujjval patel (ujp4126)

  2. Problem Defination: Implement the Ford-Fulkerson algorithm for computing network flow in bipartite graphs.

  3. Ford Fulkerson Algorithm Initialize flow f to 0 While there exists an augment path p do augmant flow f along path p Return f

  4. Maximum Bipartite Matching Given two sets of vertices Group1 and Group2 , And edges between the nodes of Group1 to nodes of Group2, find the matching with maximum cardinality. How ford fulkerson algorithm can be used in matching problem?

  5. Implementation • PLATFORM : Microsoft windows 9x,NT,2000 • PROGAMMAING LANGUAGE : Visual C++ .NET • PROGRAMMING TOOL : Microsoft Visual Studio .NET 2003 • Code implemented woks in two modes: Ford Fulkerson mode Bipartite mode

  6. DFS Algorithm is used for finding a source to sink path. • Data structures used: Adjacency matrix representation for the graph. bInput : N by N Boolean array to store graph. iCapacity = N by N int32 array to store capacities of edges. iFlow = N by N int32 array to store flow from the edges. All data structures used are instantiateddynamically .

  7. Analysis • Running Time Analysis: O (E * |f*|) , where f* is the maximum flow and E is no of edges in network. • Space Complexity: O (N * N), where N is the number of nodes in the graph.

  8. Performance of the Ford Fulkerson over different inputs.

  9. Performance of the Max. Bipartite matching over different inputs.

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