Gomory-Hu trees

Tomaž Šetina (2018) Gomory-Hu trees. EngD thesis.

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Abstract

The classical Ford-Fulkerson algorithm computes a maximum u-v flow and a minimum u-v cut between two selected nodes u, v from flow network - weighted graph. In this thesis we study Gomory-Hu trees which in one tree structure include information about all minimum in the graph. More precisely computing a minimum cut between a pair of nodes u and v nodes in flow network can be reduced to searching for an edge with smallest capacity in the unique u-v path in the Gomory-Hu tree. We implement and evaluate Gusfield algorithm for computing Gomory-Hu tree. The presented algorithm for computing Gomory-Hu trees has relatively high time complexity, so we also implement an algorithm for dinamically computing Gomory-Hu trees following a capacity change in the graph. It turns out that in the case of increasing capacity the dynamic approach outperforms the basic algorithm. However, we measure no substantial improvement in the case of reducing capacity of an edge.

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