Parametric analysis on cut-trees and its application on a protein clustering problem

Abstract

Computing the maximum flow value between a pair of nodes in a given network is a classic problem in the context of network flows. Its extension, namely, the multi-terminal maximum flow problem, comprises finding the maximum flow values between all pairs of nodes in a given undirected network. In this work, we provide an overview of the recent theory of sensitivity analysis, which examines the influence of a single edge capacity variation on the multi-terminal maximum flows, and we make remarks about extending some theoretical results to the case where more than one edge has their capacities changed. Based on these extensions, we present algorithms to construct the Gomory and Hu cut-trees dynamically, considering capacity variations in more than one edge in the network. Finally, the presented theory is applied on a clustering problem, in the field of biology, in order to improve an existing algorithm that identifies protein complexes in protein–protein interaction networks. In this application, a new result in the sensitivity analysis theory is introduced.