Edge-cuts Optimized for Average Weight: a new alternative to Ford and Fulkerson

02/01/2020

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by   Scott Payne, et al.

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Let G be a directed graph associated with a weight w: E(G) → R^+. For an edge-cut Q of G, the average weight of Q is denoted and defined as w_ave(Q)=∑_e∈ Qw(e)/|Q|. An edge-cut of optimal average weight is an edge-cut Q such that w_ave(Q) is maximum among all edge-cuts (or minimum, symmetrically). In this paper, a polynomial algorithm for this problem is proved for finding such an optimal edge-cut in a rooted tree, separating the root and the set of all leafs. This algorithm enables us to develop an automatic clustering method with more accurate detection of communities embedded in a hierarchy tree structure.