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Edge-Cuts of Optimal Average Weights

Author

Listed:
  • Scott Payne

    (Department of Mathematics, West Virginia University, Morgantown, WV 28506, USA)

  • Edgar Fuller

    (Department of Mathematics, Florida International University, Miami, FL 33199, USA)

  • Cun-Quan Zhang

    (Department of Mathematics, West Virginia University, Morgantown, WV 28506, USA)

Abstract

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 wave(Q) = ∑e∈Qw(e) |Q|. An optimal edge-cut with average weight is an edge-cut Q such that wave(Q) is maximum among all edge-cuts (or minimum, symmetrically). In this paper, a polynomial algorithm for this problem is proposed for finding 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 community output.

Suggested Citation

  • Scott Payne & Edgar Fuller & Cun-Quan Zhang, 2019. "Edge-Cuts of Optimal Average Weights," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(02), pages 1-9, April.
    • Handle: RePEc:wsi:apjorx:v:36:y:2019:i:02:n:s0217595919400062
    DOI: 10.1142/S0217595919400062
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    Cited by:

    1. Payne, Scott & Fuller, Edgar & Spirou, George & Zhang, Cun-Quan, 2022. "Automatic Quasi-Clique Merger Algorithm — A hierarchical clustering based on subgraph-density," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).

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