Clusters, Orders, and Trees: Methods and Applications by Fuad Aleskerov Boris Goldengorin & Panos M. Pardalos

Author:Fuad Aleskerov, Boris Goldengorin & Panos M. Pardalos
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

In the second part, Transfer, the weight of the assignment of any element to any class is computed. Let . If S i  ∈ Π k , A(i, k) is the contribution of S i to its own class, and also to . Otherwise, the A(i, k ′ ) value corresponds to a possible assignment to class . The difference A(i, k ′ ) − A(i, k) is the variation resulting from the transfer of S i from class Π k to class . Our procedure, consists in moving at each step the element maximizing this difference. Order S i is assigned either to class if A(i, k ′ ) ≥ 0 or a new singleton class is created. In this latter case, S i has a null contribution to , increasing the criterion value. We have implemented this algorithm, making a table A, indexed on Π and on the classes of the running partition. The transfer procedure stops when each item has a non negative contribution to its class which is larger than or equal to its contribution to any other class.

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