Search Methodologies by Edmund K. Burke & Graham Kendall

Author:Edmund K. Burke & Graham Kendall
Language: eng
Format: epub, pdf
Publisher: Springer US, Boston, MA

Fig. 13.6Illustrating a partition transfer

A useful way to study partition transfers is to represent them with a graph. Towards this end, the (S, T)-transfer graph between two k-partitions S and T (of the same element set E) is defined as follows: for each element being partitioned there is a vertex in the transfer graph. Similarly, if element v i is transferred to a subset and v j is removed from the subset that v i is transferred into, then there is a directed edge from the vertex corresponding to v i to the vertex corresponding to v j . Moreover, for each subset in T there is a vertex in the transfer graph. For each element v i that is removed from subset S i and transferred into subset T j without replacing an element in T j , there is a directed edge from the vertex corresponding to v i to the vertex corresponding to T j . Note that the (S, T)-transfer graph is a disjoint union of cycles and paths because each vertex of the graph has at most one incoming edge and at most one outgoing edge. Figure 13.7 illustrates the (S, T)-transfer graph of the partition transfer illustrated in Fig. 13.6.

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