Multi-Way Partitioning Via Geometric Embeddings, Orderings, and Dynamic Programming

30 Acknowledgements We thank Pak K. Chan, Martine Schlag and Jason Zien for past research discussions, for the use of the LASO interface written by Martine Schlag, and for the use of their KP and SB codes. Ken D. Boese supplied the 3-Opt optimization code. Lars Hagen and Jen-Hsin Huang developed the ideas behind the partitioning-speciic net model. The anonymous reviewers provided many comments which substantially improved this work, particularly in the experimental design. Part of this work (ABK) was performed in part during a Spring 1993 sabbatical visit to UC Berkeley; support from NSF MIP-9117328 and the hospitality of Professor Ernest S. Kuh and his research group is gratefully acknowledged. Benz ecri, \Construction d'une Classiication Ascendante Hi erarchique par la Rechereche en Chaine des Voisins R eciproques", Les Cahiers de l'Analyse des Donn ees (VII)2, pp. Table 7: Runtimes in seconds on a Sun Sparc 10, for a single run of DP-RP for each of the ten d-dimensional embeddings (constructed from ~ 2 ; : : :; ~ d+1). Each Embedding entry gives the time required to generate d eigenvectors, and a DP-RP entry gives the time needed to generate 2-through 10-way partitioning solutions.

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