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The complexity of ultrametric partitions on graphs. (English) Zbl 0637.68047
Summary: Partitioning of graphs has many practical applications namely in cluster analysis and in automated design of VLSI circuits. Using 1-1 correspondence between ultrametric partitions of a weighted complete graph K(w) on a finite set X and ultrametrics on X, the computational complexity of the appoximation of w by means of an ultrametric u is investigated and systematized. As a main result, a polynomial algorithm that solves the problem under some ‘min-max’ criterion is developed.

MSC:
68Q25 Analysis of algorithms and problem complexity
68R10 Graph theory (including graph drawing) in computer science
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