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A deterministic algorithm for computing a minimum spanning tree of a connected graph is presented. Its running time is 0 ( m α( m, n )), where α is the classical functional inverse of Ackermann's function and n (respectively, m ) is the number of vertices (respectively, edges). The algorithm is comparison-based : it uses pointers, not arrays, and it makes no numeric assumptions on the edge costs.
Bernard Chazelle (Wed,) studied this question.
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