Optimum multiway search trees

SummaryThe construction of optimum multiway search trees for n keys, n key weights and n+1 gap weights, is investigated. A new general optimality principle is presented, which can be “tuned” for specific applications. Moreover we consider the affects of three additional constraints, namely height, structural and node search restrictions, which lead to a number of new construction algorithms. In particular we concentrate on the construction of optimum t-ary search trees with linear and binary search within their nodes for which we obtain O(n3t) and O(n3log2t) time algorithms, respectively. Whether these algorithms are or are not optimal remains an important open problem, even in the binary case.

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