Additive weights of a special class of nonuniformly distributed backtrack trees.

*(English)*Zbl 0780.68068Summary: We introduce a family of backtrack trees which is a generalization of a special class of the binary backtrack trees defined by P. W. Purdom. In our family each internal node may have an arbitrary degree from a finite set \(D\subset N\) of allowed node degrees. We shall assign numbers \(p_ i\in (0,1)\), \(i\in D\), to each node degree and, based on these numbers, recursively define a function which assigns a probability to each backtrack tree in our family. Next we consider a general additive weight on our family of backtrack trees and derive a general approach to the computation of the average weight of a backtrack tree of height less than or equal to \(h\) for weight functions which are polynomials of degree less than or equal to 2 in the number of leaves and the total number of nodes with coefficients depending on the degree of the root of the tree. Finally we shall apply the results presented here to some tree parameters which are important for the average case analysis of algorithms.

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