Differential Balanced Trees and (0,1) Matrices

* The research was supported by INTAS 00-397 and 00-626 Projects.

Links and similarities between the combinatorial optimization problems and the hierarchical search algorithms are discussed. One is the combinatorial greedy algorithm of step-by-step construction of the column-constraint (0,1) matrices with the different rows. The second is the base search construction of databases, - the class of the well known weight-balanced binary trees. Noted, that in some approximation each of the above problems might be interpreted in terms of the second problem. The constraints in matrices imply the novel concept of a differential balance in hierarchical trees. The obtained results extend the knowledge for balanced trees and prove that the known greedy algorithm for matrices is applicable in the world of balanced trees providing optimization on trees in layers.