On Theoretical and Probabilistic and Statistical Approaches for Finding the Optimal Keyboard Layout

Dependence of objective function on several variables in layout problem and its solution by the method of structural-alphabetic search

“…Type I includes problems of the layout of units on printed-circuit boards, design of very large scale integration and optimal cut, type II includes the problem of layout of letters on a keyboard [37]. In problems of type I, we present each set as a graph whose nodes are its elements and each rib is associated with a number c R lt Î (R is the set of real numbers), i.e., there are constraints among elements of the sets A and B, we will call their numerical values the weights.…”

“…Let us use the theory of combinatorial optimization and present the mathematical formulation for a layout problem of type II on the example of the layout of letters on a keyboard [37].…”

“…In [37], to efficiently solve this problem, letters were clustered according to certain attributes and then arranged on the keyboard. The objective function in this problem depends on two variables: permutation and partition of an n-element set into subsets, and its value is searched on two combinatorial sets.…”

“…The paper [37] describes creating the optimal keyboard where letters are clustered (according to certain features) and then are placed on it. However, none of the above-mentioned studies analyzed problems of objects layout with revealing the attributes according to which one approach or another is chosen for their solution.…”