Mikhail Goubko

Degree-based topological indices: Optimal trees with given number of pendents

Abstract A dynamic programming method is elaborated, enabling the characterization of trees with a given number of pendent vertices, for which a vertex-degree-based invariant (“topological index”) achieves its extremal value. The method is applied to the chemically interesting and earlier much studied such invariants: the first and second Zagreb index, and the atom–bond connectivity index.

Semantic-Aware Optimization of User Interface Menus

While the problem of hierarchical menu design is very common in user interface design, existing approaches lack either semantic aspects or optimization techniques. We suggest a semantic-aware mathematical model of hierarchical menu optimization and algorithms developed on the basis of this theory. These algorithms are implemented in the ready-to use design tool. The approach is illustrated by optimization of a banking voice menu.

Optimal hierarchies of control for cost functions presentable as sum of homogenous functions

The problem of rational organizational structure formation is considered. The problem is reduced to the discrete optimization problem of searching a hierarchy of managers that minimizes certain criterion (normally, the cost of hierarchy maintenance). Cost functions which can be written as a sum of homogenous function are analyzed. The conditions are derived when an optimal hierarchy has the constant span of control, a closed-form expression for the lower-bound estimate of optimal hierarchy cost is found, and an example of hierarchy calculation is given.

Maximizing Wiener index for trees with given vertex weight and degree sequences

Abstract The Wiener index is maximized over the set of trees with the given vertex weight and degree sequences. This model covers the traditional “unweighed” Wiener index, the terminal Wiener index, and the vertex distance index. It is shown that there exists an optimal caterpillar. If weights of internal vertices increase in their degrees, then an optimal caterpillar exists with weights of internal vertices on its backbone monotonously increasing from some central point to the ends of the backbone, and the same is true for pendent vertices. A tight upper bound of the Wiener index value is proposed and an efficient greedy heuristics is developed that approximates well the optimal index value. Finally, a branch and bound algorithm is built and tested for the exact solution of this NP-complete problem.

Users' preference share as a criterion for hierarchical menu optimization

Recently developed computer-aided design (CAD) tools automate design of rational hierarchical user menu structures. Proper choice of the optimization criterion is the key factor of success for such a CAD tool. We suggest user preference share as a novel metric of menu layout performance. It has clear economic grounds and is sound for management. We show how the preference share of a menu layout can be evaluated from laboratory experiments and predicted using the experimental menu navigation time and menu layout characteristics. Although navigation time is the most important factor, sometimes the faster does not mean the better. The logical compliance of a menu is also valuable for users.

Bayesian Learning of Consumer Preferences for Residential Demand Response

Abstract: In coming years residential consumers will face real-time electricity tariffs with energy prices varying day to day, and effective energy saving will require automation - a recommender system, which learns consumers preferences from her actions. A consumer chooses a scenario of home appliance use to balance her comfort level and the energy bill. We propose a Bayesian learning algorithm to estimate the comfort level function from the history of appliance use. In numeric experiments with datasets generated from a simulation model of a consumer interacting with small home appliances the algorithm outperforms popular regression analysis tools. Our approach can be extended to control an air heating and conditioning system, which is responsible for up to half of a households energy bill.

Mathematical Model of Hierarchical Menu Structure Optimization

A mathematical model is proposed to optimize the structure of hierarchical menus and directories. The model considers each element popularity. The problem of discrete optimization is solved regarding the choice of menu structure minimizing the average search time. It is demonstrated that optimal menu panels should provide the user with identical number of options having popularity levels split in the same proportion. It is indicated that the model allows for comparing the types of menu, as well as for choosing the best one. A certain algorithm is developed to design optimal menu, taking into account both semantic constraints and results of optimization. Application of the algorithm is illustrated using mobile phone menu optimization as an example.

Lower-Bound Estimate for Cost-Sensitive Decision Trees

Abstract While an extensive body of literature investigates problems of decision trees growing, just a few study lower-bound estimates for the expected classification cost of decision trees, especially for varying costs of tests. In this paper the new lower-bound estimate is proposed. Computation of the estimate is reduced to solving a series of set-covering problems. Computational complexity and other properties of the lower-bound estimate are investigated. The top-down algorithm of tree construction based on the proposed estimate is tested against several popular greedy cost-sensitive heuristics on a range of standard data sets from UCI Machine Learning Repository.

Optimal Hierarchies in Firms: A Theoretical Model

Abstract A normative economic model of management hierarchy design in firms is proposed. We seek for the management hierarchy that minimizes the running costs. Along with direct maintenance expenses these costs include wastes from the loss of control. The results include analytic expressions for the optimal hierarchy attributes: span of control, headcount, efforts distribution, wages differential, etc, as functions of exogenous parameters. They are used to analyze the impact of environment parameters on a firms size, financial results, employees’ wages and shape of hierarchy. The detailed analysis of this impact can help draw up policy recommendations on rational bureaucracy formation in firms. The research is supported by the grant 07-07-0078-a of Russian Foundation for Basic Research.