Daria Lemtyuzhnikova

Russian Academy of Sciences | RAS · Institute of Control Sciences

We find a lower bound for the k-subdomination number on the set of graphs with a given upper bound for vertex degrees. We study the cases where the proposed lower bound is sharp, construct the optimal graphs and indicate the corresponding k-subdominating functions. The results are interpreted in terms of social structures.

In this paper we consider an approximation-interpolation approach based on the combination of interpolation method and approximation method. An approximation method for single-machine scheduling theory problem with an unknown objective function that depends on the completion times of jobs is studied. The idea of approximating an unknown function by...

We consider the feasibility to find approximate non-preemptive schedules by metric approach for NP-complete problem of scheduling on two parallel identical machines with precedence delays for jobs or jobs of lengths 1 and 2 with makespan minimization. The execution of the job can be started only after the completion of any of its predecessors. We r...

The problem of planning the work of operating departments with scheduled admissions of patients is investigated. Two models are constructed: with and without anesthesiologists. Approximate algorithms were developed for each model. All experiments were performed on real, high-dimensional data. The resulting solutions satisfy the hospital's requireme...

This research extends the interpolation approach to approximating the objective function value for the minimization maximum lateness problem. The interpolation approach is defined using a special objective function Lmax(α), which is proven to be continuous and depends only on α transform coefficient. Such a function is proven to be monotonically in...

We consider the instance space metric method to the two-station single-track railway scheduling problem. This method has been effectively applied to several classical NP-hard scheduling problems, but was not tested on some actual railway scheduling models. It allows to construct the solutions with absolute error in polynomial time if there are some...

This paper is aimed at the problem of scheduling surgeries in operating rooms. To solve this problem, we suggest using some variation of the bin packing problem. The model is based on the actual operation of 10 operating rooms, each of which belongs to a specific department of the hospital. Departments are unevenly loaded, so operations can be move...

An approach to estimating the objective function value of minimization maximum lateness problem is proposed. It is shown how to use transformed instances to define a new continuous objective function. After that, using this new objective function, the approach itself is formulated. We calculate the objective function value for some polynomially sol...

NP-hard scheduling problems with the criterion of minimizing the maximum penalty, e.g. maximum lateness, are considered. For such problems, a metric which delivers an upper bound on the absolute error of the objective function value is introduced. Taking the given instance of some problem and using the introduced metric, the nearest instance is det...

We consider the dynamic patient scheduling for the hospital surgery department with electronic health records. Models for increasing the throughput of the surgery are proposed. It is based on classical intellectual optimization problems, such as the assignment problem, the scheduling problem, and the forecasting problem. Various approaches to solvi...

New metrics for different classes of scheduling problems are introduced. We show how approximate solutions of NP-hard problems can be obtained using these metrics. To do this, we solve the optimization problem in which the introduced metric is used as the objective function, and a system of linear inequalities of (pseudo-)polynomial solvable instan...

We consider N P-hard multi-machine scheduling problems with the criterion of minimizing the maximum penalty, e.g. maximum lateness. For such problems, we introduce a metric which delivers an upper bound on the absolute error of the objective function value. Taking the given instance of some problem and using the introduced metric, we determine the...

Sparse large matrices with a block-staircase and block-treelike structure are studied. They are called quasi-block matrices and consist of independent blocks that are connected to each other pairwise or in a more general fashion. The interdependence of parameters of such matrices, such as the number of nonzero elements, the number of blocks, and th...

Recommender systems provide recommendations for users. In this paper, we train and test some algorithms for recommender systems on a certain dataset, as well as analyze their strengths and weaknesses. Based on this information, we construct a system that yields a better solution.

In this paper, we review problems associated with sparse matrices. We formulate several theorems on the allocation of a quasi-block structure in a sparse matrix, as well as on the relation of the degree of the quasi-block structure and the number of its blocks, depending on the dimension of the matrix and the number of nonzero elements in it. Algor...

We consider discrete optimization problems with Boolean variables and rarefied matrices of large dimensions. In some cases we manage to extract the quasi-block structure of the initial matrices. In particular, in this paper we have problems with the so-called block-stair and block-tree structures. Blocks in such problems have connecting variables w...

Лемтюжникова Д.В., Свириденко А.В., Щербина О.А. Алгоритм выделения блочно-древовидной структуры в разреженных задачах дискретной оптимизации // Таврический вестник информатики и математики. – 2012. – №1 – С. 44–55

The decomposition algorithms provide approaches to deal with NP-hardness in solving discrete optimization problems (DOPs). In this article one of the promising ways to exploit sparse matrices - local elimination algorithm in parallel interpretation (LEAP) are demonstrated. That is a graph-based structural decomposition algorithm, which allows to co...

We discuss local elimination algorithms that compute global information using local computations. Results of benchmarking show real computational capabilities of block elimination algorithms combined with SYMPHONY solver. Strategies for parallelizing a sequential local elimination algorithm for sparse discrete optimization problems are analyzed. We...