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## The computational complexity of dominating set problems for instances with bounded minors of constraint matrices

Discrete Optimization. 2018. Vol. 29. P. 103-110.

We consider boolean linear programming formulations of the vertex and edge dominating set problems and prove their polynomial-time solvability for classes of graphs with constraint matrices having bounded minors in the absolute value.

Language:
English

Gribanov D., Malyshev D., Discrete Applied Mathematics 2017 Vol. 227 P. 13-20

We consider boolean linear programming formulations of the independent set, the vertex and the edge dominating set problems and prove their polynomial-time solvability for classes of graphs with (augmented) constraint matrices having bounded minors in the absolute value ...

Added: April 23, 2017

Gribanov D., Malyshev D., Журнал Средневолжского математического общества 2016 Т. 18 № 3 С. 19-31

Мы рассматриваем естественные постановки задач о независимом множестве, о вершинном и о реберном доминирующем множестве как задач целочисленного линейного программирования и доказываем полиномиальную разрешимость этих задач для классов графов, имеющих ограниченные по абсолютному значению миноры (расширенных) матриц ограничений. ...

Added: October 20, 2016

Malyshev D., Siberian Electronic Mathematical Reports 2014 Vol. 11 P. 811-822

We obtain a complete complexity dichotomy for the edge 3- colorability within the family of hereditary classes defined by forbidden
induced subgraphs on at most 6 vertices and having at most two 6-vertex forbidden induced structures. ...

Added: April 7, 2014

Turkensteen M., Malyshev D., Goldengorin B. I. et al., Journal of Global Optimization 2017 Vol. 68 No. 3 P. 601-622

The tolerance of an element of a combinatorial optimization problem with respect to its optimal solution is the maximum change of the cost of the element while preserving the optimality of the given optimal solution and keeping all other input data unchanged. Tolerances play an important role in the design of exact and approximation algorithms, ...

Added: December 10, 2016

Goldengorin B. I., Malyshev D., Pardalos P. M., Doklady Mathematics 2013 Vol. 87 No. 3 P. 368-371

The notion of a tolerance of an element of a combinatorial optimization problem is often used for stability analysis of an optimal solution and it is a base for design branch-and-bound algorithms solving such problems. In this paper we show that for the weighted independent set problem on trees with n vertices all upper and ...

Added: June 23, 2013

Malyshev D., Pardalos P. M., Optimization Letters 2016 Vol. 10 No. 8 P. 1593-1612

The task of complete complexity dichotomy is to clearly distinguish between easy and hard cases of a given problem on a family of subproblems. We consider this task for some optimization problems restricted to certain classes of graphs closed under deletion of vertices. A concept in the solution process is based on revealing the so-called ...

Added: December 18, 2015

Malyshev D., Pardalos P. M., Doklady Mathematics 2014 Vol. 89 No. 2 P. 253-256

The notion of a tolerance of an element of a combinatorial optimization problem is often used for stability analysis of an
optimal solution and it is a base for design of branch-and-bound algorithms solving such problems. We show in this paper that for the weighted independent set problem and a bipartite graph with n vertices and ...

Added: April 18, 2014

Malyshev D., Journal of Applied and Industrial Mathematics 2013 Vol. 7 No. 3 P. 412-419

The notion is introduced of an expanding operator for the independent set problem. This notion is a useful tool for the constructive formation of new cases with the efficient solvability of the problem in the family of hereditary classes of graphs and is applied to hereditary parts of the set Free({P_5,C_5}). It is proved that ...

Added: October 3, 2013

Malyshev D., Sirotkin D., Journal of Applied and Industrial Mathematics 2017 Vol. 11 No. 3 P. 400-414

The independent set problem for a given simple graph consists in computing the size of a largest subset of its pairwise nonadjacent vertices. In this article, we prove the polynomial solvability of the problem for the subcubic planar graphs with no induced tree obtained by identifying the ends of three paths of lengths 3, 3, ...

Added: August 10, 2017

Malyshev D., Discrete Applied Mathematics 2016 Vol. 203 P. 117-126

We completely determine the complexity status of the dominating set problem for hereditary graph classes defined by forbidden induced subgraphs with at most five vertices. ...

Added: October 9, 2015

Malyshev D., Journal of Applied and Industrial Mathematics 2013 Vol. 7 No. 4 P. 537-548

We prove the polynomial solvability of the independent set problem for some family of
classes of the planar subcubic graphs. ...

Added: January 21, 2014

Malyshev D., Discrete Mathematics and Applications 2017 Vol. 27 No. 2 P. 97-101

A class of graphs is called monotone if it is closed under deletion of vertices and edges. Any such class may be defined in terms of forbidden subgraphs. The chromatic index of a graph is the smallest number of colors required for its edge-coloring such that any two adjacent edges have different colors. We obtain ...

Added: May 10, 2017

Kuznetsov V. O., Логистика и управление цепями поставок 2018 № 4 (87) С. 27-33

One of the options for a more flexible approach to analyzing the reliability of supply chains is the principal component analysis (PCA). With a large number of variables describing supply chain, it is a difficult task to analyze the structure of variables in two-dimensional space. Within the analysis of the variables dependencies PCA allows to ...

Added: November 29, 2018

Malyshev D., The coloring problem for classes with two small obstructions / Cornell University. Series math "arxiv.org". 2013. No. 1307.0278v1.

The coloring problem is studied in the paper for graph classes deﬁned by two small forbidden induced subgraphs. We prove some suﬃcient conditions for eﬀective solvability of the problem in such classes. As their corollary we determine the computational complexity for all sets of two connected forbidden induced subgraphs with at most ﬁve vertices except ...

Added: October 3, 2013

Пенза : ПГУ, 2015

В сборник трудов включены доклады юбилейного ХХ-го Международного симпозиума «Надежность и качество», проходившего с 25 по 31 мая 2015 г. в городе Пензе.
Рассмотрены актуальные проблемы теории и практики повышения надежности и качества; эффективности внедрения инновационных и информационных технологий в фундаментальных научных и прикладных исследованиях, образовательных и коммуникативных системах и средах, экономике и юриспруденции; методов и ...

Added: May 31, 2015

Lanham : University Press of America, 2012

The history of logic and analytic philosophy in Central and Eastern Europe is still known to very few people. As an exception to the rule, only two scientific schools became internationally popular: the Vienna Circle and the Lvov-Warsaw School. Nevertheless, the countries included in this region have not only joint history, but also joint cultural ...

Added: February 13, 2013

Malyshev D., Journal of Applied and Industrial Mathematics 2020 Vol. 14 No. 4 P. 706-721

The edge coloring problem for a graph is to minimize the number of colors that are sufficient to color all edges of the graph so that all adjacent edges receive distinct colors. The computational complexity of the problem is known for all graph classes defined by forbidden subgraphs with at most 6 edges. We improve ...

Added: January 30, 2021

Felikson А. A., Natanzon S. M., Differential Geometry and its Application 2012 Vol. 30 No. 5 P. 490-508

We consider (local) parameterizations of Teichmüller space Tg,n (of genus g hyperbolic surfaces with n boundary components) by lengths of 6 g- 6 + 3 n geodesics. We find a large family of suitable sets of 6 g- 6 + 3. n geodesics, each set forming a special structure called "admissible double pants decomposition". For ...

Added: February 5, 2013

Kochergin V.V., Mikhailovich A.V., Journal of Applied and Industrial Mathematics 2018 Vol. 12 No. 1 P. 40-58

The complexity of realization of k-valued logic functions by circuits in a special infinite basis is under study. This basis consists of Post negation (i.e. function x+1(mod k)) and all monotone functions. The complexity of the circuit is the total number of elements of this circuit. For an arbitrary function f, we find the lower and upper bounds ...

Added: March 11, 2018

Akopov A. S., Beklaryan L. A., Saghatelyan A. K., Environmental Modelling and Software 2019 Vol. 116 P. 7-25

Urban greenery such as trees can effectively reduce air pollution in a natural and eco-friendly way. However, how to spatially locate and arrange greenery in an optimal way remains as a challenging task. We developed an agent-based model of air pollution dynamics to support the optimal allocation and configuration of tree clusters in a city. The Pareto ...

Added: February 24, 2019

Marshirov V. V., Marshirova L. E., Сибирский журнал индустриальной математики 2013 Т. XVI № 4 С. 111-120

The paper considers the problem of determining the rate of cooling of metal during solidification at the intersection of the liquidus temperature under intense heat sink from the surface. The solution to this problem it is necessary to determine the process conditions, the boundary and initial conditions for which it is possible to get new ...

Added: November 17, 2013

Kryuchkov M., Rusakov S. V., Вестник Ижевского государственного технического университета 2015 № 2(66) С. 110-112

This paper describes the results of testing the neuronal technical trend indicator according to the exchange rate of Brent oil in 2014. Testing of the model was carried out on three time series, which characterized by their features. ...

Added: August 31, 2015

Vyalyi M., Дискретная математика 1991 Т. 3 № 3 С. 35-45

Added: October 17, 2014

D. V. Gribanov, D.S. Malyshev, P. M. Pardalos et al., Journal of Combinatorial Optimization 2018 Vol. 35 No. 4 P. 1128-1146

In this paper, we present fixed-parameter tractable algorithms for special cases of the shortest lattice vector, integer linear programming, and simplex width computation problems, when matrices included in the problems’ formulations are near square. The parameter is the maximum absolute value of the rank minors in the corresponding matrices. Additionally, we present fixed-parameter tractable algorithms ...

Added: February 19, 2018