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On decision trees for orthants
Information Processing Letters. 1997. Vol. 62. No. 5. P. 265-268.
M. Rabin's principle asserts that the depth of any algebraic decision tree, recognizing a closed orthant in scRn, is no less than n. Using the techniques of Newton polyhedra, we give the shortest possible proof of this fact, extending it to arbitrary collections of open or closed orthants, and apply it to trees distinguishing real polynomials having at least l real roots.
Antipov E. A., Pokryshevskaya E. B., Journal of Targeting, Measurement and Analysis for Marketing 2010 Vol. 18 No. 2 P. 109-117
In this study a CHAID-based approach to detecting classification accuracy heterogeneity across segments of observations is proposed. This helps to solve some important problems, facing a model-builder: (1) How to automatically detect segments in which the model significantly underperforms? and (2) How to incorporate the knowledge about classification accuracy heterogeneity across segments to partition observations ...
Added: October 4, 2012
Malyshev D., Discrete Applied Mathematics 2018 Vol. 247 P. 423-432
We show that the weighted coloring problem can be solved for {P5,banner}-free graphs and for {P5,dart}-free graphs in polynomial time on the sum of vertex weights. ...
Added: April 23, 2018
Malyshev D., Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций") 2013 Vol. 7 No. 2 P. 221-228
The notion of a boundary class of graphs is a helpful tool for the computational complexity analysis of graph theory problems in the family of hereditary classes. Some general and specific features for families of boundary classes of graphs for the vertex k-colorability problem and its “limit” variant, the chromatic index problem, were studied by ...
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
Kontchakov R., Pratt-Hartmann I., Nenov Y. et al., ACM Transactions on Computational Logic 2013 Vol. 14 No. 2 P. 13.1-13.48
We consider the quantifier-free languages, Bc and Bc°, obtained by augmenting the signature of Boolean algebras with a unary predicate representing, respectively, the property of being connected, and the property of having a connected interior. These languages are interpreted over the regular closed sets of Rn (n ≥ 2) and, additionally, over the regular closed ...
Added: March 25, 2015
Shvydun S., / Высшая школа экономики. Series WP7 "Математические методы анализа решений в экономике, бизнесе и политике". 2015. No. WP7/2015/07.
Two-stage superposition choice procedures, which sequentially apply two choice procedures so that the result of the first choice procedure is the input for the second choice procedure, are studied. We define which of them satisfy given normative conditions, showing how a final choice is changed due to the changes of preferences or a set of ...
Added: October 20, 2015
Malyshev D., / 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
Malyshev D., Discrete Mathematics and Applications 2010 Vol. 19 No. 6 P. 625-630
The notion of a boundary class is a useful notion in the investigation of the complexity of extremal problems on graphs. One boundary class is known for the independent set problem and three boundary classes are known for the dominating set problem. In this paper it is proved that the set of boundary classes for ...
Added: November 25, 2012
Malyshev D., Дискретная математика 2009 Т. 21 № 4 С. 129-134
The notion of a boundary class is a useful notion in the investigation of the complexity of extremal problems on graphs. One boundary class is known for the independent set problem and three boundary classes are known for the dominating set problem. In this paper it is proved that the set of boundary classes for ...
Added: November 25, 2012
Shitov Y., American Mathematical Monthly 2016 Vol. 123 No. 1 P. 71-77
We present an infinite sequence of pairs (An, Bn) of chess positions on an n × n board such that (1) there is a legal sequence of chess moves leading from An to Bn and (2) any legal sequence leading from An to Bn contains at least exp(n + o(n)) moves. ...
Added: February 23, 2016
Artale A., Kontchakov R., Ryzhikov V. et al., ACM Transactions on Computational Logic 2014 Vol. 15 No. 3 P. 25.1-25.50
We design temporal description logics (TDLs) suitable for reasoning about temporal conceptual data models and investigate their computational complexity. Our formalisms are based on DL-Lite logics with three types of concept inclusions (ranging from atomic concept inclusions and disjointness to the full Booleans), as well as cardinality constraints and role inclusions. The logics are interpreted ...
Added: March 25, 2015
Sirotkin D., Malyshev D., Lobachevskii Journal of Mathematics 2021 Vol. 42 No. 4 P. 760-766
The vertex 3-colourability problem is to verify whether it is possible to split the vertex set of a given graph into three subsets of pairwise nonadjacent vertices or not. This problem is known to be NP-complete for planar graphs of the maximum face length at most 4 (and, even, additionally, of the maximum vertex degree ...
Added: June 5, 2021
Malyshev D., Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций") 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
Vassiliev V., Moscow Mathematical Journal 2017 Vol. 17 No. 4 P. 825-836
The local multiplicities of the caustics, the Maxwell sets, and the complex Stokes' sets in the spaces of versal deformations of Pham singularities (that is, of germs of holomorphic functions C^n --> C^1 which are expressed by the sums of degrees of the coordinate functions) are calculated ...
Added: December 27, 2017
Malyshev D., Discrete Mathematics 2015 Vol. 338 No. 11 P. 1860-1865
We completely determine the complexity status of the 3-colorability problem for hereditary graph classes defined by two forbidden induced subgraphs with at most five vertices. ...
Added: April 7, 2014
Malyshev D., Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций") 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
Malyshev D., Дискретный анализ и исследование операций 2012 Т. 19 № 6 С. 37-48
Понятие граничного класса графов является полезным инструментом для анализа вычислительной сложности задач на графах в семействе наследственных классов. В предыдущих работах автора исследовались общие черты и особенности семейств граничных классов графов для задачи о вершинной k-раскраске и ее «предельного варианта» - задачи о хроматическом числе. В данной работе эта проблематика рассматривается применительно к реберному варианту ...
Added: November 30, 2012
Sirotkin D., Malyshev D., Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций") 2018 Vol. 12 No. 4 P. 759-769
The 3-coloring problem for a given graph consists in verifying whether it is possible
to divide the vertex set of the graph into three subsets of pairwise nonadjacent vertices. A complete
complexity classification is known for this problem for the hereditary classes defined by triples of
forbidden induced subgraphs, each on at most 5 vertices. In this article, ...
Added: November 20, 2018
Malyshev D., Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций") 2012 Vol. 6 No. 1 P. 97-99
Under study is the complexity status of the independent set problem in a class of connected graphs that are defined by functional constraints on the number of edges depending on the number of vertices. For every natural number C, this problem is shown to be polynomially solvable in the class of graphs, On the other ...
Added: December 7, 2012
Berlin : Springer, 2012
This book constitutes the refereed proceedings of the 23rd Annual Symposium on Combinatorial Pattern Matching, CPM 2012, held in Helsinki, Finalnd, in July 2012.
The 33 revised full papers presented together with 2 invited talks were carefully reviewed and selected from 60 submissions. The papers address issues of searching and matching strings and more complicated patterns ...
Added: October 30, 2013
Rybakov M., Shkatov D., Journal of Logic and Computation 2021 Vol. 31 No. 2 P. 426-443
It is shown that products and expanding relativized products of propositional modal logics where one component is the minimal monomodal logic K are polynomial-time reducible to their single-variable fragments. Therefore, the nown lower bound complexity and undecidability results for such logics are extended to their single-variable fragments. Similar results are obtained for products where one component is a polymodal logic with a K-style ...
Added: September 24, 2020
Korpelainen N., Lozin V. V., Malyshev D. et al., Theoretical Computer Science 2011 No. 412 P. 3545-3554
The notion of a boundary graph property was recently introduced as a relaxation of that of a minimal property and was applied to several problems of both algorithmic and combinatorial nature. In the present paper, we first survey recent results related to this notion and then apply it to two algorithmic graph problems: Hamiltonian cycle ...
Added: September 11, 2012
Kochergin Vadim V., Discrete Mathematics and Applications 2017 Vol. 27 No. 2 P. 81-95
Let a finite Abelian multiplicative group G be specified by the basis B = {a1, a2, …, aq}, that is, the group G is decomposed into a direct product of cyclic subgroups generated by the elements of the set B: G = 〈a1〉 × 〈a2〉 × … × 〈aq〉. The complexity L(g;B) of an element ...
Added: October 8, 2018
Kazda A., Opršal J., Valeriote M. et al., Canadian Mathematical Bulletin 2020 P. 577-591
This paper investigates the computational complexity of deciding if a given finite idempotent algebra has a ternary term operation m that satisfies the minority equations m(y,x,x)≈m(x,y,x)≈m(x,x,y)≈y . We show that a common polynomial-time approach to testing for this type of condition will not work in this case and that this decision problem lies in the class NP. ...
Added: June 15, 2020