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Matchings with Simplest Semiorder Preference Relations
P. 119–121.
Kiselgof S. G.
Matching problem with preferences being simplest semiorders is analysed. It is proved that a stable matching always exists. Furthermore, for any stable matching there exists a linear extension of preferences, which does not sontradict stability of a matching. In the college admission problem common goal is to find student-optimal stable matching. We provide a simple criteria (Stable Improvement Cycle existence), that allows to check, whether some particular stable matching is student-side Pareto optimal.
In book
St. Petersburg: Graduate School of Management, St. Petersburg University, 2011.
Дистель Р., М.: МЦНМО, 2024.
С момента выхода первого издания на английском языке в 1997 году книга известного математика, профессора Гамбургского университета Рейнгарда Дистеля стала основным учебником по теории графов во многих университетах, выдержав к настоящему времени пять изданий, перевод последнего из которых предлагается читателю. Уникальность учебника в его глубине при относительно небольшом объёме: в книге найдутся задачи как доступные ...
Added: January 25, 2026
Beaudou L., Echeverría H., Foucaud F. et al., Procedia Computer Science 2025 Vol. 273 P. 86–93
We prove that the recognition of exact cubes of trees can be done in polynomial time. More precisely, the exact distance power of a graph is a refinement of the more usual notion of graph power. Given a graph G and a positive integer p, the exact distance pth power of G is the graph G#p on the same vertex set where two vertices ...
Added: December 3, 2025
Karpov A., Automation and Remote Control 2022 Vol. 83 P. 1329–1354
A survey of papers on practically significant restrictions on the preference profile of a collective is carried out, including single-peaked preferences, group-separable preferences, preferences with the single-crossing property, and Euclidean preferences and their extensions. Both ordinal and dichotomous preferences are considered. For structured preferences, we present characterization in terms of forbidden subprofiles and the probability ...
Added: October 31, 2022
А. В. Карпов, Автоматика и телемеханика 2022 № 9 С. 3–35
Проведен обзор работ по практически значимым ограничениям на профиль предпочтений коллектива: однопиковые предпочтения, сепарабельные предпочтения, предпочтения со свойством единственного пересечения, евклидовы предпочтения и их расширения. Рассмотрены как ординальные, так и дихотомические предпочтения. Для структурированных предпочтений представлена характеризация через запрещенные подпрофили и вероятность появления профиля с заданным свойством. Для сепарабельных предпочтений описан алгоритм построения иерархического дерева. ...
Added: September 15, 2022
Avdoshin S. M., Набебин А. А., М.: ДМК Пресс, 2019.
The book contains the necessary information from the algorithm theory, graph theory, combinatorics. It is considered partially recursive functions, Turing machines, some versions of the algorithms (associative calculus, the system of substitutions, grammars, Post's productions, Marcov's normal algorithms, operator algorithms). The main types of graphs are described (multigraphs, pseudographs, Eulerian graphs, Hamiltonian graphs, trees, bipartite ...
Added: August 24, 2018
Babenko M. A., Artamonov S., , in: 28th International Symposium on Algorithms and Computation, ISAAC 2017Vol. 92.: Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl Publishing, 2017. P. 1–12.
Let G = (V,E) be an undirected graph, T ⊆ V be a set of terminals. Then a natural combinatorial problem consists in finding the maximum number of vertex-disjoint paths connecting distinct terminals. For this problem, a clever construction suggested by Gallai reduces it to computing a maximum non-bipartite matching and thus gives an O ( m ...
Added: March 1, 2018
Sofya Kiselgof, Procedia Computer Science 2014 Vol. 31 P. 807–813
We investigate models of two-sided matching markets without transfers. Examples of such markets include marriage market, universities-applicants market and others. Gale and Shapley in 1962 first introduced this kind of problems in the literature. They considered one-to-one and one-to-many markets, where preferences of individuals on the one side over individuals on the other side were ...
Added: January 23, 2015
Sofya Kisel'gof, Automation and Remote Control 2014 Vol. 75 No. 6 P. 1069–1077
We consider an extension of the classical model of generalized Gale-Shapley matchings. The model describes a two-sided market: on one side, universities each of which has a restriction on the number of enrolled students; on the other side, applicants each of which can get a single place in the university. Both applicants and universities have ...
Added: October 23, 2014
Péter Biró, Sofya Kiselgof, Central European Journal of Operations Research 2015 Vol. 23 No. 4 P. 727–741
A common feature of the Hungarian, Irish, Spanish and Turkish higher education admission systems is that students apply for programmes and are ranked according to their scores. Students who apply for a programme with the same score are tied. Ties are broken by lottery in Ireland, by objective factors in Turkey (such as date of ...
Added: October 23, 2014
Sofya Kiselgof, / Series "Matching in practice". 2012.
In this article we describe current university admission system in Ukraine. Current admission system in Ukraine is quazi-centralized. A matching mechanism consist of three stages, which are three stages of the classical deferred acceptance admission scheme. We also charachterize quota assignment process for state-financed and open-enrollment seats in Ukrainian universities. ...
Added: March 18, 2013
Péter Biró, Kiselgof S. G., / Series MT-DP "Discussion Papers of Hungarian Academy of Sciences". 2013. No. 6.
A common feature of the Hungarian, Irish, Spanish and Turkish higher education admission systems is that the students apply for programmes and they are ranked according to their scores. Students who apply for a programme with the same score are in a tie. Ties are broken by lottery in Ireland, by objective factors in Turkey ...
Added: March 11, 2013
Kiselgof S. G., Проблемы управления 2012 № 5 С. 33–40
In Russia from 2009 College admission is based on results of Unified State Exam. Entrant applies to no more than five universities. Admission mechanism is defined by government for all state universities. In the paper the authors model how entrant chooses university for application and, based on the entrant's choice prediction, the shortages of the ...
Added: November 17, 2012