Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. Vyssh. Uchebn. Zaved. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, Number 11, Pages 34–40 (Mi ivm8392)  

This article is cited in 3 scientific papers (total in 3 papers)

Relationship between matching and assignment problems

E. Yu. Lerner

Chair of Economic Cybernetics, Kazan (Volga Region) Federal University, Kazan, Russia
Full-text PDF (181 kB) Citations (3)
References:
Abstract: Let $(R_{ik})_{i,k=1}^n$ and $(J_{ik})_{i,k=1}^n$ be preference matrices in the stable matching problem and let $(J_{ik})_{i,k=1}^n$ be the measure of the mutual antipathy in the assignment problem. In this paper we describe all functions $f$ such that if $H_{i,k}=f(R_{ik},J_{ik})$ then for any matrices $R$ and $J$ solution sets in stable matching and assignment problems (partly) coincide. Thus we answer the question about the relationship between these problems stated by D. Knuth. The results are analogous to the Arrow theorem, and the proof techniques are close to those used in the group choice theory.
Keywords: stable matching, assignment problem, Knuth problems, preference matrix, group choice, Arrow theorem.
Received: 17.09.2010
Revised: 09.11.2010
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, Volume 55, Issue 11, Pages 27–32
DOI: https://doi.org/10.3103/S1066369X11110041
Bibliographic databases:
Document Type: Article
UDC: 519.157
Language: Russian
Citation: E. Yu. Lerner, “Relationship between matching and assignment problems”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 11, 34–40; Russian Math. (Iz. VUZ), 55:11 (2011), 27–32
Citation in format AMSBIB
\Bibitem{Ler11}
\by E.~Yu.~Lerner
\paper Relationship between matching and assignment problems
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2011
\issue 11
\pages 34--40
\mathnet{http://mi.mathnet.ru/ivm8392}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2963177}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2011
\vol 55
\issue 11
\pages 27--32
\crossref{https://doi.org/10.3103/S1066369X11110041}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84856240850}
Linking options:
  • https://www.mathnet.ru/eng/ivm8392
  • https://www.mathnet.ru/eng/ivm/y2011/i11/p34
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024