60 research outputs found
On stable matchings and flows
We describe a flow model related to ordinary network flows the same way as stable matchings are related to maximum matchings in bipartite graphs. We prove that there always exists a stable flow and generalize the lattice structure of stable marriages to stable flows. Our main tool is a straightforward reduction of the stable flow problem to stable allocations. For the sake of completeness, we prove the results we need on stable allocations as an application of Tarski's fixed point theorem. © 2014 by the authors
Stabil párosĂtások a kombinatorikus optimalizálásban = Stable matchings in Combinatorial Optimization
Az F 037301 sz. OTKA kutatási projekt fĹ‘ eredmĂ©nyei az alábbiak. A stabil párosĂtások Ă©s kĂĽlönbözĹ‘ más tudományterĂĽltek kapcsolatának kimutatása, a nempáros modellek stabil párosĂtásait jellemzĹ‘ Tan-fĂ©le karakterizáciĂł általánosĂtása, a stabil párosĂtások általánosĂtásainak megfelelĹ‘ stabil párosĂtás poliĂ©derek leĂrása, ezen belĂĽl Rothblum leĂrásának kiterjesztĂ©se Ă©s általánosĂtása, a stabil b-párosĂtások egy Ă©rdekes Ă©s fontos tulajdonságának felfedezĂ©se, a stabil szobatárs problĂ©ma bizonyos általánosĂtásainak visszavezetĂ©se az eredeti problĂ©mára, Irving algoritmusának általánosĂtása, a szuperstabil párosĂtások rĂ©szbenrendezĂ©ses általánosĂtásának kezelĂ©se, Ă©lĹ‘donoros szervátĂĽltetĂ©sek során fellĂ©pĹ‘ stabilitási problĂ©mák megoldása, kevĂ©s Ă©l által blokkolt párosĂtások problĂ©májának bonyolultságának megállapĂtása, az inkrementálĂł algoritmusok egy fontos tulajdonságának általánosĂtása a nempáros modellre, az Ăş.n. MS párosĂtások általánosĂtása matroidokra Ă©s Delta-matroidokra, ill. a cĂmkĂ©zett pontokon megadott fák leszámlálása a fordĂtott PrĂĽfer-kĂłd segĂtsĂ©gĂ©vel. Az elĂ©rt eredmĂ©nyek több konferencián, workshopon ill. szemináriumon hangzottak el, köztĂĽk meghĂvásos elĹ‘adáskĂ©nt is. GyĂĽmölcsözĹ‘ kutatási egyĂĽttműködĂ©s jött lĂ©tre a Kassán kutatĂł KatarĂna Cechlárovával Ă©s a glasgowi kutatĂłcsoporttal, köztĂĽk is elsĹ‘sorban David Manlove-val. | The main achievements of the OTKA F 037301 project are the following. Demonstration of the connection of stable matchings and other areas, generalizaton of Tan's characterization of nonbipartite stable matchings, linear descriptions of polyhedra corresponding to generalizations of stable matchings, in particular the extension and generalization of Rothblum's description, exploration of an interesting and important property of many-to-many stable matchings, reduction of certain generalizations of the stable roommates problem to the original one, generalization of Irving's algorithm, handling of the poset generalizations of superstable matchings, solving stability problems related to living-donor organ transplantations, determination of the complexity of finding a matching blocked by a minimum number of edges, generalization of an important property of incremental algorithms to the nonbipartite model, generalization of the so-called MS matchings to matroids and Delta-matroids, and enumeration of labelled trees with the help of reverse PrĂĽfer codes. The results of the project were performed in several conferences, workshops and semiars, even as invited talks. We started a fruitful research cooperation with KatarĂna Cechlárová from Kosice and with the Glasgow research group, in particular with David Manlove
The Kidney Exchange Game
The most effective treatment for kidney failure that is currently known is transplantation. As the number of cadaveric donors is not sufficient and kidneys from living donors are often not suitable for immunological reasons, there are attempts to organize exchanges between patient-donor pairs. In this paper we model this situation as a cooperative game and propose some algorithms for finding a solution
An Algorithm for a Super-Stable Roommates Problem
In this paper we describe an efficient algorithm that decides if a stable
matching exists for a generalized stable roommates problem, where, instead of
linear preferences, agents have partial preference orders on potential partners.
Furthermore, we may forbid certain partnerships, that is, we are looking for
a matching such that none of the matched pairs is forbidden, and yet, no
blocking pair (forbidden or not) exists.
To solve the above problem, we generalize the first algorithm for the ordi-
nary stable roommates problem
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