The kidney exchange problem: How hard is it to find a donor?

Cechlárová, Kataŕına; Lacko, Vladimír

doi:10.1007/s10479-010-0691-4

Cited by 10 publications

(6 citation statements)

References 22 publications

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“…Some more sophisticated variants consider also the differences between suitable kidneys. Sometimes the "total benefit" is maximised [28], whilst other models [4,6,7,23] require first the stability of the solution under various criteria.…”

Section: Kidney Exchange Problemmentioning

confidence: 99%

Three-Sided Stable Matchings with Cyclic Preferences

Bíró

McDermid

2009

Algorithmica

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Knuth (Mariages Stables, Les Presses de L'Université de Montréal, 1976) asked whether the stable matching problem can be generalised to three dimensions, e.g., for families containing a man, a woman and a dog. Subsequently, several authors considered the three-sided stable matching problem with cyclic preferences, where men care only about women, women only about dogs, and dogs only about men. In this paper we prove that if the preference lists may be incomplete, then the problem of deciding whether a stable matching exists, given an instance of the three-sided stable matching problem with cyclic preferences, is NP-complete. Considering an alternative stability criterion, strong stability, we show that the problem is NP-complete even for complete lists. These problems can be regarded as special types of stable exchange problems, therefore these results have relevance in some real applications, such as kidney exchange programs.

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Section: Kidney Exchange Problemmentioning

confidence: 99%

Three-Sided Stable Matchings with Cyclic Preferences

Bíró

McDermid

2009

Algorithmica

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“…The game-theoretical approaches were introduced in [43,44] and [6] to study the kidney exchange problem. In these kidney exchange game models, there also exist a lot of NP-complete problems [14,[45][46][47]. Developing randomized methods for those NP-complete problems is also an interesting research topic for the future research.…”

Section: Discussionmentioning

confidence: 99%

Randomized Parameterized Algorithms for the Kidney Exchange Problem

Lin

Wang

et al. 2019

Algorithms

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In order to increase the potential kidney transplants between patients and their incompatible donors, kidney exchange programs have been created in many countries. In the programs, designing algorithms for the kidney exchange problem plays a critical role. The graph theory model of the kidney exchange problem is to find a maximum weight packing of vertex-disjoint cycles and chains for a given weighted digraph. In general, the length of cycles is not more than a given constant L (typically 2 ≤ L ≤ 5), and the objective function corresponds to maximizing the number of possible kidney transplants. In this paper, we study the parameterized complexity and randomized algorithms for the kidney exchange problem without chains from theory. We construct two different parameterized models of the kidney exchange problem for two cases L = 3 and L ≥ 3 , and propose two randomized parameterized algorithms based on the random partitioning technique and the randomized algebraic technique, respectively.

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“…Most works relating to the core of housing markets aim for finding core allocations with some additional property that benefits global welfare, most prominently Pareto optimality [26,4,5,32,37]. Another line of research comes from kidney exchange where the length of trading cycles is of great importance and often plays a role in agents' preferences [33,16,15,7,17] or is bounded by some constant [2,10,11,24,18]. None of these papers deal with problems where a core allocation is required to fulfill some constraint regarding a given agent or set of agents-that they be trading, or that they obtain (or not obtain) a certain house.…”

Section: Related Workmentioning

confidence: 99%

The core of housing markets from an agent's perspective: Is it worth sprucing up your home?

Schlotter¹,

Bíró²,

Fleiner³

2021

Preprint

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We study housing markets as introduced by Shapley and Scarf [38]. We investigate the computational complexity of various questions regarding the situation of an agent a in a housing market H: we show that it is NP-hard to find an allocation in the core of H where (i) a receives a certain house, (ii) a does not receive a certain house, or (iii) a receives a house other than her own. We prove that the core of housing markets respects improvement in the following sense: given an allocation in the core of H where agent a receives a house h, if the value of the house owned by a increases, then the resulting housing market admits an allocation where a receives either h, or a house that she prefers to h; moreover, such an allocation can be found efficiently. We further show an analogous result in the Stable Roommates setting by proving that stable matchings in a one-sided market also respect improvement.

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The kidney exchange problem: How hard is it to find a donor?

Cited by 10 publications

References 22 publications

Three-Sided Stable Matchings with Cyclic Preferences

Three-Sided Stable Matchings with Cyclic Preferences

Randomized Parameterized Algorithms for the Kidney Exchange Problem

The core of housing markets from an agent's perspective: Is it worth sprucing up your home?

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