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Open AccessArticle

Randomized Parameterized Algorithms for the Kidney Exchange Problem

by 1,2,3, 1,*, 1 and 4
1
School of Computer Science and Engineering, Central South University, Changsha 410083, China
2
School of Computer Science and Technology, Hengyang Normal University, Hengyang 421002, China
3
Hunan Provincial Key Laboratory of Intelligent Information Processing and Application, Hengyang 421002, China
4
Department of Computer Science, The University of Texas Rio Grande Valley, Edinburg, TX 78539, USA
*
Author to whom correspondence should be addressed.
Algorithms 2019, 12(2), 50; https://doi.org/10.3390/a12020050
Received: 28 December 2018 / Revised: 20 February 2019 / Accepted: 21 February 2019 / Published: 25 February 2019
(This article belongs to the Special Issue New Frontiers in Parameterized Complexity and Algorithms)
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. View Full-Text
Keywords: kidney exchange problem; randomized algorithm; parameterized algorithm; random partitioning; multilinear monomial detection kidney exchange problem; randomized algorithm; parameterized algorithm; random partitioning; multilinear monomial detection
MDPI and ACS Style

Lin, M.; Wang, J.; Feng, Q.; Fu, B. Randomized Parameterized Algorithms for the Kidney Exchange Problem. Algorithms 2019, 12, 50.

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