scholarly journals Cycle packing

2014 ◽  
Vol 45 (4) ◽  
pp. 608-626 ◽  
Author(s):  
David Conlon ◽  
Jacob Fox ◽  
Benny Sudakov
Keyword(s):  
Cycle Packing

scholarly journals MAXIMUM WEIGHT CYCLE PACKING IN DIRECTED GRAPHS, WITH APPLICATION TO KIDNEY EXCHANGE PROGRAMS

2009 ◽  
Vol 01 (04) ◽  
pp. 499-517 ◽  
Author(s):  
PÉTER BIRÓ ◽  
DAVID F. MANLOVE ◽  
ROMEO RIZZI
Keyword(s):  
Directed Graphs ◽  
Exact Algorithm ◽  
Maximum Size ◽  
Practical Experience ◽  
Optimal Solutions ◽  
Maximum Weight ◽  
Packing Problems ◽  
Exchange Programs ◽  
Kidney Exchange ◽  
Cycle Packing

Centralized matching programs have been established in several countries to organize kidney exchanges between incompatible patient-donor pairs. At the heart of these programs are algorithms to solve kidney exchange problems, which can be modelled as cycle packing problems in a directed graph, involving cycles of length 2, 3, or even longer. Usually, the goal is to maximize the number of transplants, but sometimes the total benefit is maximized by considering the differences between suitable kidneys. These problems correspond to computing cycle packings of maximum size or maximum weight in directed graphs. Here we prove the APX-completeness of the problem of finding a maximum size exchange involving only 2-cycles and 3-cycles. We also present an approximation algorithm and an exact algorithm for the problem of finding a maximum weight exchange involving cycles of bounded length. The exact algorithm has been used to provide optimal solutions to real kidney exchange problems arising from the National Matching Scheme for Paired Donation run by NHS Blood and Transplant, and we describe practical experience based on this collaboration.

The Parameterized Complexity of Cycle Packing: Indifference is Not an Issue

Algorithmica ◽  
2019 ◽  
Vol 81 (9) ◽  
pp. 3803-3841 ◽  
Author(s):  
R. Krithika ◽  
Abhishek Sahu ◽  
Saket Saurabh ◽  
Meirav Zehavi
Keyword(s):  
Parameterized Complexity ◽  
Cycle Packing

scholarly journals Maximum cycle packing in Eulerian graphs using local traces

2015 ◽  
Vol 35 (1) ◽  
pp. 121 ◽  
Author(s):  
Peter Recht ◽  
Eva-Maria Sprengel
Keyword(s):  
Eulerian Graphs ◽  
Cycle Packing

scholarly journals Kernelization of Cycle Packing with Relaxed Disjointness Constraints

2018 ◽  
Vol 32 (3) ◽  
pp. 1619-1643
Author(s):  
Akanksha Agrawal ◽  
Daniel Lokshtanov ◽  
Diptapriyo Majumdar ◽  
Amer E. Mouawad ◽  
Saket Saurabh
Keyword(s):  
Cycle Packing

Approximation algorithms and hardness results for cycle packing problems

2007 ◽  
Vol 3 (4) ◽  
pp. 48 ◽  
Author(s):  
Michael Krivelevich ◽  
Zeev Nutov ◽  
Mohammad R. Salavatipour ◽  
Jacques Verstraete ◽  
Raphael Yuster
Keyword(s):  
Approximation Algorithms ◽  
Packing Problems ◽  
Cycle Packing
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