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.

scholarly journals BEYOND MAXIMUM INDEPENDENT SET: AN EXTENDED MODEL FOR POINT-FEATURE LABEL PLACEMENT

2016 ◽  
Vol XLI-B2 ◽  
pp. 109-114
Author(s):  
Jan-Henrik Haunert ◽  
Alexander Wolff
Keyword(s):  
Classical Problem ◽  
Independent Set ◽  
Exact Algorithm ◽  
Maximum Independent Set ◽  
Extended Model ◽  
Optimal Solutions ◽  
Maximum Weight ◽  
Map Labeling ◽  
Label Placement ◽  
Point Feature

Map labeling is a classical problem of cartography that has frequently been approached by combinatorial optimization. Given a set of features in the map and for each feature a set of label candidates, a common problem is to select an independent set of labels (that is, a labeling without label–label overlaps) that contains as many labels as possible and at most one label for each feature. To obtain solutions of high cartographic quality, the labels can be weighted and one can maximize the total weight (rather than the number) of the selected labels. We argue, however, that when maximizing the weight of the labeling, interdependences between labels are insufficiently addressed. Furthermore, in a maximum-weight labeling, the labels tend to be densely packed and thus the map background can be occluded too much. We propose extensions of an existing model to overcome these limitations. Since even without our extensions the problem is NP-hard, we cannot hope for an efficient exact algorithm for the problem. Therefore, we present a formalization of our model as an integer linear program (ILP). This allows us to compute optimal solutions in reasonable time, which we demonstrate for randomly generated instances.

scholarly journals BEYOND MAXIMUM INDEPENDENT SET: AN EXTENDED MODEL FOR POINT-FEATURE LABEL PLACEMENT

2016 ◽  
Vol XLI-B2 ◽  
pp. 109-114
Author(s):  
Jan-Henrik Haunert ◽  
Alexander Wolff
Keyword(s):  
Classical Problem ◽  
Independent Set ◽  
Exact Algorithm ◽  
Maximum Independent Set ◽  
Extended Model ◽  
Optimal Solutions ◽  
Maximum Weight ◽  
Map Labeling ◽  
Label Placement ◽  
Point Feature

Map labeling is a classical problem of cartography that has frequently been approached by combinatorial optimization. Given a set of features in the map and for each feature a set of label candidates, a common problem is to select an independent set of labels (that is, a labeling without label–label overlaps) that contains as many labels as possible and at most one label for each feature. To obtain solutions of high cartographic quality, the labels can be weighted and one can maximize the total weight (rather than the number) of the selected labels. We argue, however, that when maximizing the weight of the labeling, interdependences between labels are insufficiently addressed. Furthermore, in a maximum-weight labeling, the labels tend to be densely packed and thus the map background can be occluded too much. We propose extensions of an existing model to overcome these limitations. Since even without our extensions the problem is NP-hard, we cannot hope for an efficient exact algorithm for the problem. Therefore, we present a formalization of our model as an integer linear program (ILP). This allows us to compute optimal solutions in reasonable time, which we demonstrate for randomly generated instances.

The Mathematics behind Lifesaving Kidney Exchange Programs

Math Horizons ◽  
2010 ◽  
Vol 18 (1) ◽  
pp. 26-29
Author(s):  
Olivia M. Carducci
Keyword(s):  
Exchange Programs ◽  
Kidney Exchange

scholarly journals Approximating Maximum Weight Cycle Covers in Directed Graphs with Weights Zero and One

Algorithmica ◽  
2005 ◽  
Vol 42 (2) ◽  
pp. 121-139 ◽  
Author(s):  
Markus Bläser ◽  
Bodo Manthey
Keyword(s):  
Directed Graphs ◽  
Maximum Weight ◽  
Cycle Covers

scholarly journals Development automated capture device for picking apples

2021 ◽  
Vol 285 ◽  
pp. 07025
Author(s):  
Dmitriy Khort ◽  
Alexey Kutyrev ◽  
Igor Smirnov ◽  
Daniil Pupin
Keyword(s):  
Final Stage ◽  
Maximum Size ◽  
Stepper Motor ◽  
Fruit Crops ◽  
Maximum Weight ◽  
Operating Modes ◽  
Minimal Damage ◽  
Series Of Experiments

In the system of the mechanized process of cultivation of fruit crops, harvesting is an important final stage, which requires the development of new, convenient, including those that do not damage the fruit, automated technical devices. As a result of a series of experiments, the operability of the developed automated fruit picking device was confirmed, it gently captures the fruit and reliably holds it. The operating modes of the automated device for picking fruits have been established. The following characteristics of the device for picking fruits were revealed: the time for a complete capture of the apple is from 1.5 seconds to 2 seconds, depending on their size, the maximum size of the captured apple is 85x80 mm, the maximum weight of the captured apple is 400 g. The permissible pressure of the paws of the device on the fruit is determined ... It was found that with the force of the linear stepper motor on the pusher in 8N, the safety of the apple is ensured with minimal damage, while the apple is securely fixed in the capture paws.

scholarly journals Exact and Approximate Algorithms for Computing Betweenness Centrality in Directed Graphs

2021 ◽  
Vol 182 (3) ◽  
pp. 219-242
Author(s):  
Mostafa Haghir Chehreghani ◽  
Albert Bifet ◽  
Talel Abdessalem
Keyword(s):  
Betweenness Centrality ◽  
Directed Graphs ◽  
Randomized Algorithm ◽  
Exact Algorithm ◽  
Directed Network ◽  
Weighted Graphs ◽  
Single Vertex ◽  
Small Constant ◽  
Positive Weights ◽  
Real World Datasets

Graphs (networks) are an important tool to model data in different domains. Realworld graphs are usually directed, where the edges have a direction and they are not symmetric. Betweenness centrality is an important index widely used to analyze networks. In this paper, first given a directed network G and a vertex r ∈ V (G), we propose an exact algorithm to compute betweenness score of r. Our algorithm pre-computes a set ℛ𝒱(r), which is used to prune a huge amount of computations that do not contribute to the betweenness score of r. Time complexity of our algorithm depends on |ℛ𝒱(r)| and it is respectively Θ(|ℛ𝒱(r)| · |E(G)|) and Θ(|ℛ𝒱(r)| · |E(G)| + |ℛ𝒱(r)| · |V(G)| log |V(G)|) for unweighted graphs and weighted graphs with positive weights. |ℛ𝒱(r)| is bounded from above by |V(G)| – 1 and in most cases, it is a small constant. Then, for the cases where ℛ𝒱(r) is large, we present a simple randomized algorithm that samples from ℛ𝒱(r) and performs computations for only the sampled elements. We show that this algorithm provides an (ɛ, δ)-approximation to the betweenness score of r. Finally, we perform extensive experiments over several real-world datasets from different domains for several randomly chosen vertices as well as for the vertices with the highest betweenness scores. Our experiments reveal that for estimating betweenness score of a single vertex, our algorithm significantly outperforms the most efficient existing randomized algorithms, in terms of both running time and accuracy. Our experiments also reveal that our algorithm improves the existing algorithms when someone is interested in computing betweenness values of the vertices in a set whose cardinality is very small.

An Exact Algorithm for Large-Scale Continuous Nonlinear Resource Allocation Problems with Minimax Regret Objectives

2021 ◽  
Author(s):  
Jungho Park ◽  
Hadi El-Amine ◽  
Nevin Mutlu
Keyword(s):  
Resource Allocation ◽  
Objective Function ◽  
Large Scale ◽  
Computational Study ◽  
Optimal Solution ◽  
Exact Algorithm ◽  
Minimax Regret ◽  
Optimal Solutions ◽  
Heuristic Approaches ◽  
Exact Approach

We study a large-scale resource allocation problem with a convex, separable, not necessarily differentiable objective function that includes uncertain parameters falling under an interval uncertainty set, considering a set of deterministic constraints. We devise an exact algorithm to solve the minimax regret formulation of this problem, which is NP-hard, and we show that the proposed Benders-type decomposition algorithm converges to an [Formula: see text]-optimal solution in finite time. We evaluate the performance of the proposed algorithm via an extensive computational study, and our results show that the proposed algorithm provides efficient solutions to large-scale problems, especially when the objective function is differentiable. Although the computation time takes longer for problems with nondifferentiable objective functions as expected, we show that good quality, near-optimal solutions can be achieved in shorter runtimes by using our exact approach. We also develop two heuristic approaches, which are partially based on our exact algorithm, and show that the merit of the proposed exact approach lies in both providing an [Formula: see text]-optimal solution and providing good quality near-optimal solutions by laying the foundation for efficient heuristic approaches.

Kidney Exchange Programs in Europe (COST-ENCKEP); What Can We Learn from Each Other?

2018 ◽  
Vol 102 ◽  
pp. S508
Author(s):  
Bernadette J.J.M. Haase-Kromwijk ◽  
Aline Hemke ◽  
Peter Biró ◽  
Lisa Burnapp ◽  
Rachel Johnson ◽  
...  
Keyword(s):  
Exchange Programs ◽  
Kidney Exchange

Maximizing expected number of transplants in kidney exchange programs

2016 ◽  
Vol 52 ◽  
pp. 269-276 ◽  
Author(s):  
Filipe Alvelos ◽  
Xenia Klimentova ◽  
Abdur Rais ◽  
Ana Viana
Keyword(s):  
Expected Number ◽  
Exchange Programs ◽  
Kidney Exchange

scholarly journals Pairwise Kidney Exchange over the Blood Group Barrier

2019 ◽  
Vol 87 (3) ◽  
pp. 1091-1133 ◽  
Author(s):  
Tommy Andersson ◽  
Jörgen Kratz
Keyword(s):  
Kidney Transplant ◽  
Blood Group ◽  
Medical Technology ◽  
Immunosuppressive Treatment ◽  
Preference Domain ◽  
Exchange Programs ◽  
Kidney Exchange ◽  
Patient Groups ◽  
To Receive ◽  
Positive Effect

Abstract Advances in medical technology have made kidney transplants over the blood group barrier feasible. This article investigates how such technology should be implemented when designing pairwise kidney exchange programs. The possibility to receive a kidney transplant from a blood group incompatible donor motivates an extension of the preference domain, allowing patients to distinguish between compatible donors and half-compatible donors (i.e. blood group incompatible donors that only become compatible after undergoing an immunosuppressive treatment). It is demonstrated that the number of transplants can be substantially increased by providing an incentive for patients with half-compatible donors to participate in kidney exchange programs. The results also suggest that the technology is beneficial for patient groups that are traditionally disadvantaged in kidney exchange programs (e.g. blood group O patients). The positive effect of allowing transplants over the blood group barrier is larger than the corresponding effects of including altruistic patient–donor pairs or of allowing three-way exchanges in addition to pairwise exchanges.

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