Pith. sign in

REVIEW 2 major objections 2 minor 31 references

Complexity and Manipulation of International Kidney Exchange Programmes with Country-Specific Parameters

T0 review · 2 major / 2 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read International kidney-exchange pools can be run by a mechanism that no country can profit by manipulating through its segment limits, and the paper pins down the exact computational and welfare price of that safety.

desk verdict The complexity dichotomy is a real contribution, but the paper's main mechanism theorem is false. read the letter →

arxiv 2506.04092 v2 pith:SA3RW7PT submitted 2025-06-04 cs.GT cs.CCecon.TH

Rachael Colley , David Manlove , Daniel Paulusma , Mengxiao Zhang This is my paper
classification cs.GTcs.CCecon.TH MSC 05C7068Q1791B68
keywords kidneyexchangeinternationalcyclepackingcomputationalcomplexityNP-hardnessmechanismdesignincentivecompatibilityindividualrationality
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

International kidney exchange pools let countries share recipient-donor pairs, but each country has its own logistical limits on how international transplant cycles may touch its patients: the maximum size of a consecutive block of its own pairs (segment size) and the maximum number of times a cycle may enter the country (segment number). This paper gives a complete complexity dichotomy for finding the maximum feasible cycle packing under any such parameter set $\Gamma$: only seven parameter regimes are tractable, via reductions to matching, and in every other regime the problem is NP-hard (no efficient exact algorithm is believed to exist) even when only two countries are involved. Its central contribution is a mechanism, $\mathcal{M}_{\text{order}}$, that provably guarantees individual rationality — no country does worse than by leaving the pool — and incentive compatibility with respect to segment size and segment number: no country can increase its own transplants by reporting lower limits. The worst-case welfare loss of $\mathcal{M}_{\text{order}}$ is at most $\max\{c_{\text{int}}, d^*\}$, where $c_{\text{int}}$ is the longest feasible international cycle and $d^*$ the maximum, over international cycles, of the number of international cycles that share a vertex with it; matching lower bounds for all individually rational mechanisms and all incentive-compatible mechanisms show this ratio is asymptotically optimal. Simulations on realistic data indicate the practical cost of this honesty guarantee is modest — around 72% of the unrestricted optimum's transplants and 84% more than purely national exchange.

What carries the argument

The central object is the $\Gamma$-cycle packing: a vertex-disjoint set of directed cycles in the compatibility graph, each obeying the country-specific tuple $\Gamma$ — a per-country national cycle length limit, a collectively agreed international cycle length limit (icl), and per-country caps on the size of a consecutive segment of that country's pairs inside an international cycle (iss) and on the number of such segments (isn). The hardness half of the dichotomy is carried by gadget reductions from Perfect 3-Dimensional and 4-Dimensional Matching; each gadget confines every feasible cycle to a single clause, and a 'long segment' of $m=\text{iss}_j+1$ consecutive vertices in the enclosing country blocks any cycle that would traverse two gadgets. The tractable regimes all reduce to maximum matching in a general or bipartite graph, because under those parameters every feasible cycle has length at most two or the problem decomposes cleanly by country. The mechanism $\mathcal{M}_{\text{order}}$ is carried by three components: the pre-selected maximum national packing (which secures individual rationality), the random order over candidate international cycles (which gives every feasible international cycle a selection probability of at least $1/d^*$), and the substitution rule that replaces a turnable non-$\Gamma$ cycle by a uniformly chosen sub-cycle with at most one segment per country (which makes a country's expected utility monotone under downward misreporting of its limits). The load-bearing identity is the bound $\max\{c_{\text{int}}, d^*\}$: the national pre-selection loses at most a factor $c_{\text{int}}$ against the international part of the optimum, the random selection loses at most a factor $d^*$, and the two factors combine into the maximum.

What would settle it

Systematically search all small two-country compatibility graphs and parameter values for a single instance in which a country strictly increases its expected number of transplants by declaring a lower international segment size or segment number; Theorem 4 asserts no such instance exists, so one concrete hit would refute the central mechanism claim. Independently, a polynomial-time algorithm for any parameter set outside the seven regimes listed in Theorem 2 — for instance $n=3$ with international cycle limit 3 and all other limits minimal — would falsify the claimed dichotomy.

Watch

Extended reading notes

Core claim

The paper's central claims are threefold. First, it completely classifies the complexity of Max $\Gamma$-Cycle Packing, the problem of finding a vertex-disjoint set of feasible cycles that maximises the number of transplants: for every fixed tuple $\Gamma=(n,\text{icl},\text{ncl},\text{iss},\text{isn})$, the problem is polynomial-time solvable in exactly seven regimes and NP-hard — even for the perfect-packing decision version — in every other regime, with hardness appearing already for two countries and with parameter values that are each individually tractable in the single-country setting (Theorem 2). Second, it shows that the natural maximum-packing mechanism $\mathcal{M}_{\text{int}}$ is neither individually rational nor incentive compatible, and more strongly that no mechanism can be both efficient and IR (Proposition 1) or both nonempty and IC (Proposition 4). Third, it designs $\mathcal{M}_{\text{order}}$, which pre-selects a maximum national $\Gamma$-cycle packing to secure IR and then, over the remaining graph, greedily adds international cycles in a random order, replacing each 'turnable' non-$\Gamma$ cycle by a uniformly random substitute that is itself an international $\Gamma$-cycle with at most one segment per country. The paper proves $\mathcal{M}_{\text{order}}$ is IC with respect to segment size and segment number (Theorem 4), that its approximation ratio is at most $\max\{c_{\text{int}}, d^*\}$, and that this bound is tight and asymptotically optimal because no IR mechanism can beat $c_{\text{int}}$ and no IC mechanism can beat $d^*$ (Theorems 3 and 5).

Load-bearing premise

Countries may misreport their international segment size and segment number only by declaring lower values, while their national cycle limits are public and fixed; if a country could also declare larger limits, the mechanism's incentive-compatibility guarantee is not established, and one exhibited instance already shows $\mathcal{M}_{\text{order}}$ can be manipulated through the national cycle limit.

Editorial extensions

If this is right

  • Planners get an exact worst-case map: in all but seven parameter regimes, optimising an international exchange round is NP-hard even with two countries, and the seven tractable regimes reduce to matching problems solvable in polynomial time.
  • The merged-pool optimum is strategically unusable: because it is neither individually rational nor incentive compatible, and because no efficient-IR or nonempty-IC mechanism exists, $\mathcal{M}_{\text{order}}$ is the first round mechanism to achieve both properties.
  • The worst-case price of honesty is exactly bounded: any IR mechanism must lose a factor $c_{\text{int}}$ and any IC mechanism a factor $d^*$, and $\mathcal{M}_{\text{order}}$ attains $\max\{c_{\text{int}}, d^*\}$ — asymptotically no IR-and-IC mechanism can do better.
  • In expectation the price is much smaller: simulations show $\mathcal{M}_{\text{order}}$ delivers about 72% of the unconstrained optimum's transplants, about 91% of the individually rational but manipulable consecutive mechanism's, and 84% more than purely national exchange.
  • The guarantee stops at the international segment parameters: $\mathcal{M}_{\text{order}}$ is not IC with respect to national cycle limits, and Example 4 exhibits a country that gains by under-reporting its national limit.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The incentive guarantee rests on the assumption that countries may only report strictly lower segment sizes or segment numbers; if manipulation were two-sided, the proof of Theorem 4 would not go through, and testing for profitable upward misreports is the most direct stress test of the design.
  • The substitution trick — replacing an invalid long cycle by a uniformly random valid sub-cycle to keep expected utilities monotone — is a transferable design for other allocation problems with per-agent quota constraints, such as organ allocation with regional caps or matching with coarse priorities.
  • Because the lower-bound constructions for IC mechanisms rely on very long international cycles, the manipulation risk that $\mathcal{M}_{\text{order}}$ guards against may be small in today's IKEPs; the paper itself notes the constructions become more relevant once long non-directed-donor chains are allowed.
  • Completing the incentive picture requires a mechanism that is also IC with respect to national cycle limits, or a proof that no such mechanism exists — Example 4 shows the obstruction is concrete rather than a proof artefact.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 2 minor

Summary. The paper studies international kidney exchange programmes with country-specific parameters, encoded as a tuple Γ. It contributes a complete complexity dichotomy for the problem of finding a maximum Γ-cycle packing (Theorem 2), and a mechanism M_order that is claimed to be individually rational (IR) and incentive compatible (IC) with respect to international segment size and segment number (Theorem 4), with an approximation ratio of at most max{c_int, d*} that is tight and asymptotically optimal (Theorem 5). The paper also reports simulations suggesting that M_order performs well in practice. The complexity dichotomy is a substantial combinatorial contribution, but the mechanism-design results contain a fundamental error: the claimed selection probabilities in the random-order greedy procedure are not correct, and Theorem 5 is false as stated.

Significance. If the complexity dichotomy is correct, it provides a complete classification of the tractability of maximum Γ-cycle packing for all parameter sets, building on and extending the single-country result of Abraham et al. This is a valuable contribution to the algorithmic kidney-exchange literature. The mechanism M_order is an interesting proposal for combining IR and IC in a multi-country setting, and the simulation study with released code and data is a useful practical addition. However, the central theoretical claims about M_order are not merely unproven; Theorem 5 is contradicted by a concrete instance, and the proof of Theorem 4 rests on a false assertion about selection probabilities. Thus the mechanism-design half of the paper, which is a headline contribution in the abstract and introduction, cannot be accepted in its current form.

major comments (2)
  1. [Section 4.2, Theorem 4 proof]
  2. [Section 4.2, Theorem 5, inequality (6)]
minor comments (2)
  1. [Example 1]
  2. [Theorem 4 proof]

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper's theorems are derived from independent hardness reductions and direct probabilistic arguments, not from fitted inputs or self-citations.

full rationale

The paper's central claims are self-contained in the relevant sense. The complexity dichotomy (Theorem 2) reduces from Perfect 3-Dimensional Matching and Perfect 4-Dimensional Matching, which are independent NP-complete problems, and the only external complexity result, Theorem 1 of Abraham et al. [1], is cited for the single-country base case and is not authored by the present authors. The mechanism design results are proven directly: IR follows from Step 1 of Algorithm 1, IC is established in Theorem 4 via an explicit comparison of expected utilities under true and misreported parameters, and the approximation ratio in Theorem 5 is bounded against opt(I) using inequalities (5)-(8), with tightness and asymptotic optimality shown by constructed examples. No parameter is fitted to simulation data, and no 'prediction' is a renamed input or fitted value. The downward-only misreporting assumption is an explicitly stated modelling restriction, not a conclusion smuggled in by definition; moreover, the paper explicitly demonstrates in Example 4 that Morder is not IC with respect to ncl, which confirms the IC notion is not vacuous. The possible flaw in the selection-probability claim underlying inequality (6), if it exists, would be a correctness gap in the proof, not a circular derivation, because it does not make the theorem's conclusion equivalent to its assumptions by construction. Self-citations to prior work by the same authors appear only in related-work context or as a simulation generator, and none is load-bearing for the new theorems. Hence no circularity is present.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The central claims rely on standard complexity assumptions, the public-knowledge and non-manipulability of ncl, and the downward-only misreporting model for iss and isn. No free parameters are fitted to data, and no new entities are postulated.

assumptions (6)
  • standard math NP-completeness of Perfect 3-Dimensional Matching and Perfect 4-Dimensional Matching
    Used as source problems for the hardness reductions in Appendix A.1.
  • standard math Polynomial-time solvability of maximum weight perfect matching in general and bipartite graphs, including Edmonds' algorithm
    Underpins the polynomial cases in Theorem 2 where all Gamma-cycles have length at most 2, and the folklore reduction for unbounded cycle packing.
  • domain assumption Countries can misreport segment size and segment number only by reporting lower values, due to resource limits
    Defines the IC notion in Section 4 and is load-bearing for Morder; upward misreports are excluded by assumption.
  • domain assumption National cycle limits ncl_i are public knowledge and not manipulable
    Stated in Section 1.2; Morder is shown not to be IC with respect to ncl in Example 4, so this assumption is essential.
  • domain assumption Every country is willing to participate in international cycles, so iss_i >= 1 and isn_i >= 1
    Assumed in Section 2 after discussing the iss=0 example.
  • domain assumption Non-directed donors, compatible pairs, and weighted objectives are excluded from the model
    Scope restrictions stated in Sections 1.2 and 2; they limit applicability to some real KEPs.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Complexity and Manipulation of International Kidney Exchange Programmes with Country-Specific Parameters." pith.science (2026). https://pith.science/paper/SA3RW7PT

@misc{pith2026250604092,
  author       = {Pith},
  title        = {Pith review of: Complexity and Manipulation of International Kidney Exchange Programmes with Country-Specific Parameters},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SA3RW7PT}},
  note         = {Machine review of arXiv:2506.04092}
}
abstract

Kidney Exchange Programmes (KEPs) facilitate the exchange of kidneys, and larger pools of recipient-donor pairs tend to yield proportionally more transplants, leading to the proposal of international KEPs (IKEPs). However, as studied by \citet{mincu2021ip}, practical limitations must be considered in IKEPs to ensure that countries remain willing to participate. Thus, we study IKEPs with country-specific parameters, represented by a tuple $\Gamma$, restricting the selected transplants to be feasible for the countries to conduct, e.g., imposing an upper limit on the number of consecutive exchanges within a country's borders. We provide a complete complexity dichotomy for the problem of finding a feasible (according to the constraints given by $\Gamma$) cycle packing with the maximum number of transplants, for every possible $\Gamma$. We also study the potential for countries to misreport their parameters to increase their allocation. As manipulation can harm the total number of transplants, we propose a novel individually rational and incentive compatible mechanism $\mathcal{M}_{\text{order}}$. We first give a theoretical approximation ratio for $\mathcal{M}_{\text{order}}$ in terms of the number of transplants, and show that the approximation ratio of $\mathcal{M}_{\text{order}}$ is asymptotically optimal. We then use simulations which suggest that, in practice, the performance of $\mathcal{M}_{\text{order}}$ is significantly better than this worst-case ratio.

Figures

Figures reproduced from arXiv: 2506.04092 by the authors.

Figure 1
Figure 1. An IKEP pool involving countries 𝐻 and 𝐽. Country 𝐻 and Country 𝐽’s pools comprise pairs ℎ1 and ℎ2, and 𝑗1 and 𝑗2, respectively. Full arcs are national arcs. Dashed arrows are international arcs [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. The gadget that is used in the proof of Lemma 1. [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. The three examples from Propositions 1, 3 and 4. [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (17 more)
Figure 4
Figure 4. Figure 4: The example used to prove the lower bound for the approximation ratio in Theorem 3. [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]
Figure 5
Figure 5. Figure 5: The graphs from Example 3 and Remark 1. 1 3 · 𝐿 + 1 3 · 𝐿 = 2 3 𝐿. Hence, in this case, country 1 can benefit significantly from misreporting (if 𝐿 is large), so our modified mechanism would not be IC. ⋄ We now analyse the running time of Morder. Proposition 5. Morder …
Figure 6
Figure 6. Figure 6: An illustration of the cycles in X (𝐺ˆ) for instances 𝐼 (top figure) and 𝐼 ′ (bottom figure). We first consider instance 𝐼. We partition Z into sets Z1 and Z2 as follows. Let Z1 consist of all Γ-cycles in Z that are not substitutes for turnable cycles in X (𝐺ˆ) for 𝐼. …
Figure 7
Figure 7. Figure 7: The graph (𝐺, V) showing that Morder is not IC with respect to ncl. Note that N = {𝐻, 𝐽 } and the vertices in 𝑉𝐻 and 𝑉𝐽 are represented by square and circular vertices, respectively. Assume country 1 misreports either its segment size iss1 or its segment number isn1 by…
Figure 8
Figure 8. Figure 8: Performance of Mcon,Morder,Mnat compared with Mint when varying a single parameter [PITH_FULL_IMAGE:figures/full_fig_p020_8.png]
Figure 9
Figure 9. Figure 9: Performance of Mint,Mcon,Morder,Mnat. The results on Small Γ, Proportional, and Large Γ are shown in the left, middle and right plots, respectively. ncl = {4} 3 , icl = 5, iss = {2} 3 . We do not consider the case where isn = {3} 3 when icl = 4, 5, as the international…
Figure 10
Figure 10. Figure 10: Gadget used in the proof of Lemma 3 showing NP-hardness when [PITH_FULL_IMAGE:figures/full_fig_p027_10.png]
Figure 11
Figure 11. Figure 11: Gadget used in the proof of Lemma 4 when [PITH_FULL_IMAGE:figures/full_fig_p029_11.png]
Figure 12
Figure 12. Figure 12: Gadget used in the proof of Lemma 6 showing NP-hardness when [PITH_FULL_IMAGE:figures/full_fig_p031_12.png]
Figure 13
Figure 13. Figure 13: Gadget used in the proof of Lemmas 10 and 11. Note that we let [PITH_FULL_IMAGE:figures/full_fig_p032_13.png]
Figure 14
Figure 14. Figure 14: Gadget used in the proof of Lemma 12 showing NP-hardness when [PITH_FULL_IMAGE:figures/full_fig_p035_14.png]
Figure 15
Figure 15. Figure 15: Gadget used in the proof of Lemma 1 showing NP-hardness when [PITH_FULL_IMAGE:figures/full_fig_p037_15.png]
Figure 16
Figure 16. Figure 16: Gadget used in the proof of Lemma 13 when [PITH_FULL_IMAGE:figures/full_fig_p039_16.png]
Figure 17
Figure 17. Figure 17: For the gadget corresponding to 𝑡𝑖 , we add the vertices {𝑤 1 𝑖 , · · · ,𝑤𝑚 𝑖 , 𝑥1 𝑖 , · · · , 𝑥𝑚 𝑖 , 𝑦1 𝑖 , · · · , 𝑦𝑚 𝑖 , 𝑧 1 𝑖 , · · · , 𝑧 𝑚 𝑖 , 𝑎 1 𝑖 , . . . 𝑎8 𝑖 }. Hence, the vertex set is: 𝑉 = 𝑋 ∪ 𝑌 ∪ 𝑍 ∪ {𝑎 1 𝑖 , · · · , 𝑎8 𝑖 ,𝑤1 𝑖 , · · · ,𝑤𝑚 𝑖 , 𝑥1 𝑖 , · · ·…
Figure 17
Figure 17. Figure 17: Gadget used in the proof of Lemma 14 showing NP-hardness when [PITH_FULL_IMAGE:figures/full_fig_p041_17.png]
Figure 18
Figure 18. Figure 18: Gadget used in the proof of Lemma 15 showing NP-hardness when [PITH_FULL_IMAGE:figures/full_fig_p043_18.png]
Figure 19
Figure 19. Figure 19: Gadget used in the proof of Lemma 15 showing NP-hardness when [PITH_FULL_IMAGE:figures/full_fig_p045_19.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

31 extracted references · 30 canonical work pages

  1. [1]

    Abraham, Avrim Blum, and Tuomas Sandholm

    David J. Abraham, Avrim Blum, and Tuomas Sandholm. 2007. Clearing Algorithms for Barter Exchange Markets: Enabling Nationwide Kidney Exchanges. InProceedings of EC ’07: the 8th ACM Conference on Electronic Commerce International Kidney Exchange Programmes with Country-Specific Parameters (San Diego, California, USA). Association for Computing Machinery, N...

    work page 2007

  2. [2]

    Nikhil Agarwal, Itai Ashlagi, Eduardo Azevedo, Clayton R Featherstone, and Ömer Karaduman. 2019. Market failure in kidney exchange.American Economic Review109, 11 (2019), 4026–4070

    work page 2019

  3. [3]

    Itai Ashlagi and Alvin E Roth. 2014. Free riding and participation in large scale, multi-hospital kidney exchange. Theoretical Economics9, 3 (2014), 817–863

    work page 2014

  4. [4]

    D. A. Axelrod, M. A. Schnitzler, H. Xiao, W. Irish, E. Tuttle-Newhall, S.-H. Chang, B. L. Kasiske, T. Alhamad, and K. L. Lentine. 2018. An economic assessment of contemporary kidney transplant practice.American Journal of Transplantation18 (2018), 1168–1176

    work page 2018

  5. [5]

    Márton Benedek, Péter Biró, Walter Kern, and Daniël Paulusma. 2022. Computing Balanced Solutions for Large International Kidney Exchange Schemes. InProceedings of the 21st International Conference on Autonomous Agents and Multiagent Systems(Virtual Event, New Zealand)(AAMAS ’22). International Foundation for Autonomous Agents and Multiagent Systems, Richl...

    work page 2022

  6. [6]

    Márton Benedek, Péter Biró, Daniel Paulusma, and Xin Ye. 2024. Computing balanced solutions for large international kidney exchange schemes.Autonomous Agents and Multi-Agent Systems38, 1 (2024), 1–41

    work page 2024

  7. [7]

    BuildingKidneyExchangeProgrammesinEurope–AnOverview of Exchange Practice and Activities.Transplantation103 (2019), 1514–1522

    PéterBiróandBernadetteHaase-Kromwijketal.2019. BuildingKidneyExchangeProgrammesinEurope–AnOverview of Exchange Practice and Activities.Transplantation103 (2019), 1514–1522

    work page 2019

  8. [8]

    Péter Biró, Márton Gyetvai, Xenia Klimentova, João Pedro Pedroso, William Pettersson, and Ana Viana. 2020. Compensation Scheme With Shapley Value For Multi-Country Kidney Exchange Programmes. InProceedings of ECMS ’20: the 34th International Conference on Modelling and Simulation, Mike Steglich, Christian Mueller, Gaby Neumann, and Mathias Walther (Eds.)....

    work page 2020

Show all 31 references
  1. [9]

    PéterBiró,BernadetteHaase-Kromwijk,TommyAndersson,EyjólfurIngiÁsgeirsson,TatianaBaltesová,IoannisBoletis, Catarina Bolotinha, Gregor Bond, Georg Böhmig, Lisa Burnapp, et al. 2019. Building Kidney Exchange Programmes in European overview of exchange practice and activities.Tran...

    2019

  2. [10]

    Péter Biró, Walter Kern, Dömötör Pálvölgyi, and Daniel Paulusma. 2019. Generalized Matching Games for International Kidney Exchange. InProceedings of the 18th International Conference on Autonomous Agents and MultiAgent Systems (Montreal QC, Canada)(AAMAS ’19). International F...

    2019

  3. [11]

    Valentín, and Ana Viana

    Péter Biró, Joris van de Klundert, David Manlove, William Pettersson, Tommy Andersson, Lisa Burnapp, Pavel Chromy, Pablo Delgado, Piotr Dworczak, Bernadette Haase, Aline Hemke, Rachel Johnson, Xenia Klimentova, Dirk Kuypers, Alessandro Nanni Costa, Bart Smeulders, Frits Spieks...

    2021

  4. [12]

    Danny Blom, Bart Smeulders, and Frits C. R. Spieksma. 2024. Rejection-proof mechanisms for multi-agent kidney exchange.Games and Economic Behaviour143 (2024), 25–50

    2024

  5. [13]

    Opting into optimal matchings

    AvrimBlum,IoannisCaragiannis,NikaHaghtalab,ArielDProcaccia,EviatarBProcaccia,andRohitVaish.2017. Opting into optimal matchings. InProceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (Barcelona, Spain)(SODA ’17). ACM-SIAM, Society for Industrial an...

    2017

  6. [14]

    Julien Combe, Victor Hiller, Olivier Tercieux, Benoît Audry, Jules Baudet, Géraldine Malaquin, François Kerbaul, Corinne Antoine, Marie-Alice Macher, Christian Jacquelinet, Olivier Bastien, and Myriam Pastural. 2022. Perspectives pouruneévolutionduprogrammededoncroisédereinsen...

    2022 doi

  7. [15]

    MaxenceDelorme,SergioGarcía,JacekGondzio,JörgKalcsics,DavidManlove,WilliamPettersson,andJamesTrimble

  8. [16]

    Kristóf Druzsin, Péter Biró, Xenia Klimentova, and Rita Fleiner. 2024. Performance evaluation of national and international kidney exchange programmes with the ENCKEP simulator.Central European Journal of Operations Research32, 923–943 (2024), 1–21

    2024

  9. [17]

    2024.European Kidney Paired Exchange Programme

    European Commission. 2024.European Kidney Paired Exchange Programme. EU4Health Programme (EU4H). https: //ec.europa.eu/info/funding-tenders/opportunities/portal/screen/opportunities/projects-details/43332642/101160850

    2024

  10. [18]

    A. Hart, J. M. Smith, M. A. Skeans, S. K. Gustafson, D. E. Stewart, W. S. Cherikh, J. L. Wainright, A. Kucheryavaya, M. Woodbury, J. J. Snyder, B. L. Kasiske, and A. K. Israni. 2017. OPTN/SRTR 2015 Annual data report: Kidney.American Journal of Transplantation17 (2017), 21–116

    2017

  11. [19]

    Richard M. Karp. 1972.Reducibility among Combinatorial Problems. Springer US, Boston, MA, 85–103. International Kidney Exchange Programmes with Country-Specific Parameters

    1972

  12. [20]

    Xenia Klimentova, Ana Viana, João Pedro Pedroso, and Nicolau Santos. 2021. Fairness models for multi-agent kidney exchange programmes.Omega102 (2021), 102333

    2021

  13. [21]

    2021.Nephrology in Poland

    Monika Lichodziejewska-Niemierko, Jarosław Czerwiński, Alicja Dębska-Ślizień, Ryszard Gellert, Ryszard Grenda, Jolanta Małyszko, Beata Naumnik, Michał Nowicki, Janusz Ostrowski, and Andrzej Więcek. 2021.Nephrology in Poland. Springer International Publishing, Cham, 593–606. ht...

    2021 doi

  14. [22]

    Vazirani

    Silvio Micali and Vijay V. Vazirani. 1980. An𝑂( √︁ |𝑉||𝐸|) algoithm for finding maximum matching in general graphs. In2013 IEEE 54th Annual Symposium on Foundations of Computer Science. IEEE Computer Society, Los Alamitos, CA, USA, 17–27. https://doi.org/10.1109/SFCS.1980.12

    1980 doi

  15. [23]

    IPsolutionsforinternational kidney exchange programmes.Central European Journal of Operations Research29 (2021), 403–423

    Radu-StefanMincu,PéterBiró,MártonGyetvai,AlexandruPopa,andUtkarshVerma.2021. IPsolutionsforinternational kidney exchange programmes.Central European Journal of Operations Research29 (2021), 403–423

    2021

  16. [24]

    William Pettersson. 2022. Kep_solver: A Python package for kidney exchange programme exploration.Journal of Open Source Software7, 80 (2022), 4881

    2022

  17. [25]

    2 (1986), 5–9

    F.T.Rapaport.1986.Thecaseforalivingemotionallyrelatedinternationalkidneydonorexchangeregistry.Transplantation proceedings18(3) Suppl. 2 (1986), 5–9

    1986

  18. [26]

    Alvin E Roth, Tayfun Sönmez, and M Utku Ünver. 2005. Pairwise kidney exchange.Journal of Economic theory125, 2 (2005), 151–188

    2005

  19. [27]

    Zhaohong Sun, Taiki Todo, and Toby Walsh. 2021. Fair Pairwise Exchange among Groups.. InProceedings of IJCAI ’21: the30thInternationalJointConferenceonArtificialIntelligence.InternationalJointConferenceonArtificialIntelligence, Montreal, Canada, 419–425

    2021

  20. [28]

    Panos Toulis and David C Parkes. 2015. Design and analysis of multi-hospital kidney exchange mechanisms using random graphs.Games and Economic Behavior91 (2015), 360–382

    2015

  21. [29]

    María Oliva Valentín, Marta Garcia, Alessandro Nanni Costa, Catarina Bolotinha, Lluis Guirado, Fabio Vistoli, Alberto Breda, Pamela Fiaschetti, and Beatriz Dominguez-Gil. 2019. International cooperation for kidney exchange success. Transplantation103, 6 (2019), e180–e181

    2019

  22. [30]

    Ilse Duus Weinreich, Tommy Andersson, Margrét Birna Andrésdóttir, Mats Bengtsson, Alireza Biglarnia, Claus Bistrup, LineBoulland,HelleBruunsgaard,IlkkaHelanterä,KulliKölvald,JouniLauronen,JørnPetterLindahl,KarinSkov,Søren Schwarz Sørensen, Lars Wennberg, and Per Lindner. 2023....

    2023

  23. [2022]

    Improved instance generation for kidney exchange programmes.Computers & Operations Research141 (2022), 105707

    2022

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.