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arxiv: 2504.18298 · v2 · submitted 2025-04-25 · 🪐 quant-ph

Optimizing Resource Allocation in a Distributed Quantum Computing Cloud: A Game-Theoretic Approach

Bernard Ousmane Sane , Michal Hajdu\v{s}ek , Rodney Van Meter This is my paper

Pith reviewed 2026-05-22 18:04 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum cloud computingresource allocationgame theorycircuit partitioningdistributed quantum computingcost optimizationQC-PRAGMremote gates
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The pith

A game-theoretic model for partitioning quantum circuits across cloud nodes bounds total client cost at most 4/3 of the minimum possible cost.

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

The paper models resource allocation for quantum circuits running on multiple connected quantum processors as a game between clients seeking low bills and providers seeking high utilization. It introduces the QC-PRAGM game in which clients choose partitions and the resulting equilibrium allocation is shown analytically to keep aggregate payments no higher than four-thirds the cost of the best centralized schedule. An extension called QC-PRAGM++ refines the partition selection to favor larger blocks of local gates and thereby cut inter-node communication. The authors report that simulations of the resulting schedules improve on conventional methods across cost-per-node, total cost, maximum cost, partition count, and remote-gate count. A sympathetic reader cares because the bound supplies a concrete guarantee that quantum cloud services will not overcharge users while still packing work onto scarce hardware.

Core claim

The QC-PRAGM model treats circuit partitioning as a game whose utility functions encode fixed additive penalties for remote gates and inter-node links; the equilibrium of this game yields allocations whose total client cost is at most 4/3 of the optimal cost, and the QC-PRAGM++ variant selects qubit groupings that maximize the number of local gates within each partition.

What carries the argument

The QC-PRAGM utility functions that add fixed remote-gate and communication penalties, allowing derivation of the 4/3 cost bound from the existence of a Nash equilibrium in the partitioning game.

If this is right

  • In any equilibrium allocation produced by the game, aggregate client payments remain at most 4/3 of the lowest attainable cost.
  • Quantum cloud providers obtain higher utilization because partitions are chosen to respect both client cost and hardware packing constraints.
  • The number of remote gates and inter-node messages drops when QC-PRAGM++ is used instead of standard partitioning heuristics.
  • Simulations show lower cost per node, lower maximum cost, and fewer partitions than traditional multi-objective schedulers.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same fixed-penalty game could be applied to classical distributed systems where latency or data-transfer costs are roughly constant.
  • If entanglement-generation costs turn out to vary strongly with hardware state, the 4/3 guarantee would need recalibration for each calibration epoch.
  • Real deployment would allow direct measurement of whether the observed total cost stays inside the predicted bound on current quantum-cloud testbeds.

Load-bearing premise

The cost of every remote gate and every inter-node communication link can be expressed as a fixed additive penalty that does not change with the entanglement protocol or the current calibration state of the hardware.

What would settle it

Execute the QC-PRAGM allocation on a concrete multi-node circuit whose actual remote-gate costs are measured on hardware; if the resulting client total exceeds 4/3 of the minimum-cost schedule found by exhaustive search, the bound fails.

Figures

Figures reproduced from arXiv: 2504.18298 by Bernard Ousmane Sane, Michal Hajdu\v{s}ek, Rodney Van Meter.

Figure 1
Figure 1. Figure 1: A fully connected network via quantum and classical with [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: A diagram illustrating our solution, which incorporates game theory and an inter-node communication optimization process. Using the game model, [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: An illustration of the GHZ state in circuit and graph. The direction [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Example of circuit partitioning based on Algorithm 1, where we illustrate two arbitrary quantum algorithms in circuits 4(a), 4(c) and graphs 4(b), [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of the cost per quantum node under round-robin, random, and QC-PRAGM++, according to the number of circuits [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Variation in system costs, the maximum cost, the number of partitions, [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
read the original abstract

Quantum cloud computing is essential for achieving quantum supremacy by utilizing multiple quantum computers connected via an entangling network to deliver high performance for practical applications that require extensive computational resources. With such a platform, various clients can execute their quantum jobs (quantum circuits) without needing to manage the quantum hardware and pay based on resource usage. Hence, defining optimal quantum resource allocation is necessary to avoid overcharging clients and to allow quantum cloud providers to maximize resource utilization. Prior work has mainly focused on minimizing communication delays between nodes using multi-objective techniques. Our approach involves analyzing the problem from a game theory perspective. We propose a quantum circuit partitioning resource allocation game model (QC-PRAGM) that minimizes client costs while maximizing resource utilization in quantum cloud environments. We extend QC-PRAGM to QC-PRAGM++ to maximize local gates in a partition by selecting the best combinations of qubits, thereby minimizing both cost and inter-node communication. We demonstrate analytically that clients are charged appropriately (with a total cost at most $\frac{4}{3}$ the optimal cost) while optimizing quantum cloud resources. Further, our simulations indicate that our solutions perform better than traditional ones in terms of the cost per quantum node, total cost, maximum cost, number of partitions, and number of remote gates.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes QC-PRAGM, a game-theoretic model for partitioning quantum circuits across distributed quantum nodes to minimize client costs while maximizing provider resource utilization. It extends the model to QC-PRAGM++ via a qubit-selection heuristic that prioritizes local gates. The central analytical claim is that the Nash equilibrium yields a total client cost at most 4/3 of the optimal cost; simulations are reported to outperform unspecified traditional baselines on cost-per-node, total cost, maximum cost, partition count, and remote-gate count.

Significance. A rigorously established 4/3 bound under the paper's modeling assumptions would supply a concrete, falsifiable guarantee for fair charging in quantum cloud platforms, which is a practically relevant contribution. The game-theoretic framing of client-provider incentives is a fresh angle relative to prior multi-objective optimization work. Credit is due for attempting an analytical approximation result alongside empirical evaluation, even if the bound's derivation steps and baseline details require strengthening.

major comments (2)
  1. [§3 and §4] §3 (QC-PRAGM utility functions) and §4 (4/3 bound derivation): the proof that the Nash equilibrium cost is at most (4/3)·OPT treats every remote gate and inter-node communication as a fixed additive constant penalty inside each player's utility. This modeling choice is load-bearing for the ratio; any fidelity- or protocol-dependent overhead would change best-response dynamics and could invalidate the guarantee. The manuscript should either derive the bound from first principles without the constant-penalty assumption or supply a sensitivity analysis showing robustness.
  2. [Simulation results section] Simulation results section: the reported improvements in cost per quantum node, total cost, and number of remote gates are presented without naming the baseline algorithms, the number of Monte-Carlo trials, or the statistical tests used to establish significance. This prevents verification that the gains are not artifacts of particular parameter choices or weak comparators.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'traditional ones' for baseline methods is undefined; replace with a brief parenthetical naming the compared algorithms.
  2. [Notation] Notation: the symbols for local-gate weight, remote-gate penalty, and inter-node communication cost should be introduced once with a table and used consistently thereafter.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive review. We address each major comment below and indicate the revisions we will make to improve the manuscript.

read point-by-point responses

  1. Referee: [§3 and §4] §3 (QC-PRAGM utility functions) and §4 (4/3 bound derivation): the proof that the Nash equilibrium cost is at most (4/3)·OPT treats every remote gate and inter-node communication as a fixed additive constant penalty inside each player's utility. This modeling choice is load-bearing for the ratio; any fidelity- or protocol-dependent overhead would change best-response dynamics and could invalidate the guarantee. The manuscript should either derive the bound from first principles without the constant-penalty assumption or supply a sensitivity analysis showing robustness.

    Authors: We agree that the constant-penalty modeling of remote gates and inter-node communication in the utility functions of §3 is central to the derivation of the 4/3 bound in §4. This choice is intentional under the paper's assumptions to reflect fixed overheads in current distributed quantum cloud settings. We will revise the manuscript to add an explicit discussion of these modeling assumptions in §3 and include a sensitivity analysis that varies the penalty values to examine effects on best-response dynamics and the approximation ratio. revision: yes

  2. Referee: [Simulation results section] Simulation results section: the reported improvements in cost per quantum node, total cost, and number of remote gates are presented without naming the baseline algorithms, the number of Monte-Carlo trials, or the statistical tests used to establish significance. This prevents verification that the gains are not artifacts of particular parameter choices or weak comparators.

    Authors: We acknowledge that the simulation results section omits key details required for reproducibility. In the revised manuscript we will name the specific baseline algorithms, report the number of Monte-Carlo trials performed, and describe the statistical tests used to evaluate significance of the reported improvements. revision: yes

Circularity Check

0 steps flagged

No circularity: 4/3 bound is a derived property of the defined game model

full rationale

The paper defines the QC-PRAGM utility functions with explicit additive penalty terms for remote gates and inter-node communication, then derives the 4/3 total-cost bound as an analytical consequence of Nash equilibrium analysis within that model. This is a standard game-theoretic approximation result (price-of-anarchy style) that follows from the stated assumptions rather than reducing to a fitted parameter, self-citation, or tautological renaming. The derivation chain is self-contained: the bound is proven from the model's equations, not smuggled in via prior work or by re-labeling an input. No load-bearing step collapses to its own definition or to a self-citation chain. The modeling choice of constant penalties is an explicit assumption, not a hidden circularity.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claims rest on standard assumptions about additive communication costs and fixed per-gate pricing; no new physical entities are introduced and the only free parameters appear to be the relative weights of local versus remote gate costs, which are not numerically specified in the abstract.

free parameters (1)
  • relative cost weight between local and remote gates
    The utility functions in QC-PRAGM implicitly treat remote-gate cost as a tunable penalty; its exact numerical value is not given but must be chosen to obtain the 4/3 bound.
axioms (1)
  • domain assumption Communication cost between nodes is additive and independent of the specific entanglement protocol
    Invoked when defining the total cost that is bounded by 4/3 of optimal.

pith-pipeline@v0.9.0 · 5764 in / 1473 out tokens · 42041 ms · 2026-05-22T18:04:41.045652+00:00 · methodology

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Reference graph

Works this paper leans on

56 extracted references · 56 canonical work pages · 2 internal anchors

  1. [1]

    Cloud computing and emerging it platforms: Vision, hype, and reality for delivering computing as the 5th utility,

    R. Buyya, C. S. Yeo, S. Venugopal, J. Broberg, and I. Brandic, “Cloud computing and emerging it platforms: Vision, hype, and reality for delivering computing as the 5th utility,”Future Gener. Comput. Syst., vol. 25, p. 599–616, June 2009

    work page 2009

  2. [2]

    A review of virtualization, hypervisor and VM allocation security: Threats, vulnerabilities, and countermeasures,

    B. O. Sane, I. Niang, and D. Fall, “A review of virtualization, hypervisor and VM allocation security: Threats, vulnerabilities, and countermeasures,” inIEEEInternational Conference on Computational Science and Computational Intelligence (CSCI), pp. 1317–1322, 2018

    work page 2018

  3. [3]

    The nist definition of cloud computing,

    P. Mell, T. Grance,et al., “The nist definition of cloud computing,” Computer Security Division, Information Technology Laboratory, National Institute of Standards & Technology, Gaithersburg, MD, USA, 2011

    work page 2011

  4. [4]

    Cloud based qc with amazon braket,

    C. Gonzalez, “Cloud based qc with amazon braket,”Digitale Welt, vol. 5, pp. 14–17, Apr 2021

    work page 2021

  5. [5]

    A quantum-classical cloud platform optimized for variational hybrid algorithms,

    P. J. Karalekas, N. A. Tezak, E. C. Peterson, C. A. Ryan, M. P. Da Silva, and R. S. Smith, “A quantum-classical cloud platform optimized for variational hybrid algorithms,”Quantum Science and Technology, vol. 5, no. 2, p. 024003, 2020

    work page 2020

  6. [6]

    Azure quantum,

    Microsoft, “Azure quantum,” 2023. Accessed: 2025-01-20. Available at https://azure.microsoft.com/en-us/services/quantum

    work page 2023

  7. [7]

    IBM quantum computing services,

    IBM, “IBM quantum computing services,” 2023. Accessed: 2025-01-20. Available at https://quantum-computing.ibm.com/

    work page 2023

  8. [8]

    Performing quantum computing experiments in the cloud,

    S. J. Devitt, “Performing quantum computing experiments in the cloud,” Phys. Rev. A, vol. 94, p. 032329, Sep 2016

    work page 2016

  9. [9]

    Qfaas: A serverless function- as-a-service framework for quantum computing,

    H. T. Nguyen, M. Usman, and R. Buyya, “Qfaas: A serverless function- as-a-service framework for quantum computing,”Future Generation Computer Systems, vol. 154, pp. 281–300, 2024

    work page 2024

  10. [10]

    Towards quantum-algorithms-as-a-service,

    M. De Stefano, D. Di Nucci, F. Palomba, D. Taibi, and A. De Lucia, “Towards quantum-algorithms-as-a-service,” inProceedings of the 1st International Workshop on Quantum Programming for Software Engineering, QP4SE 2022, (New York, NY , USA), p. 7–10, Association for Computing Machinery, 2022

    work page 2022

  11. [11]

    Engineering software systems for quantum computing as a service: A mapping study,

    A. Ahmad, M. Waseem, P. Liang, M. Fehmideh, A. A. Khan, D. G. Reichelt, and T. Mikkonen, “Engineering software systems for quantum computing as a service: A mapping study,”arXiv preprint arXiv:2303.14713, 2023

    work page arXiv 2023

  12. [12]

    A serverless cloud integration for quantum computing,

    M. Grossi, L. Crippa, A. Aita, G. Bartoli, V . Sammarco, E. Picca, N. Said, F. Tramonto, and F. Mattei, “A serverless cloud integration for quantum computing,”arXiv preprint arXiv:2107.02007, 2021

    work page arXiv 2021

  13. [13]

    Quantum cloud computing: a review, open problems, and future directions,

    H. T. Nguyen, P. Krishnan, D. Krishnaswamy, M. Usman, and R. Buyya, “Quantum cloud computing: a review, open problems, and future directions,”arXiv preprint arXiv:2404.11420, 2024

    work page arXiv 2024

  14. [14]

    Quantum chemistry in the age of quantum computing,

    Y . Cao, J. Romero, J. P. Olson, M. Degroote, P. D. Johnson, M. Kieferov ´a, I. D. Kivlichan, T. Menke, B. Peropadre, N. P. Sawaya, et al., “Quantum chemistry in the age of quantum computing,”Chemical reviews, vol. 119, no. 19, pp. 10856–10915, 2019

    work page 2019

  15. [15]

    The variational quantum eigensolver: a review of methods and best practices,

    J. Tilly, H. Chen, S. Cao, D. Picozzi, K. Setia, Y . Li, E. Grant, L. Wossnig, I. Rungger, G. H. Booth,et al., “The variational quantum eigensolver: a review of methods and best practices,”Physics Reports, vol. 986, pp. 1–128, 2022

    work page 2022

  16. [16]

    Variational quantum algorithms,

    M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio,et al., “Variational quantum algorithms,”Nature Reviews Physics, vol. 3, no. 9, pp. 625– 644, 2021

    work page 2021

  17. [17]

    Quantum computational chemistry,

    S. McArdle, S. Endo, A. Aspuru-Guzik, S. C. Benjamin, and X. Yuan, “Quantum computational chemistry,”Reviews of Modern Physics, vol. 92, no. 1, p. 015003, 2020

    work page 2020

  18. [18]

    An adaptive variational algorithm for exact molecular simulations on a quantum computer,

    H. R. Grimsley, S. E. Economou, E. Barnes, and N. J. Mayhall, “An adaptive variational algorithm for exact molecular simulations on a quantum computer,”Nature communications, vol. 10, no. 1, p. 3007, 2019

    work page 2019

  19. [19]

    Scalable quantum simulation of molecular energies,

    P. J. J. O’Malley, R. Babbush, I. D. Kivlichan, J. Romero, J. R. McClean, R. Barends, J. Kelly, P. Roushan, A. Tranter, N. Ding, B. Campbell, Y . Chen, Z. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Jeffrey, E. Lucero, A. Megrant, J. Y . Mutus, M. Neeley, C. Neill, C. Quintana, D. Sank, A. Vainsencher, J. Wenner, T. C. White, P. V . Coveney, P. J. Lov...

    work page 2016

  20. [20]

    Fast quantum modular exponentiation,

    R. Van Meter and K. M. Itoh, “Fast quantum modular exponentiation,” Physical Review A, vol. 71, p. 052320, May 2005

    work page 2005

  21. [21]

    How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits,

    C. Gidney and M. Eker ˚a, “How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits,”Quantum, vol. 5, p. 433, Apr. 2021

    work page 2048

  22. [22]

    Estimating the cost of generic quantum pre-image attacks on SHA-2 and SHA-3,

    M. Amy, O. Di Matteo, V . Gheorghiu, M. Mosca, A. Parent, and J. Schanck, “Estimating the cost of generic quantum pre-image attacks on SHA-2 and SHA-3,” inSelected Areas in Cryptography – SAC 2016(R. Avanzi and H. Heys, eds.), (Cham), pp. 317–337, Springer International Publishing, 2017

    work page 2016

  23. [23]

    Quantum random number generator using a cloud superconducting quantum computer based on source-independent protocol,

    Y . Li, Y . Fei, W. Wang, X. Meng, H. Wang, Q. Duan, and Z. Ma, “Quantum random number generator using a cloud superconducting quantum computer based on source-independent protocol,”Scientific Reports, vol. 11, no. 1, p. 23873, 2021

    work page 2021

  24. [24]

    A case for multi- programming quantum computers,

    P. Das, S. S. Tannu, P. J. Nair, and M. Qureshi, “A case for multi- programming quantum computers,” inProceedings of the 52nd Annual IEEE/ACM International Symposium on Microarchitecture, MICRO ’52, (New York, NY , USA), p. 291–303, Association for Computing Machinery, 2019

    work page 2019

  25. [25]

    Simultaneous execution of quantum circuits on current and near-future NISQ systems,

    Y . Ohkura, T. Satoh, and R. Van Meter, “Simultaneous execution of quantum circuits on current and near-future NISQ systems,”IEEE Transactions on Quantum Engineering, vol. 3, pp. 1–10, 2022

    work page 2022

  26. [26]

    System design for large-scale ion trap quantum information processor,

    J. Kimet al., “System design for large-scale ion trap quantum information processor,”Quantum Information and Computation, vol. 5, no. 7, pp. 515–537, 2005

    work page 2005

  27. [27]

    R. D. Van Meter III,Architecture of a Quantum Multicomputer Optimized for Shor’s Factoring Algorithm. PhD thesis, Keio University,

    work page

  28. [28]

    available as arXiv:quant-ph/0607065

    work page internal anchor Pith review Pith/arXiv arXiv

  29. [29]

    Arquin: Architectures for multinode superconducting quantum computers,

    J. Ang, G. Carini, Y . Chen, I. Chuang, M. DeMarco, S. Economou, A. Eickbusch, A. Faraon, K.-M. Fu, S. Girvin, M. Hatridge, A. Houck, P. Hilaire, K. Krsulich, A. Li, C. Liu, Y . Liu, M. Martonosi, D. McKay, J. Misewich, M. Ritter, R. Schoelkopf, S. Stein, S. Sussman, H. Tang, W. Tang, t. tomesh, N. Tubman, C. Wang, N. Wiebe, Y . Yao, D. Yost, and Y . Zhou...

    work page 2024

  30. [30]

    Review of distributed quantum computing: From single qpu to high performance quantum computing,

    D. Barral, F. J. Cardama, G. D ´ıaz-Camacho, D. Fa ´ılde, I. F. Llovo, M. Mussa-Juane, J. V ´azquez-P´erez, J. Villasuso, C. Pi ˜neiro, N. Costas, J. C. Pichel, T. F. Pena, and A. G ´omez, “Review of distributed quantum computing: From single qpu to high performance quantum computing,” Computer Science Review, vol. 57, p. 100747, 2025

    work page 2025

  31. [31]

    Optimal local implementation of nonlocal quantum gates,

    J. Eisert, K. Jacobs, P. Papadopoulos, and M. Plenio, “Optimal local implementation of nonlocal quantum gates,”Physical Review A, vol. 62, no. 5, p. 52317, 2000

    work page 2000

  32. [32]

    Distributed quantum computing across an optical network link,

    D. Main, P. Drmota, D. Nadlinger, E. Ainley, A. Agrawal, B. Nichol, R. Srinivas, G. Araneda, and D. Lucas, “Distributed quantum computing across an optical network link,”Nature, pp. 1–6, 2025

    work page 2025

  33. [33]

    An optical interconnect for modular quantum computers,

    D. Sakuma, A. Taherkhani, T. Tsuno, T. Sasaki, H. Shimizu, K. Teramoto, A. Todd, Y . Ueno, M. Hajduˇsek, R. Ikuta, R. V . Meter, and S. Nagayama, “An optical interconnect for modular quantum computers,” arXiv preprint arXiv:2412.09299, 2024

    work page arXiv 2024

  34. [34]

    Cost-efficient dragonfly topology for large-scale systems,

    J. Kim, W. Dally, S. Scott, and D. Abts, “Cost-efficient dragonfly topology for large-scale systems,”IEEE micro, vol. 29, no. 1, pp. 33–40, 2009

    work page 2009

  35. [35]

    A parallel workload model and its implications for processor allocation,

    A. Downey, “A parallel workload model and its implications for processor allocation,” inProceedings. The Sixth IEEE International Symposium on High Performance Distributed Computing (Cat. No.97TB100183), pp. 112–123, 1997

    work page 1997

  36. [36]

    Cloud resource allocation games,

    V . Jalaparti and G. D. Nguyen, “Cloud resource allocation games,” Technical Report, 03 2019. https://www.ideals.illinois.edu/items/17505

    work page 2019

  37. [37]

    Resource Management and Circuit Scheduling for Distributed Quantum Computing Interconnect Networks

    S. Bahrani, R. D. Oliveira, J. M. Parra-Ullauri, R. Wang, and D. Simeonidou, “Resource management and circuit scheduling for distributed quantum computing interconnect networks,”arXiv preprint arXiv:2409.12675, 2024

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  38. [38]

    Virtual machine allocation policies against co-resident attacks in cloud computing,

    Y . Han, J. Chan, T. Alpcan, and C. Leckie, “Virtual machine allocation policies against co-resident attacks in cloud computing,” in2014 IEEE International Conference on Communications (ICC), pp. 786–792, IEEE, 2014

    work page 2014

  39. [39]

    Bas ¸ar and G

    T. Bas ¸ar and G. J. Olsder,Dynamic noncooperative game theory. Society for Industrial and Applied Mathematics (SIAM), 1998

    work page 1998

  40. [40]

    Maschler, S

    M. Maschler, S. Zamir, and E. Solan,Game theory. Cambridge University Press, 2020

    work page 2020

  41. [41]

    A threshold-based dynamic resource allocation scheme for cloud computing,

    W. Lin, J. Z. Wang, C. Liang, and D. Qi, “A threshold-based dynamic resource allocation scheme for cloud computing,”Procedia Engineering, vol. 23, pp. 695 – 703, 2011. PEEA 2011

    work page 2011

  42. [42]

    D. M. Kreps,Game theory and economic modelling. Oxford University Press, 1990

    work page 1990

  43. [43]

    Using virtual machine allocation policies to defend against co-resident attacks in cloud computing,

    Y . Han, J. Chan, T. Alpcan, and C. Leckie, “Using virtual machine allocation policies to defend against co-resident attacks in cloud computing,”IEEE Transactions on Dependable and Secure Computing, vol. 14, pp. 95–108, Jan 2017

    work page 2017

  44. [44]

    A dynamic dispatching method of resource based on particle swarm optimization for cloud computing environment,

    H. Zhao and W. Chenyu, “A dynamic dispatching method of resource based on particle swarm optimization for cloud computing environment,” in2013 10th Web Information System and Application Conference, pp. 351–354, IEEE, 2013

    work page 2013

  45. [45]

    Interdependency attack-aware secure and performant virtual machine allocation policies with low attack efficiency and coverage,

    B. O. San ´e, M. Ba, D. Fall, Y . Taenaka, I. Niang, and Y . Kadobayashi, “Interdependency attack-aware secure and performant virtual machine allocation policies with low attack efficiency and coverage,”IEEE Access, vol. 12, pp. 74944–74960, 2024

    work page 2024

  46. [46]

    Interdependent security: The case of identical agents,

    H. Kunreuther and H. Kunreuther, “Interdependent security: The case of identical agents,”Journal of Risk and Uncertainty, vol. 26, p. 2003, 2002

    work page 2003

  47. [47]

    A survey of game theoretic solutions for cloud computing security issues,

    B. O. Sane, C. S. M. Babou, D. Fall, and I. Niang, “A survey of game theoretic solutions for cloud computing security issues,” in SpringerInnovations and Interdisciplinary Solutions for Underserved Areas(G. Bassioni, C. M. Kebe, A. Gueye, and A. Ndiaye, eds.), (Cham), pp. 1–12, Springer International Publishing, 2019

    work page 2019

  48. [48]

    Solving the interdependency problem: A secure virtual machine allocation method relying on the attacker’s efficiency and coverage,

    B. O. San ´e, M. Ba, D. Fall, S. Kashihara, Y . Taenaka, I. Niang, and Y . Kadobayashi, “Solving the interdependency problem: A secure virtual machine allocation method relying on the attacker’s efficiency and coverage,” in20thIEEE/ACMInternational Symposium on Cluster, Cloud and Internet Computing, CCGRID 2020, Melbourne, Australia, May 11-14, 2020, pp. ...

    work page 2020

  49. [49]

    Designing quantum repeater networks,

    R. Van Meter and J. Touch, “Designing quantum repeater networks,” IEEE Communications Magazine, vol. 51, no. 8, pp. 64–71, 2013

    work page 2013

  50. [50]

    How bad is selfish routing?,

    T. Roughgarden and E. Tardos, “How bad is selfish routing?,”J. ACM, vol. 49, p. 236–259, Mar. 2002

    work page 2002

  51. [51]

    Convex optimization with sparsity-inducing norms,

    F. Bach, R. Jenatton, J. Mairal, G. Obozinski,et al., “Convex optimization with sparsity-inducing norms,”Optimization for machine learning, vol. 5, no. 19-53, p. 8, 2011

    work page 2011

  52. [52]

    CVXPY: A Python-embedded modeling language for convex optimization,

    S. Diamond and S. Boyd, “CVXPY: A Python-embedded modeling language for convex optimization,”Journal of Machine Learning Research, vol. 17, no. 83, pp. 1–5, 2016

    work page 2016

  53. [53]

    A rewriting system for convex optimization problems,

    A. Agrawal, R. Verschueren, S. Diamond, and S. Boyd, “A rewriting system for convex optimization problems,”Journal of Control and Decision, vol. 5, no. 1, pp. 42–60, 2018

    work page 2018

  54. [54]

    An efficient heuristic procedure for partitioning graphs,

    B. W. Kernighan and S. Lin, “An efficient heuristic procedure for partitioning graphs,”The Bell System Technical Journal, vol. 49, no. 2, pp. 291–307, 1970

    work page 1970

  55. [55]

    The MQT handbook: A summary of design automation tools and software for quantum computing,

    R. Wille, L. Berent, T. Forster, J. Kunasaikaran, K. Mato, T. Peham, N. Quetschlich, D. Rovara, A. Sander, L. Schmid, D. Schoenberger, Y . Stade, and L. Burgholzer, “The MQT handbook: A summary of design automation tools and software for quantum computing,” inIEEE International Conference on Quantum Software (QSW)

    work page

  56. [56]

    Exploring network structure, dynamics, and function using NETWORKX,

    A. A. Hagberg, D. A. Schult, and P. J. Swart, “Exploring network structure, dynamics, and function using NETWORKX,” inProceedings of the 7th Python in Science Conference(G. Varoquaux, T. Vaught, and J. Millman, eds.), (Pasadena, CA USA), pp. 11 – 15, 2008

    work page 2008