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Multiagent Matroid Upgrading: Greedy is Fair and Efficient

T0 review · 1 major / 0 minor · reviewed 2026-06-28 · grok-4.3

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Pith's one-line read The greedy algorithm optimally selects at most k upgrades to minimize a non-decreasing convex function over agents' matroid basis costs.

desk verdict New multiagent matroid upgrading formulation with a greedy claim that looks plausible from the abstract but lacks visible proof. read the letter →

arxiv 2606.01309 v1 pith:QTGHODXF submitted 2026-05-31 cs.DS

Qingwen Ma , Chao Peng , Changfeng Xu , Chenyang Xu , Ruilong Zhang This is my paper · ORCID
classification cs.DS
keywords multiagentmatroidupgradinggreedyalgorithmconvexobjectivefairnessefficiencyresourceallocationminimumbasiscoststructure
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

This paper defines a multiagent matroid upgrading problem where a ground set of elements can be chosen for upgrade to lower their costs, with each agent having its own matroid whose minimum-cost basis is computed after upgrades. The task is to pick at most k upgrades to minimize a non-decreasing convex function of the resulting basis costs across agents. A sympathetic reader would care because the setup captures resource allocation tasks that must balance total efficiency against fairness among multiple agents. The paper proves that a greedy selection rule solves this exactly.

What carries the argument

The greedy algorithm that repeatedly picks the single upgrade yielding the largest marginal drop in the convex objective, with each agent's minimum basis recomputed via its matroid after each choice.

What would settle it

An explicit instance of costs, matroids, and k where the set chosen by greedy produces a strictly higher objective value than some other set of k upgrades.

Watch

Extended reading notes

Core claim

In the multiagent matroid upgrading problem, selecting at most k elements to upgrade minimizes a non-decreasing convex function over the agents' minimum basis costs, and the greedy algorithm finds this optimal selection.

Load-bearing premise

The function that combines the agents' basis costs is non-decreasing and convex, and each agent's feasible sets form an independent matroid.

Editorial extensions

If this is right

  • The upgrades can be found in polynomial time without enumerating combinations.
  • Any non-decreasing convex fairness measure is optimized by the same procedure.
  • The result holds for every matroid that admits efficient minimum-basis computation.
  • Efficiency and fairness are achieved together by the identical selection rule.

Reading between the lines

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

  • The same marginal-gain ordering might succeed on other independence systems that satisfy a weakened exchange property.
  • The model could describe shared infrastructure upgrades where each user has different feasible routes or schedules.
  • Practical performance on large random matroids would reveal whether the theoretical guarantee translates to observed running times.
  • pith_inferences
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 0 minor

Summary. The paper introduces the multiagent matroid upgrading problem involving multiple agents each associated with its own matroid on a shared ground set of elements. Each element has a default cost and a reduced upgraded cost; the task is to select at most k elements for upgrading so as to minimize a non-decreasing convex function of the vector of agents' minimum-cost basis values. The central claim is that a greedy algorithm is fair and efficient for this problem.

Significance. If the claimed optimality of the greedy algorithm holds, the result supplies a polynomial-time method for a broad class of multiagent allocation tasks that combine matroid feasibility with convex fairness objectives, extending classical single-agent matroid results to the multiagent setting while preserving computational tractability via the matroid greedy algorithm.

major comments (1)
  1. [Abstract] Abstract: the claim that greedy is optimal (and fair/efficient) for minimizing the non-decreasing convex function over agents' min-basis costs is asserted, yet the manuscript supplies neither a proof, an algorithm description, nor any verification steps (counterexample checks, reduction to known matroid results, or runtime analysis). This is load-bearing for the central contribution, as the soundness of the result cannot be evaluated from the given text.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their review and for highlighting the need to strengthen the presentation of our central result. We address the comment below and will revise the manuscript to improve clarity around the algorithm and its analysis.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that greedy is optimal (and fair/efficient) for minimizing the non-decreasing convex function over agents' min-basis costs is asserted, yet the manuscript supplies neither a proof, an algorithm description, nor any verification steps (counterexample checks, reduction to known matroid results, or runtime analysis). This is load-bearing for the central contribution, as the soundness of the result cannot be evaluated from the given text.

    Authors: The full manuscript contains the greedy algorithm description (Section 3), a proof of optimality and fairness via reduction to the standard matroid greedy algorithm with convex marginal analysis (Section 4), polynomial runtime, and verification via reduction to single-agent matroid results. The abstract is intentionally concise and does not repeat these details. We will revise the abstract to briefly reference the greedy algorithm and its guarantees, add an explicit pointer to the proof sections in the introduction, and include a short verification example if space allows. We believe this addresses the concern without altering the technical content. revision: partial

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; derivation is self-contained

full rationale

The paper defines a new multiagent matroid upgrading problem and proves that greedy upgrade selection is optimal for a non-decreasing convex objective over agents' min-cost bases. This rests on standard matroid properties (greedy algorithm computes min-cost basis in poly time) and convexity, with no reduction of the claimed result to fitted parameters, self-definitional loops, or load-bearing self-citations. The central algorithmic claim is independent of its inputs and does not rename or smuggle prior results circularly.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

Relies on standard matroid axioms for each agent's basis computation and the assumption that the objective is non-decreasing and convex; no free parameters or invented entities are mentioned.

assumptions (2)
  • domain assumption Each agent is associated with its own matroid
    Stated directly in the abstract as the structure defining each agent's minimum-cost basis.
  • domain assumption The objective function is non-decreasing and convex
    Central modeling choice in the abstract for capturing efficiency and fairness.

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Cite this review

Pith. "Pith review of Multiagent Matroid Upgrading: Greedy is Fair and Efficient." pith.science (2026). https://pith.science/paper/QTGHODXF

@misc{pith2026260601309,
  author       = {Pith},
  title        = {Pith review of: Multiagent Matroid Upgrading: Greedy is Fair and Efficient},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QTGHODXF}},
  note         = {Machine review of arXiv:2606.01309}
}
read the original abstract

This paper introduces a general multiagent matroid upgrading problem that models a broad class of real-world resource allocation tasks. In this setting, there are multiple agents and a ground set of elements, where each element is assigned to a specific agent and has two associated costs: a default cost and a reduced (upgraded) cost. Upgrading an element lowers its cost to the upgraded value, while non-upgraded elements retain their default costs. Each agent is associated with its own matroid, with the goal of finding a minimum-cost basis. The central task is to select at most k elements to upgrade so as to minimize a non-decreasing convex function over the agents' minimum basis costs, capturing both efficiency and fairness objectives in multiagent systems.

Figures

Figures reproduced from arXiv: 2606.01309 by the authors.

Figure 1
Figure 1. An illustration of MGUP. The original input graphs are shown on the left: two agents, agent A and agent B, each own [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Illustration for the two cases of Lemma 5. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

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Reference graph

Works this paper leans on

33 extracted references · 6 canonical work pages

  1. [1]

    Manzoor Ahmed, Noor Fatima, Salman Raza, Hamid Ali, Abdul Qayum, Wali Ul- lah Khan, Muhammad Sheraz, and Teong Chee Chuah. 2025. Optimizing Resource Allocation and Task Offloading in Multi-UAV MEC Networks.IEEE Access13 (2025), 68710–68725. https://doi.org/10.1109/ACCESS.2025.3562102

    work page doi:10.1109/access.2025.3562102 2025

  2. [2]

    Susanne Albers and Alexander Eckl. 2020. Explorable Uncertainty in Scheduling with Non-uniform Testing Times. InW AOA (Lecture Notes in Computer Science, Vol. 12806). Springer, 127–142

    2020

  3. [3]

    Susanne Albers and Alexander Eckl. 2021. Scheduling with Testing on Multi- ple Identical Parallel Machines. InW ADS (Lecture Notes in Computer Science, Vol. 12808). Springer, 29–42

    2021

  4. [4]

    Sanae Amani and Christos Thrampoulidis. 2021. Decentralized Multi-Agent Linear Bandits with Safety Constraints. InThirty-Fifth AAAI Conference on Artifi- cial Intelligence, AAAI 2021, Thirty-Third Conference on Innovative Applications of Artificial Intelligence, IAAI 2021, The Eleventh Symposium on Educational Advances in Artificial Intelligence, EAAI 202...

    work page doi:10.1609/aaai.v35i8.16820 2021

  5. [5]

    Bader and Paul Burkhardt

    David A. Bader and Paul Burkhardt. 2022. A Simple and Efficient Algorithm for Finding Minimum Spanning Tree Replacement Edges.J. Graph Algorithms Appl. 26, 1 (2022), 577–588

    2022

  6. [6]

    Anantaram Balakrishnan, Prakash Mirchandani, and Harihara Prasad Natarajan

  7. [7]

    Connectivity Upgrade Models for Survivable Network Design.Oper. Res. 57, 1 (2009), 170–186

    2009

  8. [8]

    BlueAlly. 2020. Network Upgrade to Enhance Operational Efficiency and Cost Savings. https://www.blueally.com/success-stories/

    2020

Show all 33 references
  1. [9]

    2006.Road network upgrading and overland trade expansion in Sub-Saharan Africa

    Piet Buys, Uwe Deichmann, and David Wheeler. 2006.Road network upgrading and overland trade expansion in Sub-Saharan Africa. Vol. 4097. World Bank Publications

    2006

  2. [10]

    Jerry Chee, Megan Flynn, Anil Damle, and Christopher De Sa. 2022. Model Preserving Compression for Neural Networks. InNeurIPS

    2022

  3. [11]

    Cormen, Charles E

    Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. 2009.Introduction to Algorithms, 3rd Edition. MIT Press

    2009

  4. [12]

    Shuang Cui, Kai Han, Shaojie Tang, Feng Li, and Jun Luo. 2024. Fairness in Streaming Submodular Maximization Subject to a Knapsack Constraint. InKDD. ACM, 514–525

    2024

  5. [13]

    Christoph Damerius, Peter Kling, Minming Li, Chenyang Xu, and Ruilong Zhang

  6. [14]

    InESA (LIPIcs, Vol

    Scheduling with a Limited Testing Budget: Tight Results for the Offline and Oblivious Settings. InESA (LIPIcs, Vol. 274). 38:1–38:15

  7. [15]

    Christoph Dürr, Thomas Erlebach, Nicole Megow, and Julie Meißner. 2020. An Adversarial Model for Scheduling with Testing.Algorithmica82, 12 (2020), 3630– 3675

    2020

  8. [16]

    Mingyang Gong, Randy Goebel, Guohui Lin, and Eiji Miyano. 2022. Improved approximation algorithms for non-preemptive multiprocessor scheduling with testing.Journal of Combinatorial Optimization44, 1 (2022), 877–893

    2022

  9. [17]

    Ravi, Mohit Singh, and Rico Zenklusen

    Fabrizio Grandoni, R. Ravi, Mohit Singh, and Rico Zenklusen. 2014. New ap- proaches to multi-objective optimization.Math. Program.146, 1-2 (2014), 525–554

    2014

  10. [18]

    Curtis Greene. 1973. A multiple exchange property for bases.Proc. Amer. Math. Soc.39, 1 (1973), 45–50

    1973

  11. [19]

    Grupen, Bart Selman, and Daniel D

    Niko A. Grupen, Bart Selman, and Daniel D. Lee. 2022. Cooperative Multi-Agent Fairness and Equivariant Policies. InThirty-Sixth AAAI Conference on Artificial Intelligence, AAAI 2022, Thirty-Fourth Conference on Innovative Applications of Artificial Intelligence, IAAI 2022, The...

    2022 doi

  12. [20]

    Marwa El Halabi, Federico Fusco, Ashkan Norouzi-Fard, Jakab Tardos, and Jakub Tarnawski. 2023. Fairness in Streaming Submodular Maximization over a Matroid Constraint. InICML (Proceedings of Machine Learning Research, Vol. 202). PMLR, 9150–9171

    2023

  13. [21]

    Song Han, Huizi Mao, and William J. Dally. 2016. Deep Compression: Compress- ing Deep Neural Network with Pruning, Trained Quantization and Huffman Coding. InICLR

    2016

  14. [22]

    Mao Luo, Huigang Qin, Xinyun Wu, Caiquan Xiong, Dahai Xia, and Yuanzhi Ke

  15. [23]

    Efficient Maintenance of Minimum Spanning Trees in Dynamic Weighted Undirected Graphs.Mathematics12, 7 (2024), 1021

    2024

  16. [24]

    Gunasekaran Manogaran, Jiechao Gao, and Tu N. Nguyen. 2023. Optimizing Resource and Service Allocations for IoT-Assisted Intelligent Transportation Systems.IEEE Trans. Intell. Transp. Syst.24, 11 (2023), 12877–12887. https: //doi.org/10.1109/TITS.2022.3182649

    2023 doi

  17. [25]

    Avishek Nag, Massimo Tornatore, and Biswanath Mukherjee. 2012. Energy- Efficient and Cost-Efficient Capacity Upgrade in Mixed-Line-Rate Optical Net- works.JOCN4, 12 (2012), 1018–1025

    2012

  18. [26]

    Carlos Natalino, Aysegül Yayimli, Lena Wosinska, and Marija Furdek. 2019. Infras- tructure upgrade framework for Content Delivery Networks robust to targeted attacks.Opt. Switch. Netw.31 (2019), 202–210

    2019

  19. [27]

    Elyas Oustad, Abolfazl Younesi, Mohsen Ansari, Sepideh Safari, Mohammad Ar- man Soleimani, Jörg Henkel, and Alireza Ejlali. 2025. DIST: Distributed Learning- Based Energy-Efficient and Reliable Task Scheduling and Resource Alloca- tion in Fog Computing.IEEE Trans. Serv. Comput...

    2025 doi

  20. [28]

    James G. Oxley. 1992.Matroid theory. Oxford University Press

    1992

  21. [29]

    Tumanov, and Vinod John

    Roopsi Rathi, Saurav Dixit, Shweta Bansal, Kaushal Kumar, Natalia Taskaeva, Alexander Yu. Tumanov, and Vinod John. 2022. Stackelberg game approach for resource allocation in device-to-device communication with heterogeneous networks.Robotics Auton. Syst.156 (2022), 104222. htt...

    2022 doi

  22. [30]

    Ravi and Michel X

    R. Ravi and Michel X. Goemans. 1996. The Constrained Minimum Spanning Tree Problem (Extended Abstract). InSW AT (Lecture Notes in Computer Science, Vol. 1097). Springer, 66–75

    1996

  23. [31]

    Thiago Serra, Xin Yu, Abhinav Kumar, and Srikumar Ramalingam. 2021. Scaling Up Exact Neural Network Compression by ReLU Stability. InNeurIPS. 27081– 27093

    2021

  24. [32]

    Quang Hieu Vo, Linh-Tam Tran, Sung-Ho Bae, Lok-Won Kim, and Choong Seon Hong. 2023. MST-compression: Compressing and Accelerating Binary Neural Networks with Minimum Spanning Tree. InICCV. IEEE, 6068–6077

    2023

  25. [33]

    Kanhere, and Mahbub Hassan

    Jun Yao, Salil S. Kanhere, and Mahbub Hassan. 2012. Improving QoS in High- Speed Mobility Using Bandwidth Maps.IEEE Trans. Mob. Comput.11, 4 (2012), 603–617. Algorithm 3Greedy Upgrading for MMUP Input:A set of matroids{M (𝑖) =(𝐸 (𝑖) ,I (𝑖) )}𝑖∈ [𝑛] , two element cost functions...

    2012

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