Enhancing Data Processing Efficiency in Blockchain Enabled Metaverse over Wireless Communications

Jun Zhao; Liangxin Qian

REVIEW 3 major objections 5 minor 30 references

Enhancing Data Processing Efficiency in Blockchain Enabled Metaverse over Wireless Communications

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read The paper claims that the DAUR algorithm turns the nonconvex problem of maximizing data processing efficiency in blockchain-enabled Metaverse wireless systems into a solvable convex optimization, and that in simulation it reaches 87.87…

desk verdict A useful rounding-comparison study and a plausible simulation story are currently attached to a central equivalence proof that does not hold as written; worth a referee, but only with a clear demand to fix Lemma 2. read the letter →

arxiv 2507.04657 v1 pith:3RVXD5RP submitted 2025-07-07 eess.SP

Liangxin Qian , Jun Zhao This is my paper · ORCID

classification eess.SP

keywords dataprocessingefficiencyblockchain-enabledMetaverseuserassociationresourceallocationfractionalprogrammingsemidefiniterelaxationdifference-of-convexwirelesscommunications

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 introduces data processing efficiency (DPE), the ratio of processed data bits to the sum of delay and energy consumption, as a system-level objective for blockchain-enabled Metaverse wireless networks where users offload NFT-related tasks to servers. The central claim is that the DAUR algorithm jointly optimizes user association, work offloading ratios, task-specific server resource splits, bandwidth, transmit power, and computing allocations by transforming the nonconvex sum-of-ratios problem into a sequence of solvable convex subproblems. The transformation alternates a fractional-programming block for communication and computing resources with a QCQP/SDP block, keeping the rank-one constraint and recovering discrete association by rank-1 approximation. Simulation results reported in the paper show DAUR achieving DPE 87.87 Mbit/(s·J), above RUCAA (80.78), GUCAA (80.38), AAUCO (83.25), and GUCRO (84.82). A sympathetic reader would take the paper's claim as: coordinated user-server association and resource allocation can be made tractable and measurably raises DPE, provided the server resource split is fixed at its assumed optimum.

What carries the argument

The central objects are the DPE ratio itself, DPE := processed bits/(delay + energy), and the DAUR algorithm that alternates two optimization blocks. The first block fixes user association $x$, offloading ratio $\phi$, and server split $\gamma$, and uses the auxiliary variable $\upsilon^{(s)}_{n,m} = 1/(2 x_{n,m}\rho_n p_n \phi_n d_n r_{n,m})$ to turn the nonconvex transmission-cost ratio into a convex surrogate. The second block fixes bandwidth, power, and computing allocations and relaxes the remaining mixed-integer QCQP into an SDR problem, whose rank-one constraint is handled by the DC penalty $\mathrm{Tr}(S)-\|S\|_2$ and linearized as Problem P12; rank-1 approximation then recovers the discrete association. Lemma 4 does key work: it sets the data size changing ratio $\omega_b = 1$ and declares the validation delay $T^{sv}$ negligible, so the optimal server resource split is $\gamma^* = 1/2$.

What would settle it

Take the same DPE maximization with $\omega_b = 2$ and with non-negligible validation delay, allow $\gamma$ to vary over $(0,1)$ while recomputing the optimal association and resources, and compare the resulting DPE with the value obtained at the fixed split $\gamma = 1/2$; if the variable-$\gamma$ solution is materially higher, Lemma 4's premise fails and DAUR's reported optimum holds only for the special case.

Watch

Extended reading notes

Core claim

The central claim is that the nonconvex problem P1, maximizing the sum of DPE ratios over discrete user association and continuous offloading and resource variables, can be relaxed into convex subproblems without losing solution quality. The argument proceeds by a fractional-programming transformation that rewrites each ratio with auxiliary variables $\alpha$ and $\vartheta$, then splits optimization into two blocks: with user association, offloading ratio, and server split fixed, the communication and computing block becomes concave through the auxiliary variable $\upsilon^{(s)}_{n,m}$; with the communication block fixed, the residual QCQP over $x$ and $\phi$ is relaxed by semidefinite relaxation, and the rank-one constraint is retained through a difference-of-convex penalty $\mathrm{Tr}(S)-\|S\|_2$ that is linearized into a convex problem. The discrete association is recovered by rank-1 approximation, which the paper's numerical comparison selects over Hungarian, randomized, secondary-discrete, and greedy rounding. The headline numeric result is DPE 87.87 Mbit/(s·J) at default settings, versus 80.78, 80.38, 83.25, and 84.82 for the four baselines.

Load-bearing premise

The paper's argument assumes that the data size changing ratio $\omega_b = 1$ and that the blockchain validation delay $T^{sv}$ is negligible; if either assumption fails, fixing the server resource split at $\gamma = 1/2$ is not optimal and the claimed joint optimization is not actually being carried out.

Editorial extensions

If this is right

Under the paper's simulation settings, DAUR achieves DPE 87.87 Mbit/(s·J), exceeding RUCAA, GUCAA, AAUCO, and GUCRO by about 7.09, 7.49, 4.62, and 3.05 Mbit/(s·J), respectively.
Retaining the rank-one constraint in the SDR step yields a slightly higher objective than dropping it, improving the conference-version values from 81.87 and 86.48 to 83.25 and 87.87.
The DAUR algorithm converges within one outer iteration for the tested (10,2), (20,3), and (30,4) setups, with total runtimes from 0.22 s to 228.86 s.
The paper states DAUR extends beyond DPE to energy-efficiency and utility-cost problems, with successive convex approximation available for nonconcave utility functions.
The method requires a centralized optimizer, which the paper identifies as a privacy risk and a target for future decentralized implementation.

Reading between the lines

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

If $\omega_b \neq 1$ or the validation delay is not negligible, the fixed split $\gamma = 1/2$ is no longer provably optimal, so the claimed joint optimization would need $\gamma$ as a decision variable; rerunning the simulations with $\omega_b = 2$ and optimizing over $\gamma$ is a direct test.
The reported DPE values scale with the preference weights $c_n$ and $c_{n,m}$; at low preference settings the paper reports DPE dropping to 17.29, so the absolute numbers are preference-dependent even if the ordering over baselines persists.
The validation delay $T^{sv}$ is modeled but then declared negligible; real systems with many validator servers may see block-generation and validation costs dominate, a regime the default simulation does not stress.
Because Algorithm 1 initializes $\gamma_{n,m} = 0.5$ and never updates it, the 'joint' optimization in the code is effectively over the other variables only; a version that treats $\gamma$ as an optimized variable would separate the paper's algorithmic contribution from its strongest simplifying assumption.

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.

Desk Editor's Note

read the letter

Colleague,

Quick take: this paper has a useful incremental result hiding behind an overclaimed equivalence proof. The new material compared with the MobiHoc version—DC-based rank-one retention, five rounding methods, updated simulations—is real and mostly described in enough detail to reimplement. The rounding comparison is the most valuable part: it gives concrete evidence for choosing rank-1 approximation over Hungarian/randomized/greedy, and the convergence plots match what the algorithm text says. The authors are also transparent about what changed from [1] and about the centralized limitation. That is honest work.

The problem is Lemma 2. As written, P3 is not equivalent to P2, and it is not even bounded: α and ϑ appear with no box or linking constraints, so for any feasible point with a positive term, you can drive that term to infinity. The "KKT values" in (17)-(20) are derived from the Lagrangian of P2, not P3, and plugging them into P3 makes every α(num−ϑ·cost) term zero, whereas P2's objective at the same point is the sum of DPE ratios. The proof in Appendix B therefore supports neither the transformation nor the claimed optimality. This is the load-bearing wall behind the abstract's "transforms into a solvable convex problem," and it currently does not stand. The fix is straightforward in spirit—present P3 as a fixed-parameter subproblem where α and ϑ are updated externally, as Algorithm 1 actually does, and prove convergence of that fixed-point iteration—but that is not what Lemma 2 states.

The γ=1/2 issue is real but secondary. Lemma 4 sets ωb=1 and ignores T^sv to get γ=1/2; Algorithm 1 initializes γ=0.5 and never updates it. So the "joint optimization" of task-specific computing split is not actually performed for ωb≠1 or nontrivial validation delay. Minor-to-moderate: the numerical conclusions use ωb=1, so at least the simulations are internally consistent with the assumption.

I would not call this a fundamental rejection of the engineering. The simulations are self-contained, the gains over the four baselines are modest but consistent across resource sweeps, and the method is plausibly useful for blockchain-MEC resource allocation. But the baselines are weak—random/greedy/average combinations—and there are no error bars or code, so the 80-to-88 Mbit/(s·J) story is a lower bound on what a skeptical reader needs.

Bottom line: worth a serious referee, but only with a clear instruction that Lemma 2 must be rewritten, γ justified, and stronger baselines added. I would not cite the theorem as it stands. I'd bring it to reading group only if someone wants to workshop the repair.

Referee Report

3 major / 5 minor

Summary. The paper introduces a data processing efficiency (DPE) metric for blockchain-enabled Metaverse wireless systems and proposes the DAUR algorithm to jointly optimize user association, work offloading, task-specific computing resource distribution, bandwidth, transmit power, and computing allocations. The optimization problem P1 is a nonconvex sum-of-ratios problem. The authors claim to transform P1 into a solvable convex problem through a sequence of auxiliary variables and relaxations (P2, P3, ..., P12), solved by an alternating fractional-programming and QCQP/SDR-with-DC-penalty approach. Simulations over several user/server configurations show that DAUR achieves a higher DPE (87.87 M bits/(s·J)) than four baseline schemes (80.38–84.82).

Significance. If the transformations and convergence claims are sound, the paper offers a practical joint user-association and resource-allocation algorithm for a timely application domain, and it proposes a meaningful efficiency metric (processed bits per delay-plus-energy) that generalizes earlier utility-cost metrics. The manuscript is unusually transparent: it clearly lists differences from the authors' conference version [1], provides an extensive appendix with proofs, reports running times and iteration counts, and compares several rounding techniques. The numerical study is self-contained and shows consistent improvements across bandwidth, server capacity, user capacity, transmit power, and weight-ratio sweeps. The central weakness is that the main theoretical transformation (Lemma 2) is not a valid equivalence as written; this undermines the paper's stated central claim, though the algorithmic framework and simulations may remain useful if the theoretical gap can be repaired.

major comments (3)

[Section V, Lemma 2, Eq. (16)–(20), Appendix B] The claimed equivalence of P2 and P3 is not correct as stated. In Problem P3, the variables α and ϑ appear only in the objective and have no constraints or bounds. For any feasible (x, ϕ, γ, φ, ρ, ζ, ψ, T), pick a term with x_{n,m} ϕ_n d_n > 0, set ϑ^s_{n,m} = 0, and let α^s_{n,m} → +∞; the objective tends to +∞. Hence P3 is unbounded above and cannot be equivalent to P2 or P1. Moreover, substituting the KKT values (17)–(20) into the P3 objective makes each bracketed term α(·)(num − ϑ·cost) equal to zero, so the P3 objective value at those points is zero, not the sum of DPE ratios of P2. The proof in Appendix B derives stationarity and complementary slackness of P2, not a transformation of P2 into P3. The intended statement appears to be that P3 is a fixed-parameter subproblem when α and ϑ are held constant and updated externally, as done in Algorithm 1; that formulation can be a valid algorithmic device, but Lemma 2 and the surrounding text must be rewritten to state and prove convergence of that fixed-point iteration rather than an equivalence.
[Section V-B, Lemma 4, Appendix D, Algorithm 1] Lemma 4 sets ω_b = 1 and treats the validation delay T^sv as negligible to conclude γ*? = 1/2. For general ω_b, the expression γ^2 + ω_b(1−γ)^2 is minimized at γ = ω_b/(1+ω_b), and the sum T^sp + T^sg is minimized at γ = 1/(1+ω_b), neither of which equals 1/2 unless ω_b = 1. The validation delay T^sv is not negligible in general, and it depends on the γ values of other servers, so the optimal γ would couple across servers. Algorithm 1 initializes γ_{n,m} = 0.5 and never updates it, so the claimed joint optimization of the task-specific computing resource split (variable γ) is not actually performed. This issue affects the validity of Theorem 3 and the interpretation of the simulation results, which set ω_b = 1 by default.
[Section V, paragraphs after Lemma 2 and Algorithm 1] The paper claims that the alternating block-coordinate update converges to a stationary point of Problem P3, but no convergence proof is provided for the outer loop of Algorithm 1 or for the overall DAUR procedure. Given that P3 as currently stated is unbounded, the stationarity claim is not meaningful without a corrected formulation. If the authors adopt the fixed-point interpretation of P3, they should prove that the sequence produced by the α/ϑ updates and the inner FP and QCQP loops converges to a stationary point of the original P1 (or of a properly defined surrogate), with explicit assumptions on the penalty parameter and rounding step.

minor comments (5)

[Abstract and Section V] The phrase 'transforms the nonconvex problem of maximizing the sum of DPE ratios into a solvable convex optimization problem' is repeated in the abstract, introduction, and Section V; given the issues in Lemma 2, this claim should be softened or made conditional on the fixed-point interpretation until the theory is repaired.
[Table I and Eq. (1)] The notation σ^2 φ_{n,m} b_m in the Shannon formula is introduced without defining σ^2 as a noise power spectral density; consider clarifying whether the bandwidth scaling is intentional.
[Appendix C, Lemma 3] The proof of Lemma 3 shows equality of partial derivatives between F and G at the specific value υ^s = 1/(2 x ρ p φ d r), which is a local first-order argument; the text should explain more precisely that this is a standard fractional-programming surrogate rather than an exact problem transformation, since the equality of functions is only shown at the stationary update value.
[Section VII and Fig. 5(c)] In Fig. 5(c), the vertical axis labels 'delay(s)', 'energy(J)', and 'DPE(Mbits/(s·J))' are combined in one plot, but the delay and energy values appear to be on different scales; clarifying the scaling or using separate subplots would improve readability.
[Overall] There are several typographical and formatting issues, including 'Karush-–Kuhn—Tucker' in the statement of Lemma 2, and inconsistent use of 'different-of-convex' versus 'difference-of-convex' in Section I; a careful pass for language and notation is needed.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the DPE definition, the DAUR derivation, and the simulation comparisons are self-contained, with self-citations used only as context or incremental comparison.

full rationale

The paper's central claim is that DAUR transforms the nonconvex sum-of-ratios problem P1 into a tractable sequence of convex subproblems. The derivation is carried out in the paper itself: Lemma 1 introduces auxiliary variables ϑ and T; Lemma 2 introduces α and states KKT relationships; Lemma 3 introduces υ(s); and Lemmas 4-6, together with the DC penalty reformulation, produce the final SDP/DC problems. The proofs are given in Appendices A-F, so the transformation chain does not rely on importing an external result as a black box. The numerical section compares DAUR against four self-implemented baselines (RUCAA, GUCAA, AAUCO, GUCRO) under the same simulation model; no parameter is fitted to an external target, and the reported DPE values are computed from the paper's own definition of DPE. Self-citations appear in two places: the conference version [1] is used only to state differences and improved DPE values, and prior work [22] by the same research group is mentioned in related work as having studied a utility-cost ratio. Neither citation is load-bearing for the paper's main theorem or algorithmic construction. The assumption in Lemma 4 that ωb=1 and that T^sv is negligible is a modeling/optimality assumption, not a circular reduction: the P1 objective and Algorithm 1 are not defined in terms of each other, and the correctness of the γ=1/2 claim is a separate mathematical issue rather than a circularity issue. The paper even acknowledges a limitation in the conclusion (centralized implementation risk), which further indicates that the claimed contribution is not merely restating its inputs. Overall, the derivation chain is self-contained enough that no specific circular step can be exhibited with quotes.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central derivation rests on standard wireless and blockchain cost models plus two load-bearing simplifications (ωb=1 and validation delay neglect); no new physical entities are introduced.

free parameters (3)

Penalty weight ̟ = 175
Hand-tuned in Section V.E using Fig. 3(a) so that the DC rank penalty term (Tr(S)-||S||_2) approaches zero; no principled selection rule is given.
Delay/energy weights ωt, ωe = 0.5 each
Chosen equal in the default settings (Section VII); changing them strongly changes DPE (Fig. 7(e)), and no calibration to real data is provided.
DPE preference weights cn, cn,m = 1/(5×10^5)
Set to scale DPE into the range 1-100 (Section VII); a normalization choice that affects all reported DPE values though not the comparative ranking.

assumptions (4)

standard math Shannon capacity formula for FDMA uplink (Eq. (1)) with no interference
Standard information-theoretic model, cited to [25]; the optimization depends on this rate expression throughout.
domain assumption Blockchain block propagation and validation costs follow the model of Feng et al. [7] (Eqs. (10)-(11))
The consensus delay T^bp=S_b/R_m and validation time T^sv are taken from [7] without re-derivation; errors in that model propagate into DPE.
ad hoc to paper Data size changing ratio ωb is set to 1 and validation delay is negligible (Lemma 4)
This allows fixing γ=1/2 in Algorithm 1; if ωb≠1 or validation delay matters, γ should be optimized and DAUR does not solve P1 as stated.
ad hoc to paper The alternating block-coordinate update and the DC penalty converge to a stationary point of the relaxed problem
Convergence is asserted with reference to DC algorithms [26], but no proof is given for the joint alternating P5/P12 procedure or for the quality of the rank-1 approximation.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Enhancing Data Processing Efficiency in Blockchain Enabled Metaverse over Wireless Communications." pith.science (2026). https://pith.science/paper/3RVXD5RP

@misc{pith2026250704657,
  author       = {Pith},
  title        = {Pith review of: Enhancing Data Processing Efficiency in Blockchain Enabled Metaverse over Wireless Communications},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3RVXD5RP}},
  note         = {Machine review of arXiv:2507.04657}
}

read the original abstract

In the rapidly evolving landscape of the Metaverse, enhanced by blockchain technology, the efficient processing of data has emerged as a critical challenge, especially in wireless communication systems. Addressing this challenge, our paper introduces the innovative concept of data processing efficiency (DPE), aiming to maximize processed bits per unit of resource consumption in blockchain-empowered Metaverse environments. To achieve this, we propose the DPE-Aware User Association and Resource Allocation (DAUR) algorithm, a tailored optimization framework for blockchain-enabled Metaverse wireless communication systems characterized by joint computing and communication resource constraints. The DAUR algorithm transforms the nonconvex problem of maximizing the sum of DPE ratios into a solvable convex optimization problem. It alternates the optimization of key variables, including user association, work offloading ratios, task-specific computing resource distribution, bandwidth allocation, user power usage ratios, and server computing resource allocation ratios. Our extensive numerical results demonstrate the DAUR algorithm's effectiveness in DPE.

Figures

Figures reproduced from arXiv: 2507.04657 by the authors.

**Figure 2.** Performance comparison of different rounding tech [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗

**Figure 3.** Performance comparison of different penalty weight [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: Relationships between Problems, Theorems, and Lem [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]

**Figure 5.** Figure 5: Convergence of FP and QCQP methods; Performance comp [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]

**Figure 6.** Figure 6: Comparison of convergence behavior with baselines. [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

**Figure 7.** Figure 7: Performance comparison of different communication [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

30 extracted references · 27 canonical work pages

[1]

Data processing efﬁciency aware use r association and resource allocation in blockchain enabled Metaverse ov er wireless communications,

L. Qian and J. Zhao, “Data processing efﬁciency aware use r association and resource allocation in blockchain enabled Metaverse ov er wireless communications,” in ACM MobiHoc, 2024, pp. 201–210

work page 2024
[2]

Non-fungible token ( NFT): Overview, evaluation, opportunities and challenges,

Q. Wang, R. Li, Q. Wang, and S. Chen, “Non-fungible token ( NFT): Overview, evaluation, opportunities and challenges,” arXiv preprint arXiv:2105.07447, 2021

arXiv 2021
[3]

Mapping the NFT revolution: Market tre nds, trade networks, and visual features,

M. Nadini, L. Alessandretti, F. Di Giacinto, M. Martino, L. M. Aiello, and A. Baronchelli, “Mapping the NFT revolution: Market tre nds, trade networks, and visual features,” Scientiﬁc Reports , vol. 11, no. 1, p. 20902, 2021

work page 2021
[4]

NFTs and the Metaverse revolution: Research p erspectives and open challenges,

K. Christodoulou, L. Katelaris, M. Themistocleous, P . C hristodoulou, and E. Iosif, “NFTs and the Metaverse revolution: Research p erspectives and open challenges,” Blockchains and the Token Economy: Theory and Practice, pp. 139–178, 2022

work page 2022
[5]

Edge intelligence-based ultra-reliable and l ow-latency communications for digital twin-enabled metaverse,

D. V an Huynh, S. R. Khosravirad, A. Masaracchia, O. A. Dob re, and T. Q. Duong, “Edge intelligence-based ultra-reliable and l ow-latency communications for digital twin-enabled metaverse,” IEEE Wireless Communications Letters , vol. 11, no. 8, pp. 1733–1737, 2022

work page 2022
[6]

The en ergy consumption of blockchain technology: Beyond myth,

J. Sedlmeir, H. U. Buhl, G. Fridgen, and R. Keller, “The en ergy consumption of blockchain technology: Beyond myth,” Business & Information Systems Engineering , vol. 62, no. 6, pp. 599–608, 2020. 15

work page 2020
[7]

Joint optimiza tion of radio and computational resources allocation in blockchain-ena bled mobile edge computing systems,

J. Feng, F. R. Y u, Q. Pei, J. Du, and L. Zhu, “Joint optimiza tion of radio and computational resources allocation in blockchain-ena bled mobile edge computing systems,” IEEE Transactions on Wireless Communica- tions, vol. 19, no. 6, pp. 4321–4334, 2020

work page 2020
[8]

Joint computati on ofﬂoading and user association in multi-task mobile edge computing,

Y . Dai, D. Xu, S. Maharjan, and Y . Zhang, “Joint computati on ofﬂoading and user association in multi-task mobile edge computing,” IEEE Transactions on V ehicular Technology , vol. 67, no. 12, pp. 12 313– 12 325, 2018

work page 2018

Show all 30 references

[9]

An energy efﬁcient and spectrum efﬁc ient wireless heterogeneous network framework for 5G systems,

R. Q. Hu and Y . Qian, “An energy efﬁcient and spectrum efﬁc ient wireless heterogeneous network framework for 5G systems,” IEEE Communications Magazine , vol. 52, no. 5, pp. 94–101, 2014

2014
[10]

Lifesaving wi th RescueChain: Energy-efﬁcient and partition-tolerant blo ckchain based secure information sharing for UA V-aided disaster rescue,

Y . Wang, Z. Su, Q. Xu, R. Li, and T. H. Luan, “Lifesaving wi th RescueChain: Energy-efﬁcient and partition-tolerant blo ckchain based secure information sharing for UA V-aided disaster rescue, ” in IEEE IN- FOCOM 2021-IEEE Conference on Computer Communications . V an- couver,...

2021
[11]

Near-optimal and practical jamming-resistant energy-efﬁcient cognitive r adio communi- cations,

P . Zhou, Q. Wang, W. Wang, Y . Hu, and D. Wu, “Near-optimal and practical jamming-resistant energy-efﬁcient cognitive r adio communi- cations,” IEEE Transactions on Information F orensics and Security , vol. 12, no. 11, pp. 2807–2822, 2017

2017
[12]

Towards efﬁcient and energy-aware query processing for industrial Internet of Things,

L. Liu, Y . Wang, W. Meng, Z. Xu, W. Gao, and Z. Ma, “Towards efﬁcient and energy-aware query processing for industrial Internet of Things,” Peer-to-Peer Networking and Applications , vol. 14, no. 6, pp. 3895– 3914, 2021

2021
[13]

Safe and pr actical energy-efﬁcient detour routing in IP networks,

Q. Li, M. Xu, Y . Y ang, L. Gao, Y . Cui, and J. Wu, “Safe and pr actical energy-efﬁcient detour routing in IP networks,” IEEE/ACM Transactions on Networking , vol. 22, no. 6, pp. 1925–1937, 2014

1925
[14]

Cloudshare: Towards a cost-efﬁcient and privacy-p reserving alliance cloud using permissioned blockchains,

Y . Li, L. Zhu, M. Shen, F. Gao, B. Zheng, X. Du, S. Liu, and S. Yin, “Cloudshare: Towards a cost-efﬁcient and privacy-p reserving alliance cloud using permissioned blockchains,” in Mobile Networks and Management: 9th International Conference . Melbourne, Australia: Springer, ...

2018
[15]

Throughput maximization in wireles s powered communication networks,

H. Ju and R. Zhang, “Throughput maximization in wireles s powered communication networks,” IEEE Transactions on Wireless Communica- tions, vol. 13, no. 1, pp. 418–428, 2013

2013
[16]

Proof of learn ing (PoLe): Empowering neural network training with consensus building on blockchains,

Y . Liu, Y . Lan, B. Li, C. Miao, and Z. Tian, “Proof of learn ing (PoLe): Empowering neural network training with consensus building on blockchains,” Computer Networks , vol. 201, p. 108594, 2021

2021
[17]

A daptive resource allocation in future wireless networks with block chain and mo- bile edge computing,

F. Guo, F. R. Y u, H. Zhang, H. Ji, M. Liu, and V . C. Leung, “A daptive resource allocation in future wireless networks with block chain and mo- bile edge computing,” IEEE Transactions on Wireless Communications , vol. 19, no. 3, pp. 1689–1703, 2019

2019
[18]

Blockchain assisted federated learning over wirele ss channels: Dynamic resource allocation and client scheduling,

X. Deng, J. Li, C. Ma, K. Wei, L. Shi, M. Ding, W. Chen, and H . V . Poor, “Blockchain assisted federated learning over wirele ss channels: Dynamic resource allocation and client scheduling,” IEEE Transactions on Wireless Communications , vol. 22, no. 5, pp. 3537–3553, 2022

2022
[19]

Decentralized IoT resource monitoring and scheduling fra mework based on blockchain,

D. Li, R. Chen, Q. Wan, Z. Guan, Y . Sun, Q. Wu, J. Hu, and J. L iu, “Decentralized IoT resource monitoring and scheduling fra mework based on blockchain,” IEEE Internet of Things Journal , vol. 10, no. 24, pp. 21 135–21 142, 2023

2023
[20]

H ealthchain: A blockchain-based privacy preserving scheme for large-sc ale health data,

J. Xu, K. Xue, S. Li, H. Tian, J. Hong, P . Hong, and N. Y u, “H ealthchain: A blockchain-based privacy preserving scheme for large-sc ale health data,” IEEE Internet of Things Journal , vol. 6, no. 5, pp. 8770–8781, 2019

2019
[21]

Efﬁcie nt QoS support for robust resource allocation in blockchain-base d femtocell networks,

Z. Liu, L. Gao, Y . Liu, X. Guan, K. Ma, and Y . Wang, “Efﬁcie nt QoS support for robust resource allocation in blockchain-base d femtocell networks,” IEEE Transactions on Industrial Informatics , vol. 16, no. 11, pp. 7070–7080, 2019

2019
[22]

Human-centric resource all ocation in the Metaverse over wireless communications,

J. Zhao, L. Qian, and W. Y u, “Human-centric resource all ocation in the Metaverse over wireless communications,” IEEE Journal on Selected Areas in Communications , vol. 42, no. 3, pp. 514–537, 2024

2024
[23]

MetaSlicing: A novel resource alloca tion framework for Metaverse,

N. H. Chu, D. T. Hoang, D. N. Nguyen, K. T. Phan, E. Dutkiew icz, D. Niyato, and T. Shu, “MetaSlicing: A novel resource alloca tion framework for Metaverse,” IEEE Transactions on Mobile Computing , vol. 1, pp. 1–18, 2023

2023
[24]

Uniﬁed resource allocation framework for the edge intelli gence-enabled Metaverse,

W. C. Ng, W. Y . B. Lim, J. S. Ng, Z. Xiong, D. Niyato, and C. M iao, “Uniﬁed resource allocation framework for the edge intelli gence-enabled Metaverse,” in ICC 2022-IEEE International Conference on Communi- cations. Seoul, Korea: IEEE, 2022, pp. 5214–5219

2022
[25]

A mathematical theory of communication ,

C. E. Shannon, “A mathematical theory of communication ,” The Bell System Technical Journal , vol. 27, no. 3, pp. 379–423, 1948

1948
[26]

Over-the-air computation via inte lligent reﬂecting surfaces,

T. Jiang and Y . Shi, “Over-the-air computation via inte lligent reﬂecting surfaces,” in 2019 IEEE Global Communications Conference (GLOBE- COM). IEEE, 2019, pp. 1–6

2019
[27]

The Hungarian method for the assignment pro blem,

H. W. Kuhn, “The Hungarian method for the assignment pro blem,” Naval Research Logistics Quarterly , vol. 2, no. 1-2, pp. 83–97, 1955

1955
[28]

Sem ideﬁnite relaxation of quadratic optimization problems,

Z.-Q. Luo, W.-K. Ma, A. M.-C. So, Y . Y e, and S. Zhang, “Sem ideﬁnite relaxation of quadratic optimization problems,” IEEE Signal Processing Magazine, vol. 27, no. 3, pp. 20–34, 2010

2010
[29]

Tutorial: Complexity analys is of singular value decomposition and its variants,

X. Li, S. Wang, and Y . Cai, “Tutorial: Complexity analys is of singular value decomposition and its variants,” arXiv preprint arXiv:1906.12085 , 2019

1906 arXiv
[30]

Performa nce analysis and location optimization for massive MIMO systems with cir cularly distributed antennas,

A. Y ang, Y . Jing, C. Xing, Z. Fei, and J. Kuang, “Performa nce analysis and location optimization for massive MIMO systems with cir cularly distributed antennas,” IEEE Transactions on Wireless Communications , vol. 14, no. 10, pp. 5659–5671, 2015. APPENDIX A PROOF OF LEMMA 1...

2015

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

Data processing efﬁciency aware use r association and resource allocation in blockchain enabled Metaverse ov er wireless communications,

L. Qian and J. Zhao, “Data processing efﬁciency aware use r association and resource allocation in blockchain enabled Metaverse ov er wireless communications,” in ACM MobiHoc, 2024, pp. 201–210

work page 2024

[2] [2]

Non-fungible token ( NFT): Overview, evaluation, opportunities and challenges,

Q. Wang, R. Li, Q. Wang, and S. Chen, “Non-fungible token ( NFT): Overview, evaluation, opportunities and challenges,” arXiv preprint arXiv:2105.07447, 2021

arXiv 2021

[3] [3]

Mapping the NFT revolution: Market tre nds, trade networks, and visual features,

M. Nadini, L. Alessandretti, F. Di Giacinto, M. Martino, L. M. Aiello, and A. Baronchelli, “Mapping the NFT revolution: Market tre nds, trade networks, and visual features,” Scientiﬁc Reports , vol. 11, no. 1, p. 20902, 2021

work page 2021

[4] [4]

NFTs and the Metaverse revolution: Research p erspectives and open challenges,

K. Christodoulou, L. Katelaris, M. Themistocleous, P . C hristodoulou, and E. Iosif, “NFTs and the Metaverse revolution: Research p erspectives and open challenges,” Blockchains and the Token Economy: Theory and Practice, pp. 139–178, 2022

work page 2022

[5] [5]

Edge intelligence-based ultra-reliable and l ow-latency communications for digital twin-enabled metaverse,

D. V an Huynh, S. R. Khosravirad, A. Masaracchia, O. A. Dob re, and T. Q. Duong, “Edge intelligence-based ultra-reliable and l ow-latency communications for digital twin-enabled metaverse,” IEEE Wireless Communications Letters , vol. 11, no. 8, pp. 1733–1737, 2022

work page 2022

[6] [6]

The en ergy consumption of blockchain technology: Beyond myth,

J. Sedlmeir, H. U. Buhl, G. Fridgen, and R. Keller, “The en ergy consumption of blockchain technology: Beyond myth,” Business & Information Systems Engineering , vol. 62, no. 6, pp. 599–608, 2020. 15

work page 2020

[7] [7]

Joint optimiza tion of radio and computational resources allocation in blockchain-ena bled mobile edge computing systems,

J. Feng, F. R. Y u, Q. Pei, J. Du, and L. Zhu, “Joint optimiza tion of radio and computational resources allocation in blockchain-ena bled mobile edge computing systems,” IEEE Transactions on Wireless Communica- tions, vol. 19, no. 6, pp. 4321–4334, 2020

work page 2020

[8] [8]

Joint computati on ofﬂoading and user association in multi-task mobile edge computing,

Y . Dai, D. Xu, S. Maharjan, and Y . Zhang, “Joint computati on ofﬂoading and user association in multi-task mobile edge computing,” IEEE Transactions on V ehicular Technology , vol. 67, no. 12, pp. 12 313– 12 325, 2018

work page 2018