## What is/are Complexity Analysis?

Complexity Analysis - Through 0-1 test, Lyapunov exponent, bifurcation diagram and complexity analysis, the system is deeply investigated.^{[1]}We provide evidence through numerical tests, mathematical error bound estimation, and complexity analysis that the method can address the “curse of dimensionality,” where each additional input parameter no longer leads to an exponential growth of the computational cost.

^{[2]}A complexity analysis of the algorithm reveals that the proposed algorithm is computationally significantly less expensive for systems with high redundancy, such as RBS, than existing algorithms that compute all MSO sets.

^{[3]}The performance evaluation and the computational-complexity analysis of our proposed new NOMA scheme are also conducted.

^{[4]}Accordingly, we propose an iterative algorithm to effectively obtain the locally optimal solution to our throughput optimization problems and further present the complexity analysis of this algorithm.

^{[5]}The competence and strength of the proposed OBL-MO-SSA is characterised by using performance metrics, complexity analysis, convergence rate and statistical significance.

^{[6]}More importantly, for the complexity analysis of the CAD computation via a perfect elimination ordering, an (m,d)-property of the full set of projection polynomials obtained via such an ordering is given, through which the "size'' of this set is characterized.

^{[7]}Finally, the time-complexity analysis of our algorithmic proposal is carried out.

^{[8]}A complexity analysis of the taint analysis algorithm is presented along with a detailed ‘deep’ multilingual example with Python and C/C++ software.

^{[9]}We carefully document the computational savings via complexity analysis and an extensive empirical study.

^{[10]}The approach builds an extended meta-model of the Problem Frames approach to support representing causal behaviours of the environment of CPS, which are essential domain knowledge of the environment for modelling CPS requirements and complexity analysis.

^{[11]}This largely alleviates the dominant computational burden pointwise at each time instant or system state, which is supported by complexity analysis, and validated through simulations.

^{[12]}The algorithmic complexity existing theory lack is noted - the calculation result and cognitive complexity quality exclusion from the complexity analysis.

^{[13]}Fibonacci sequence (Bhattacharyya in complexity analysis of a lossless data compression algorithm using Fibonacci sequence.

^{[14]}We present the results of the comparative performance-versus-complexity analysis for the several types of artificial neural networks (NNs) used for nonlinear channel equalization in coherent optical communication systems.

^{[15]}The complexity analysis is based on a conservative computation model using a writer monad.

^{[16]}The experimental results and complexity analysis have demonstrated that the proposed algorithm has significant improvement in terms of its performance and computational efficiency in largescale multi-objective optimization.

^{[17]}The chaotic characteristics of the new chaotic system are analyzed by phase diagram, Lyapunov exponent, bifurcation diagram and complexity analysis.

^{[18]}Numerical results and complexity analysis show that the proposed methods have good bit error rate versus complexity trade-off for various applications when compared with some existing algorithms.

^{[19]}The complexity analysis has shown that the proposed SD-based QCSS-MC-CDMA receiver for multiuser communication provides lower complexity than that of ML-based QCSS-MC-CDMA receiver.

^{[20]}A complexity analysis of the problem has been performed, and then graph theory notions has been employed by reducing the problem to incompatibility graphs that make the storage constraints more clearly visible.

^{[21]}In addition, in a systems course, these algorithms are typically covered in an informal way, avoiding proofs of correctness or complexity analysis.

^{[22]}Furthermore, we propose an alternative computation efficiency maximization algorithm, followed by the convergence and complexity analysis.

^{[23]}The improved map has been proven to be random and unpredictable by complexity analysis.

^{[24]}In this paper, we study this technique from the standpoints of complexity analysis and the algorithm’s practical performance.

^{[25]}The complexity analysis of this algorithm uses at the same time the techniques developed by Sidford et al.

^{[26]}Complexity analysis and simulation results demonstrate the efficacy of the proposed computation method and the DFE-based detectors.

^{[27]}This research has contributed to academic literature and practice by: (1) advancing decision-support systems for construction management by developing a dynamic simulation environment that uses real-time data to enhance simulation predictability; (2) developing integrated analytical methods for improved modeling in fabrication quality-associated decision making; and (3) creating reliable and interpretable decision-support metrics for quality performance measurement, complexity analysis, and rework cost management to reduce the data interpretation load of practitioners and to uncover valuable knowledge and information from available data sources.

^{[28]}A complexity analysis of the algorithm is done to prove its efficiency in terms of memory usage and runtime.

^{[29]}In order to meet this challenge, it is necessary to conduct a complexity analysis of social manufacturing.

^{[30]}For that end, computational simulations and a complexity analysis for different detectors are carried out.

^{[31]}Finally, numerical analysis shows the proposed model can perform better over other baseline methods in terms of deprived AI services, server utilization, and complexity analysis.

^{[32]}The article comprises of introductory pattern matching tactics, quantum basics, Grover's search method, quantum based pattern matching algorithms, their illustration followed by complexity analysis, and finally concludes with the possible algorithmic variations and relevant applications.

^{[33]}After discussing the properties of the proposed approach, we validate our methods through the complexity analysis and extensive simulated experiments.

^{[34]}Furthermore, an efficient optimization method is developed and the complexity analysis of CSLMR is presented for completeness.

^{[35]}These protocols are also evaluated for performance efficiency with respect to various aspects like call setup and management issues, addressing and security aspects, complexity analysis.

^{[36]}Through extensive simulations under various channel conditions and complexity analysis, it is shown that proposed OWMMSE-CML detection scheme offers performance nearer to optimal ML and also outperforms suboptimal signal vector based minimum mean square error (SVMMSE) detection scheme with a significant reduction in computational complexity.

^{[37]}Finally, a complexity analysis has been performed and simulation results have been also presented.

^{[38]}The activation analysis, PE based complexity analysis, and k-means clustering analysis were conducted.

^{[39]}The problem’s complexity analysis is provided.

^{[40]}The complexity analysis and experiments on two real datasets showed that our proposed can reduce time consuming significantly in computation when compared to the existing algorithm that also apply power set for this task.

^{[41]}The complexity analysis and simulation results validate the superiority of the proposed DL-NML detector.

^{[42]}Simulation results and complexity analysis show that the proposed method has better performance without increasing computation complexity, as compared to the central-symmetry-based feature detection method.

^{[43]}The paper presents the complexity analysis of financing innovations associated with limited budgetary opportunities, insufficient participation of banks in the implementation of innovative investment projects.

^{[44]}To end this, the complexity analysis is performed in terms of beam generations as a function of speed of user.

^{[45]}A complexity analysis of this solution in terms of imprint over 5G Architecture, latency and dimensionality is used to validate the proposal.

^{[46]}The complexity analysis and simulation experiments are given, and the results of Monte Carlo experiments show that compared with the traditional source number estimation method, this method can not only improve the accuracy of the source number estimation but also realize the effective estimation of the source number in undetermined conditions.

^{[47]}Permutation entropy (PE) is a powerful tool for complexity analysis, but it has some limitations.

^{[48]}

## Computational Complexity Analysis

Computational complexity analysis and numerical results show that LAC-OFDM has nearly the same spectral efficiency as layered asymmetrically clipped optical OFDM (LACO-OFDM) and enhanced unipolar OFDM (eU-OFDM) but is less complex.^{[1]}Additionally, we carried out a brief computational complexity analysis where ELM presented only 1.

^{[2]}The paper also includes an exhaustive list of all other SCs that can be directly computed using nodal voltage SCs, a computational complexity analysis of the proposed method and a numerical benchmarking.

^{[3]}In addition, we have also presented a novel computational complexity analysis for the AURA-5G framework as well as a solvability and convergence time analysis.

^{[4]}Subsequently, we provide the theoretical analysis of VVAMo, including the convergence proof and computational complexity analysis.

^{[5]}Controller tuning rules are used for the process using a test bench, and it also the computational complexity analysis and process algorithms dynamics and sampled non- dominant pole type different types of distribution of data point's stable solution that provides an implementation of the hypothesis test for robustness.

^{[6]}Finally, simulation results and computational complexity analysis verify the superiority of the proposed DS-AMP algorithm over state-of-the-art algorithms in the uncoded case.

^{[7]}Furthermore, computational complexity analysis and data transport costs of the algorithms are presented.

^{[8]}We also provide the finite convergence analysis and computational complexity analysis to KPνSVC and KEP.

^{[9]}We also give the convergence conditions of the iteration algorithm and the computational complexity analysis of CEEKF.

^{[10]}The article proposes the algorithm for the suggested method and presents its computational complexity analysis.

^{[11]}Further, the computational complexity analysis and BER performance of the proposed method are presented in comparison to typical existing methods.

^{[12]}In addition, the computational complexity analysis shows that compared with the conventional DOA and polarization estimation algorithms, our proposed QNC-MUSIC has much lower computational complexity, especially when the source number is large.

^{[13]}In addition, according to the computational complexity analysis, it is verified CD has the same time complexity with original k-means method.

^{[14]}Additionally, a computational complexity analysis is presented.

^{[15]}A closed-form mean square error expression and computational complexity analysis are derived to quantify the achievable advantages.

^{[16]}Furthermore, an alternative joint NOMA-SU assignment and power allocation scheme are proposed with its average computational complexity analysis given.

^{[17]}Furthermore, we present an inverse transform to recover the signal from its spatial-Slepian coefficients, formulate an algorithm for fast computation of SST, and carry out computational complexity analysis.

^{[18]}We also derive the diversity order, sum-rate, and perform the computational complexity analysis of the NOMA-HetNet system employing the proposed scheme.

^{[19]}In addition, this paper also performs fault detectability analysis and computational complexity analysis on these two methods.

^{[20]}Using computational complexity analysis, we show that this is not an implementational artifact, but instead it reflects a deeper theoretical issue: these models are (in their current formulation) computationally intractable.

^{[21]}These computational complexity analysis at the binary logical level can be further used with other error correcting codes adopted in different communication standards.

^{[22]}The proposed algorithms have been verified through numerical results with computational complexity analysis.

^{[23]}DL to generate 1-D acoustic synthetic seismograms without solving wave equation Solution to the 1-D problem through custom Recurrent Neural Network Retraining strategy to improve flexibility and applicability Computational complexity analysis.

^{[24]}Simulation results and computational complexity analysis validate the efficiency of the bidding framework.

^{[25]}The convergence of the proposed algorithm is proved and the corresponding computational complexity analysis is also presented.

^{[26]}The computational complexity analysis and simulation results confirm the effectiveness of the proposed iterative algorithm where no existing alternatives are available.

^{[27]}Computational complexity analysis is carried out along with a numerical case study to compare the accuracy and efficiency of both methods against the analytical solutions.

^{[28]}Our contributions in improving RIS-aided links include (1) design of gradient ascent co-design algorithms, (2) asymptotic (Big O) computational complexity analysis of proposed and considered prior algorithms, and (3) comparison of seven co-design algorithms in spectral efficiency vs.

^{[29]}Furthermore, computational complexity analysis is performed for the three best-performing algorithms, and random forest emerges as the most viable model for our envisioned LiHEA.

^{[30]}Mutual information and computational complexity analysis suggests that 2x oversampling of the signal is a good tradeoff between receiver performance and its complexity.

^{[31]}Despite the several theoretical analyses on the computational structure of an HPSM in connection to LOC, the experimental demonstration and the computational complexity analysis via the linear optical system have not been performed yet.

^{[32]}The superiority of the SPM for oil spill detection compared to traditional spectral similarity measures is demonstrated for the first time based on accuracy assessments and computational complexity analysis by comparing with four traditional spectral similarity measures, random forest (RF), support vector machine (SVM), and decision tree (DT).

^{[33]}The efficiency of the proposed condensation method was also investigated using a computational complexity analysis with an $n$ -flexible body pendulum.

^{[34]}Further, we also present the convergence proof and the computational complexity analysis of our method.

^{[35]}The simulation results and computational complexity analysis indicate that the proposed algorithm can significantly reduce the computational burden of the BFLANN-based ANC system without suffering from noise-canceling performance degradation.

^{[36]}These are the convergence analysis, statistical analysis, search history analysis, trajectory analysis, average distance analysis, computational complexity analysis.

^{[37]}The experimental and computational complexity analysis demonstrate the significant performance improvement of the proposed method over the state-of-the-art techniques in terms of recognition rate.

^{[38]}Additionally, computational complexity analysis of the classifier using the proposed fingerprints is provided.

^{[39]}Computational complexity analysis shows that the new method with low computation overhead and high communication efficiency can be effectively adapted to the electronic commerce scene.

^{[40]}Furthermore, a detailed computational complexity analysis of the proposed algorithm is presented which shows that the algorithm has moderate computational complexity and has good performance in fast time varying channel conditions with high node mobility in a MIMO-OFDM system.

^{[41]}Subsequently, a computational complexity analysis of the proposed model has been discussed with an eye toward hardware implementation.

^{[42]}A closed-form mean-square error expression and computational complexity analysis are derived to quantify the achievable advantages.

^{[43]}Additionally, computational complexity analysis of all salient dictionary learning and related methods is presented.

^{[44]}Computational complexity analysis and numerical results show that LAC-OFDM has the same spectral efficiency as layered asymmetrically clipped optical OFDM (LACO-OFDM) and enhanced unipolar OFDM (eU-OFDM) but is less complex in terms of both the number of real multiplications and real additions required.

^{[45]}Likewise, a computational complexity analysis is presented.

^{[46]}Then, we analyze the effects of presented codes on the phase differences and provide the computational complexity analysis.

^{[47]}First, proposers or guest editors of special issues should note that the thrust of Journal of RealTime Image Processing is on the real-time aspects of image and video processing; examples of these aspects include, but not limited to, computational complexity analysis and reduction compared to existing solutions, real-time hardware implementation, and steps taken to achieve real-time throughput.

^{[48]}A greedy algorithm is developed with computational complexity analysis.

^{[49]}A computational complexity analysis of the unified approach is also provided.

^{[50]}

## Time Complexity Analysis

Evaluation results of memory usage and time complexity analysis, beside the experimental evaluations efficiency and effectiveness measures show that the proposed multi-dimensional indexing technique significantly improves both efficiency and effectiveness for a medical image search engine.^{[1]}Furthermore, we present the convergence analysis and the time complexity analysis of our algorithm.

^{[2]}The performance comparison includes the error minimization and time complexity analysis.

^{[3]}Our time complexity analysis shows that the two proposed robust defense approaches are efficient.

^{[4]}We provide an overview of the state-of-the-art in the time complexity analysis of selection hyper-heuristics for combinatorial optimisation.

^{[5]}Results show that in accordance with time complexity analysis, our algorithms can dramatically reduce the running time for the first two problems compared with existing work, and effectively solve the general optimal set stabilization problem.

^{[6]}Then we give the time complexity analysis and space complexity analysis of the two methods.

^{[7]}Time complexity analysis is used to develop a real-time crank-angle resolved model with high accuracy in this study.

^{[8]}Besides time complexity analysis, we perform sensitivity analysis and ranking order comparison to check the correctness, stability, and reliability of the rankings generated by each method.

^{[9]}Furthermore, time complexity analysis, parameter analysis and motif analysis are conducted to demonstrate the effectiveness of our proposed algorithm from several perspectives.

^{[10]}Time complexity analysis shows that our scheme is asymptotically superior to known solutions.

^{[11]}The method time complexity analysis is explained.

^{[12]}The asymptotic time complexity analysis shows the algorithm routes packages in O (n log n).

^{[13]}Our time complexity analysis shows that the two proposed robust defense approaches are efficient.

^{[14]}A comparative time complexity analysis of 01IP and QUBO is also presented.

^{[15]}Time complexity analysis further shows that our heuristic runs in polynomial time.

^{[16]}Besides, time complexity analysis, convergence analysis, and parameter analysis are conducted to demonstrate the robustness of the proposed algorithm from different perspectives.

^{[17]}Time complexity analysis and practical computational results showed that the naive implementation of the CGA is not as efficient as classical formulation.

^{[18]}Time complexity analysis shows that the CPSS is more efficient than that of the polynomial time solutions.

^{[19]}With the time complexity analysis, we theoretically deduce that the time complexity of FLGSS is not beyond that of KNN.

^{[20]}Through time complexity analysis between different methods, the improved algorithm reduces the time consumption of comparisons and connections when processing large-scale data.

^{[21]}Time complexity analysis of the the heuristic approach presented in this paper for the circulation algorithm takes O(n) time.

^{[22]}In this paper, we present a first time complexity analysis of Cartesian Genetic Programming.

^{[23]}The time complexity analysis explains the theoretical superiority over the state-of-the-art CPU sequential algorithm ( O ( $$\ell ^2)$$ ℓ 2 ) ).

^{[24]}Finally, the time complexity analysis is discussed to conclude that HGSA has the same computational efficiency in comparison with other GSAs.

^{[25]}Furthermore, a time complexity analysis is performed to show the effectiveness of the model in NFV applications.

^{[26]}The time complexity analysis demonstrates the low time complexity of the proposed parallel algorithm.

^{[27]}The results of robustness analysis and time complexity analysis show that L1 trend filtering can extract the trend items accurately in the time series under given different noise levels, and the execution time is also lower than 176.

^{[28]}Finally, we also present a time complexity analysis of the SecureSurgiNET through simulations.

^{[29]}In this work, we first perform a time complexity analysis of IDS and RAPID, and show the significant advantages of the proposed method.

^{[30]}In addition, time complexity analysis and parameter analysis are conducted to demonstrate the robustness of the proposed methods.

^{[31]}

## Detailed Complexity Analysis

We validate the functional correctness and usefulness of the proposed work via a realistic wireless application and detailed complexity analysis demonstrates its feasibility in realizing intelligent radios.^{[1]}Moreover, detailed complexity analysis showed that the proposed UAD algorithm has relatively low complexity and good scalability.

^{[2]}Further, we present the detailed complexity analysis comparison of each algorithm.

^{[3]}Furthermore, an integer program, a detailed complexity analysis, and a computational study are presented.

^{[4]}We provide a detailed complexity analysis including results on approximations as well as polynomial-time algorithms for the general setting and important restricted settings.

^{[5]}We provide a detailed complexity analysis and compare our method to three state-of-the-art methods on a large dataset.

^{[6]}We propose improvements for all implementations, which take this fact into account, and we give a detailed complexity analysis, which is validated by an experimental analysis.

^{[7]}We conduct a detailed complexity analysis of the features provided by FLUID.

^{[8]}To validate our proposal we present a detailed complexity analysis and an extensive set of experiments with synthetic and real datasets, which corroborate the efficiency of the algorithms and the utility of the new operators.

^{[9]}Then, we present the general formulation and detailed complexity analysis.

^{[10]}Numerical simulations have been performed to evaluate the performance of this proposed scheme, while a detailed complexity analysis shows that the proposed scheme can result in significant simplification in the receiver design complexity without incurring much performance loss.

^{[11]}We provide a detailed complexity analysis for different fragments of HyperLTL and different system types: tree-shaped, acyclic, and general Kripke structures.

^{[12]}A detailed complexity analysis and extensive simulation analysis of the proposed method is executed to prove its efficiency compared to some standard approaches.

^{[13]}Finally, detailed complexity analysis and comparison have been conducted to prove the efficiency of the proposed strategy.

^{[14]}Our detailed complexity analysis shows that our newly proposed variants are at least as efficient as previously known algorithms, and in many cases significantly better.

^{[15]}We provide a detailed complexity analysis for FIA over LFMs and conduct extensive experiments to evaluate its performance using real-world datasets.

^{[16]}Applications of the given procedure to system analysis and to control design problems are reported as well as a detailed complexity analysis.

^{[17]}To successfully carry out the proposed design strategy, we have used the modified shifted polynomial basis (MSPB) to represent the field and have conducted three coherent interdependent stages of efforts: (i) a novel 1-bit parity based detection scheme for bit-serial MSPB multiplier is presented after thorough mathematical derivation; (ii) a novel Toeplitz matrix-vector product (TMVP)-based multi-bit parity detection scheme for digit-serial MSPB multiplier is proposed then to obtain both high detection performance and low-complexity implementation; (iii) detailed complexity analysis and comparison show that the proposed designs have significantly better performance over the best of existing ones.

^{[18]}

## Theoretical Complexity Analysis

A theoretical complexity analysis and a recent application of 3D FD-FWI based upon direct solver suggest that the FP algorithm should reduce the cost of IR-WRI by a factor of approximately 2 and 10 for 3D dense ocean bottom cable and sparse ocean bottom node acquisitions, respectively.^{[1]}Our theoretical complexity analysis shows that the proposed framework is more efficient compared to its vector-based counterpart in both memory and computation requirement.

^{[2]}The authors perform theoretical complexity analysis in this situation and show that the computational complexity of the algorithm is $${\cal O}\left( {d{n^4} + {d^2}{n^3}} \right)$$ O ( d n 4 + d 2 n 3 ) , where n is the dimension of the polynomial vector and d is the maximum degree of the polynomials in the vector.

^{[3]}Theoretical complexity analysis suggests, and experimental evidence confirms, that the Generalized ADMM is far more efficient for large problems.

^{[4]}We provide theoretical complexity analysis as well as detailed experimental results.

^{[5]}In attempt to establish the basis for a relative theoretical complexity analysis, this paper introduces a method to compute the Shattering coefficient of DT models using recurrence equations.

^{[6]}In addition theoretical complexity analysis of the block matching part inside NSF is provided.

^{[7]}Theoretical complexity analysis and numerical simulation results testify the efficiency of the proposed method over state-of-the-art algorithms.

^{[8]}

## My Complexity Analysis

Our complexity analysis takes place in the multitape Turing machine model, with integers encoded in the usual binary representa- tion.^{[1]}Our complexity analysis justifies that the quantum algorithmic solutions achieve computational speedup over classical methods.

^{[2]}Our complexity analysis shows that the proposed vector codes yield much lower encoding/decoding complexity than the scalar codes.

^{[3]}Our complexity analysis indicates that our system could be used in practical settings.

^{[4]}Our complexity analysis and proof-of-concept implementation results show that DECOUPLES is a feasible traceability system for the supply chain.

^{[5]}Our complexity analysis characterizes the complexity reduction brought by the transform and shows high rate codes benefit a greater complexity reduction.

^{[6]}

## Space Complexity Analysis

Space complexity analysis of various formats with its representation is discussed.^{[1]}Clustering algorithm analysis, including time and space complexity analysis, has always been discussed in the literature.

^{[2]}This chapter will focus on the concept of Big-O notation for time and algorithmic space complexity analysis.

^{[3]}In this sense, this paper presents an empirical analysis to evaluate this hypothesis, particularly in higher scale, through performance assessment along with time and space complexity analysis of a theoretical approach to the problem of assembly proposed by [2] using the RL algorithm Q-learning.

^{[4]}

## Thorough Complexity Analysis

We provide a thorough complexity analysis (NP-hardness proofs and (pseudo-)polynomial algorithms) for different members of these four classes.^{[1]}We present a thorough complexity analysis of two computational problems, namely verification (checking whether a query is an s-to-o rewriting of a given data service), and computation (computing an s-to-o rewriting of a data service).

^{[2]}Finally, a thorough complexity analysis is given to verify the superior performance of the proposed design (the proposed structure involves better complexities than the newly reported design).

^{[3]}We provide a thorough complexity analysis for several decision problems associated with minimal explanations under existential rules.

^{[4]}

## Parameterized Complexity Analysis

We build on recent theoretical work focusing on linear-time data reduction rules for finding maximum-cardinality matchings and complement the theoretical results by presenting and analyzing (thereby employing the kernelization methodology of parameterized complexity analysis) new (near-)linear-time data reduction rules for both the unweighted and the positive-integer-weighted case.^{[1]}For the NP-hard cases, focusing on the natural parameter "budget" (that is, the number of manipulative actions one is allowed to perform), we also conduct a parameterized complexity analysis and encounter mostly parameterized hardness results.

^{[2]}We continue and extend previous work on the parameterized complexity analysis of the NP-hard Stable Roommates with Ties and Incomplete Lists problem, thereby strengthening earlier results both on the side of parameterized hardness as well as on the side of fixed-parameter tractability.

^{[3]}Evolutionary multiobjective optimization for the classical vertex cover problem has been analysed in Kratsch and Neumann (2013) in the context of parameterized complexity analysis.

^{[4]}

## Iteration Complexity Analysis

From traditional iteration complexity analysis point of view, the binary logistic regression loss functions with our worst-case datasets are new worst-case function instances among the class of smooth convex optimization problems.^{[1]}In this paper we present a complete iteration complexity analysis of inexact first-order Lagrangian and penalty methods for solving cone-constrained convex problems that have or may not have optimal Lagrange multipliers that close the duality gap.

^{[2]}On the theory side, we will cover convergence rate and iteration complexity analysis of ZO algorithms and make comparisons to their first-order counterparts.

^{[3]}From traditional iteration complexity analysis point of view, the binary logistic regression loss functions with our worst-case datasets are new worst-case function instances among the class of smooth convex optimization problems.

^{[4]}

## Network Complexity Analysis

Thus, these results establish that isomorphisms between finite multidimensional networks and finite monoplex networks do not preserve algorithmic information in general and highlight that the algorithmic information of the multidimensional space itself needs to be taken into account in multidimensional network complexity analysis.^{[1]}In this paper, we examine how an AI-enabled IoT platform, combined with network complexity analysis and 5G can be used to design, develop and implement new cyber-physical systems (CPS) optimized for specific applications and markets.

^{[2]}In addition, a network complexity analysis of the quantum circuit suggests that the proposed filtering approach can perform enormous speed-up over its corresponding classical counterparts.

^{[3]}

## Facilitate Complexity Analysis

Its use would facilitate complexity analysis from a larger variety of gait measures, such as body accelerations.^{[1]}Its use would facilitate complexity analysis from a larger variety of gait measures, such as body accelerations.

^{[2]}

## Case Complexity Analysis

The theoretical results of this work extend tools of the average-case complexity analysis of the algorithm.^{[1]}Moreover, we conduct an average-case complexity analysis of finding the leftmost-outermost redex in random lambda terms showing that it is on average constant.

^{[2]}