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Recent papers on Computational Complexity and Scalability

Sorted by publication year (newest first) via OpenAlex. List regenerates every 24h.

High-speed arithmetic units are foundational to modern computing architectures. However, the performance of these units is fundamentally constrained by the carry propagation delay. In conventional architectures, generating an output bit or digit relies on the temporal propagation of a carry signal from less significant positions. For an operand of length N, traditional Ripple Carry Adders (RCA) exhibit a linear time complexity of O(N), while advanced parallel- prefix structures, such as Carry-Lookahead Adders (CLA) or Wallace trees, reduce this delay to a logarithmic bound of O(log N). [12]. This paper challenges the necessity of this tempo- ral dependency in specific arithmetic domains. We in- troduce a novel Radix-10 scalar multiplication architec- ture—multiplying an N-digit operand by a single-digit multiplier (M ∈ {0, 1, . . . , 9})—that operates in strictly constant time, O(1). Rather than treating the carry as a dynamic signal that must ripple through the circuit, our methodology frames multiplication as a localized state-space mapping problem. We demonstrate that for any single-digit multiplier M, the maximum influence of a carry generated at any position i does not propagate beyond position i+2. By establishing this strict mathematical boundary (∆ = 2), the computational dependency of any output digit yi is **spatially truncated** [6]. Consequently, the output digit yi is computed as a direct, parallel combinational function of only three vari- ables: the current input digit (di) and its two immediate less-significant adjacent digits (di−1 and di−2). To handle the boundaries of the operand without breaking the O(1) property, we introduce the concept of **Structural Imaginary Zeros**—fixed zero digits appended at both ends of the digit sequence—which act as static boundary conditions. This localized dependency allows the entire multiplication process to be mapped into parallel Look-Up Tables (LUTs), resolving the N-digit output in a single standard gate delay cycle (tgate), independent of N. The primary contributions of this paper are: • A formal mathematical proof (Section 5) bounding the carry propagation in scalar Radix-10 multiplication to a strict dependency window of ∆ = 2. • The design of a parallel, O(1) hardware architecture using localized combinational mapping (LUTs) to replace sequential carry logic. • Hardware complexity analysis demonstrating O(1) time delay with strictly linear O(N) area scaling.
2026 · Zenodo (CERN European Organization for Nuclear Research) · Al-Naami, Abdul Raouf
2026
Principles of Quantum Machine Learning: Algorithms, Computational Complexity, and Resource Scaling
2026 · Borey, Mr. Sujit Ramesh, Padiya, Puja, Hirekar, Kishor et al.
2026
Unified Time Scale and Continuous Complexity Geometry\\of Computational Universes:\\Scattering Mother Scale, Control Manifold, and Construction of Metric G
2025 · Zenodo (CERN European Organization for Nuclear Research) · Haobo, Ma,, Wenlin, Zhang,
2025
Error Control and Spectral Windowing Readout\\in Computational Universe:\\Time--Frequency--Complexity Role of PSWF/DPSS Window Functions\\Under Unified Time Scale
2025 · Zenodo (CERN European Organization for Nuclear Research) · Haobo, Ma,, Wenlin, Zhang,
2025
Geometric Complexity Hierarchy and Complexity Classes\\in Computational Universe:\\Volume Growth, Curvature, and Computability Boundaries\\Under Unified Time Scale
2025 · Zenodo (CERN European Organization for Nuclear Research) · Haobo, Ma,, Wenlin, Zhang,
2025
Theory of Categorical Equivalence\\Between Computational Universe and Physical Universe:\\Reversible QCA, Unified Time Scale,\\and Complexity Geometric Invariants
2025 · Zenodo (CERN European Organization for Nuclear Research) · Haobo, Ma,, Wenlin, Zhang,
2025
Topological Complexity, Self-Reference, and Undecidability\\in Computational Universe:\\Loop Structure, Fundamental Group,\\and Second Law of Complexity Under Unified Time Scale
2025 · Zenodo (CERN European Organization for Nuclear Research) · Haobo, Ma,, Wenlin, Zhang,
2025
A Novel Optimization DMPC Algorithm With Reduced-Order Computational Complexity: Applications in IIoT-Based BMS for the Optimal Heating/Cooling of Large-Scale Buildings
2025 · IEEE Transactions on Automation Science and Engineering · Partovi, Asghar, Farhadi, Alireza, Sharifzadeh, Mahdi
2025
A Reliable and Computationally Efficient Soft-Output Fixed-Complexity Sphere Decoder for Large-Scale MIMO Systems
2025 · Chen, Yen‐Ming, Jhang, Shih-Jie, Ueng, Yeong-Luh
2025
A Novel Approach for Addressing Scalability and Computational Complexity Issues of the Ontology Integration Process
2025 · Journal of Information Systems Engineering & Management · Pardeshi, Sujata A.
2025
Dynamic Channel Token Vision Transformer with linear computation complexity and multi-scale features
2025 · Neurocomputing · Guan, Yijia, Wang, Kundong
2025
While classical arithmetic sequences are a cornerstone of mathemat ics, their simplicity limits their ability to model systems with intertwined, multi-layered rhythms. This article introduces a natural extension—arithmetico hierarchical sequences—by incorporating a hierarchy of ratios {ri} and steps {pi}, enabling the modeling of nested dynamic progressions through an elegant stratified recurrence. Beyond their theoretical appeal, these sequences offer promising cryptographic applications, as their multi-scale complexity enhances security by making them difficult to reverse-engineer. Additionally, their asymptotic behavior and algorithmic properties could advance the modeling of complex systems in economics, biology, and com puter science. We formally define these sequences, derive key theorems, present efficient computation algorithms, and explore applications, aiming to establish a foundation for future research in this versatile framework.
2025 · Open MIND · TUMUSAVYEYESU, François
2025
VMGNet: A Low Computational Complexity Robotic Grasping Network Based on VMamba with Multi-Scale Feature Fusion
2024 · arXiv (Cornell University) · Jin, Yuhao, Qizhong, Gao,, Zhu, Xiaohui et al.
2024
Overcoming Computational Complexity: A Scalable Agent-Based Model of Traffic Activity Using FLAME-GPU
2024 · Lecture notes in computer science · Smilovitskiy, Maxim, Olmez, Sedar, Richmond, Paul et al.
2024
Planetary-Scale Computation, Political Economic Complexity and Hegemony
2024 · Scholz-Wäckerle, Manuel
2024
SOI: Scaling Down Computational Complexity by Estimating Partial States of the Model
2024 · arXiv (Cornell University) · Stefański, Grzegorz, Daniluk, Paweł, Szumaczuk, Artur et al.
2024
Freya PAGE: First Optimal Time Complexity for Large-Scale Nonconvex Finite-Sum Optimization with Heterogeneous Asynchronous Computations
2024 · arXiv (Cornell University) · Tyurin, Alexander, Gruntkowska, Kaja, Richtárik, Peter
2024
Fast Support Vector Machine With Low-Computational Complexity for Large-Scale Classification
2024 · IEEE Transactions on Systems Man and Cybernetics Systems · Wang, Huajun, Zhu, Zhibin, Shao, Yuan‐Hai
2024
Optimization of algorithmic efficiency in AI: Addressing computational complexity and scalability challenges
2024 · Applied and Computational Engineering · Meng, Xianghui
2024
Investigating the Impact of Local Manipulations on Spontaneous and Evoked Brain Complexity Indices: A Large-Scale Computational Model
2024 · Applied Sciences · Gaglioti, Gianluca, Nieus, Thierry, Massimini, Marcello et al.
2024