| viXra.org > Data Structures and Algorithms > 2509 |
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| viXra.org > Data Structures and Algorithms > 2509 |
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[4] viXra:2509.0135 [pdf] replaced on 2025-10-02 23:38:52
Authors: Nathan O. Schmidt
Comments: 78 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
The Tri-Quarter framework unleashes a radial dual triangular lattice graph with unified complex-Cartesian-polar coordinates, structured orientation phase pair assignments for directional labeling, and topological zones to build exact bijective mappings without approximations. By establishing combinatorial duality for radial separation, Escher reflective duality for zone swapping, and bijective self-duality for reversible transformations, the discretized framework leverages the lattice graph's order-6 rotational symmetry to natively support angular sectors, modular decompositions, equivariant encodings, and trihexagonal six-coloring for conflict-free parallel algorithms. At this discretized framework's core is the Tri-Quarter Inversive Hexagonal Dihedral Symmetry Group T24—the order-24 semidirect product D6 ⋊ Z2—which exploits rotational, reflective, and inversive symmetries to unlock these bijective transformations with exact precision. We provide formal proofs of these dualities, along with numerous step-by-step examples, and demonstrate practical efficiency through benchmarked simulations to achieve ~2x speedups with inversion-based path mirroring via bijections and up to ~6x reductions in symmetry-reduced clustering via rotational orbits. This work advances scalable computations on symmetric structures, with applications in computational geometry, graph traversals, tiling, robotics path planning, multi-agent coordination, lattice-based cryptography, image processing, and signal processing. This work aims to solidify a mathematical and computational foundation for both classical and non-classical computing paradigms—targeting future integrations in complex emergent systems that harness intricate “superposition-like” symmetries to advance symmetry-aware algorithms and data structures across diverse computing architectures.
Category: Data Structures and Algorithms
[3] viXra:2509.0106 [pdf] submitted on 2025-09-17 03:20:55
Authors: Andy Wang
Comments: 7 Pages.
This paper proposes a distributed blogging system [1] [2] [3] [4] [5] [6] based on independent HTML fragments, which we term TOM (Time Object Model) [7]. The core characteristics of this blogging system are: "individual authors have full autonomy over managing their own blog content, using independent HTML fragments (in JSON format, with unique HTTP addresses) as the content carrier, and supporting other blogs to embed these fragments without notifying the original author."
Category: Data Structures and Algorithms
[2] viXra:2509.0101 [pdf] submitted on 2025-09-16 03:48:16
Authors: Ran Qin
Comments: 6 Pages.
Microservices architecture, which enhances large-scale distributed systems by breaking applications into small, independent service units, offers significant benefits in scalability, fault tolerance, and the ability to integrate diverse technologies. This paper details the characteristics of microservices architecture and its practical implementation in distributed systems. Furthermore, it analyzes cutting-edge applications, such as service mesh, edge computing, and intelligent observability, considering the convergence of AI and cloud-native technologies. The paper concludes by proposing future development directions, including modular design, automated operations, and ecosystem-based toolchains.
Category: Data Structures and Algorithms
[1] viXra:2509.0043 [pdf] submitted on 2025-09-08 01:00:28
Authors: Mario Stöckli
Comments: 3 Pages. (Note by viXra Admin: Please cite and list scientific references)
We prove P ≠ NP by contradiction by showing that there is no polynomial-time algorithm to solve the set partition problem.
Category: Data Structures and Algorithms
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